A. Books and Theses€¦ · References A. Books and Theses [Abr97] P. Abry, Ondelettes et turbulences — Multirésolutions, algorithmes de décomposition, invariance d’échelle
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Transcript
References
A Books and Theses
[Abr97] P Abry Ondelettes et turbulences mdash Multireacutesolutions algorithmes de deacutecompositioninvariance drsquoeacutechelle et signaux de pression (Diderot Paris 1997)
[Adl95] SL Adler Quaternionic Quantum Mechanics and Quantum Fields (Oxford Univer-sity Press New York 1995)
[Akh65] NI Akhiezer The Classical Moment Problem and Some Related Questions inAnalysis (Oliver and Boyd Edinburgh and London 1965)
[Ala94] A Alaux Lrsquoimage par reacutesonance magneacutetique (Sauramps Meacutedical Montpellier 1994)[Ald96] A Aldroubi M Unser (eds) Wavelets in Medicine and Biology (CRC Press Boca
Raton 1996)[Ali07] ST Ali M Engliš Berezin-Toeplitz quantization over matrix domains in Contribu-
tions in Mathematical Physics ndash A tribute to Geacuterard Emch Ed by ST Ali KB Sinha(Hindustan Book Agency New Delhi India 2007)
[And13] TD Andrews R Balan JJ Benedetto W Czaja KA Okoudjou (eds) Excursionsin Harmonic Analysis vol 1 2 (Birkhaumluser Boston 2013)
[Ant04] J-P Antoine R Murenzi P Vandergheynst ST Ali Two-Dimensional Wavelets andtheir Relatives (Cambridge University Press Cambridge (UK) 2004)
[Ant09] J-P Antoine C Trapani Partial Inner Product Spaces mdash Theory and ApplicationsLecture Notes in Mathematics vol 1986 (Springer Berlin Heidelberg 2009)
[Arn95] A Arneacuteodo F Argoul E Bacry J Elezgaray JF Muzy Ondelettes multifractaleset turbulences ndash De lrsquoADN aux croissances cristallines (Diderot Paris 1995)
[Asc72] E Ascher Extensions et cohomologie de groupes Lecture Notes Enseignement dutroisiegraveme cycle de la physique en Suisse Romande (CICP) (1972)
[Bar77] AO Barut R Raczka Theory of Group Representations and Applications (PWNWarszawa 1977)
[Bec06] K Becker M Becker JH Schwarz String Theory and M-Theory A ModernIntroduction (Cambridge University Press Cambridge 2006)
[Ben01] JJ Benedetto PJSG Ferreira Modern Sampling Theory Mathematics and Appli-cations (Birkhaumluser Boston Basel Berlin 2001)
[Ben04] JJ Benedetto and AI Zayed Sampling Theory Wavelets and Tomography(Birkhaumluser Boston Basel Berlin 2004)
[Ben07] I Bengtsson K Zyczkowski Geometry of Quantum States An Introduction toQuantum Entanglement (Cambridge University Press Cambridge 2007)
[Ber66] SK Berberian Notes on Spectral Theory (Van Nostrand Princeton NJ 1966)
ST Ali et al Coherent States Wavelets and Their Generalizations Theoreticaland Mathematical Physics DOI 101007978-1-4614-8535-3copy Springer Science+Business Media New York 2014
541
542 References
[Ber99] JC van den Berg (ed) Wavelets in Physics (Cambridge University Press Cambridge1999)
[Ber98] G Bernuau Proprieacuteteacutes spectrales et geacuteomeacutetriques des quasicristaux Ondelettesadapteacutees aux quasicristaux Thegravese de Doctorat CEREMADE Universiteacute Paris IXDauphine France 1998
[Bie81] L Biedenharn JD Louck The Racah-Wigner Algebra in Quantum Theory Ency-clopaedia of Mathematics vol 9 (Addison-Wesley Reading MA 1981)
[Bis10] S Biskri Deacutetection et analyse des boucles magneacutetiques solaires par traitementdrsquoimages Thegravese de Doctorat UST Houari Boumediegravene Alger 2010
[Bog05] I Bogdanova Wavelets on non-Euclidean manifolds PhD thesis EPFL 2005[Bog74] J Bognar Indefinite Inner Product Spaces (Springer Berlin 1974)[Bor72] A Borel Repreacutesentations des groupes localement compacts Lecture Notes in
Mathematics vol 276 (Springer Berlin 1972)[Bou93] K Bouyoucef Sur des aspects multireacutesolution en reconstruction drsquoimages Applica-
tion au Teacutelescope Spatial de Hubble Thegravese de Doctorat Univ P Sabatier Toulouse1993
[Bou97] A Bouzouina Comportement semi-classique de symplectomorphismes du tore quan-tifieacutes Thegravese de Doctorat Univ Paris-Dauphine 1997
[Bus91] P Busch PJ Lahti P Mittelstaedt The Quantum Theory of Measurement (SpringerBerlin and Heidelberg 1991)
[Can98] EJ Candegraves Ridgelets Theory and applications PhD thesis Department of Statis-tics Stanford University 1998
[Chr03] O Christensen An Introduction to Frames and Riesz Bases (Birkhaumluser BaselBoston Berlin 2003)
[Chu92] CK Chui An Introduction to Wavelets (Academic San Diego 1992)[Coh77] C Cohen-Tannoudji B Diu F Laloeuml Meacutecanique Quantique Tome I (Hermann
Paris 1977)[Com90] J-M Combes A Grossmann P Tchamitchian (eds) Wavelets Time-Frequency
Methods and Phase Space (Proc Marseille 1987) 2nd edn (Springer Berlin 1990)[Com12] M Combescure D Robert Shape Analysis and Classification Theory and Practice
(Springer Dordrecht Heidelberg 2012)[Cos01] LF Costa RM Cesar Jr Coherent States and Applications in Mathematical Physics
(CRC Press Boca Raton FL 2001)[Dau92] I Daubechies Ten Lectures on Wavelets (SIAM Philadelphia 1992)[Dav90] EB Davies Heat Kernels and Spectral Theory (Cambridge University Press Cam-
bridge 1990)[DeV88] R De Valois K De Valois Spatial Vision (Oxford University Press New York 1988)
[Dir01] PAM Dirac Lectures on Quantum Mechanics (Dover New York 2001)[Dix64] J Dixmier Les C-algegravebres et leurs repreacutesentations (Gauthier-Villars Paris 1964)[Dod03] VV Dodonov VI Manrsquoko (eds) Theory of Nonclassical States of Light (Taylor and
Francis London New York 2003)[Duv91] M Duval-Destin Analyse spatiale et spatio-temporelle de la stimulation visuelle agrave
lrsquoaide de la transformeacutee en ondelettes Thegravese de Doctorat Universiteacute drsquoAix-MarseilleII 1991
[Fea90] J-C Feauveau Analyse multireacutesolution par ondelettes non orthogonales et bancs defiltres numeacuteriques Thegravese de Doctorat Universiteacute Paris-Sud 1990
[Fei98] HG Feichtinger T Strohmer (eds) Gabor Analysis and Algorithms ndash Theory andApplications (Birkhaumluser Boston-Basel-Berlin 1998)
[Fei01] HG Feichtinger T Strohmer (eds) Advances in Gabor Analysis (BirkhaumluserBoston 2001)
[Fen94] DH Feng JR Klauder M Strayer (eds) Coherent States Past Present and Future(Proc Oak Ridge 1993) (World Scientific Singapore 1994)
[Fla98] P Flandrin Temps-Freacutequence (Hermegraves Paris 1993) Engliah translation Time-FrequencyTime-Scale Analysis (Academic New York 1998)
References 543
[Fol95] GB Folland A Course in Abstract Harmonic Analysis (CRC Press Boca Raton FL1995)
[Fre97] W Freeden M Schreiner T Gervens Constructive Approximation on the Spherewith Applications to Geomathematics (Clarendon Press Oxford 1997)
[Fue05] H Fuumlhr Abstract Harmonic Analysis of Continuous Wavelet Transforms LectureNotes in Mathematics vol 1863 (Springer Berlin Heidelberg 2005)
[Gaa73] SA Gaal Linear Analysis and Representation Theory (Springer Berlin 1973)[Gaz09] J-P Gazeau Coherent States in Quantum Physics (Wiley-VCH Berlin 2009)[Gel64] IM Gelfand NY Vilenkin Generalized Functions vol 4 (Academic New York
1964)[Gen13] G Gentili C Stoppato DC Struppa Regular Functions for a Quaternionic Variable
Springer Monographs in Mathematics (Springer Berlin 2013)[Gol81] H Goldstein C Poole J Safko Classical Mechanics 3rd edn (Addison-Wesley
Reading MA 1981)[Got66] K Gottfried Quantum Mechanics Fundamentals vol I (Benjamin New York and
Amsterdam 1966)[Grouml01] K Groumlchenig Foundations of Time-Frequency Analysis (Birkhaumluser Boston 2001)[Gun94] H Guumlnther NMR Spectroscopy 2nd edn (Wiley Chichester New York 1994)[Gui84] V Guillemin S Sternberg Symplectic Techniques in Physics (Cambridge University
Press Cambridge 1984)[Hei06] C Heil D Walnut (eds) Fundamental Papers in Wavelet Theory (Princeton Univer-
sity Press Princeton NJ 2006)[Hel78] S Helgason Differential Geometry Lie Groups and Symmetric Spaces (Academic
New York 1978)[Hel76] CW Helstrom Quantum Detection and Estimation Theory (Academic New York
1976)[Her89] G Herzberg Molecular Spectra and Molecular Structure Spectra of Diatomic
Molecules 2nd edn (Krieger Pub Malabar FL 1989)[Hil71] P Hilton U Stammbach A Course in Homological Algebra (Springer Berlin 1971)[H0l01] AS Holevo Statistical Structure of Quantum Theory (Springer Berlin 2001)[Hol95] M Holschneider Wavelets An Analysis Tool (Oxford University Press Oxford 1995)[Hon07] G Honnouvo Gabor analysis and wavelet transforms on some non-Euclidean 2-
dimensional manifolds PhD thesis Concordia University Montreal PQ Canada2007
[Hua63] LK Hua Harmonic Analysis of Functions of Several Complex Variables in the Clas-sical Domains Translations of Mathematical Monographs (American MathematicalSociety Providence RI 1963)
[Hum72] JE Humphreys Introduction to Lie Algebras and Representation Theory (SpringerBerlin 1972)
[Inouml54] E Inoumlnuuml A study of the unitary representations of the Galilei group in relation toquantum mechanics PhD thesis University of Ankara 1954
[Ino92] A Inomata H Kuratsuji CC Gerry Path Integrals and Coherent States of SU(2)and SU(11) (World Scientific Singapore 1992)
[Jac62] N Jacobson Lie Algebras (Interscience New York and London 1962)[Jac04] L Jacques Ondelettes repegraveres et couronne solaire Thegravese de Doctorat Univ Cath
Louvain Louvain-la-Neuve 2004[Jaf96] S Jaffard Y Meyer Wavelet Methods for Pointwise Regularity and Local Oscillations
of Functions Memoirs of the American Mathematical Society vol 143 (AmericanMathematical Society Providence RI 1996)
[Kah98] J-P Kahane PG Lemarieacute-Rieusset Fourier Series and Wavelets (Gordon and BreachLuxembourg 1995) French translation Seacuteries de Fourier et ondelettes (Cassini Paris1998)
[Kai94] G Kaiser A Friendly Guide to Wavelets (Birkhaumluser Boston 1994)[Kat76] T Kato Perturbation Theory for Linear Operators (Springer Berlin 1976)
544 References
[Kem37] EC Kemble Fundamental Principles of Quantum Mechanics (McGraw Hill NewYork 1937)
[Kir76] AA Kirillov Elements of the Theory of Representations (Springer Berlin 1976)[Kla68] JR Klauder ECG Sudarshan Fundamentals of Quantum Optics (Benjamin New
York 1968)[Kla85] JR Klauder BS Skagerstam Coherent States ndash Applications in Physics and
Mathematical Physics (World Scientific Singapore 1985)[Kla00] JR Klauder Beyond Conventional Quantization (Cambridge University Press Cam-
bridge 2000)[Kla11] JR Klauder A Modern Approach to Functional Integration (BirkhaumluserSpringer
New York 2011)[Kna96] AW Knapp Lie Groups Beyond an Introduction (Birkhaumluser Basel 1996 2nd edn
2002)[Kut12] G Kutyniok D Labate (eds) Shearlets Multiscale Analysis for Multivariate Data
(Birkhaumluser Boston 2012)[Lan81] L Landau E Lifchitz Mechanics 3rd edn (Pergamon Oxford1981)[Lan93] S Lang Algebra 3rd edn (Addison-Wesley Reading MA 1993)[Lie97] EH Lieb M Loss Analysis (American Mathematical Society Providence RI 1997)[Lip74] RL Lipsman Group Representations Lecture Notes in Mathematics vol 388
(Springer Berlin 1974)[Lyn82] PA Lynn An Introduction to the Analysis and Processing of Signals 2nd edn
(MacMillan London 1982)[Mac68] GW Mackey Induced Representations of Groups and Quantum Mechanics (Ben-
jamin New York 1968)[Mac76] GW Mackey Theory of Unitary Group Representations (University of Chicago
Press Chicago 1976)[Mad95] J Madore An Introduction to Noncommutative Differential Geometry and Its Physical
Applications (Cambridge University Press Cambridge 1995)[Mae94] S Maes The wavelet transform in signal processing with application to the extraction
of the speech modulation model features Thegravese de Doctorat Univ Cath LouvainLouvain-la-Neuve 1994
[Mag66] W Magnus F Oberhettinger RP Soni Formulas and Theorems for the SpecialFunctions of Mathematical Physics (Springer Berlin 1966)
[Mal99] SG Mallat A Wavelet Tour of Signal Processing 2nd edn (Academic San Diego1999)
[Mar82] D Marr Vision (Freeman San Francisco 1982)[Mes62] H Meschkowsky Hilbertsche Raumlume mit Kernfunktionen (Springer Berlin 1962)[Mey91] Y Meyer (ed) Wavelets and Applications (Proc Marseille 1989) (Masson and
Springer Paris and Berlin 1991)[Mey92] Y Meyer Les Ondelettes Algorithmes et Applications (Armand Colin Paris 1992)
English translation Wavelets Algorithms and Applications (SIAM Philadelphia1993)
[Mey00] CD Meyer Matrix Analysis and Applied Linear Algebra (SIAM Philadelphia 2000)[Mey93] Y Meyer S Roques (eds) Progress in Wavelet Analysis and Applications (Proc
Toulouse 1992) (Ed Frontiegraveres Gif-sur-Yvette 1993)[Mur90] R Murenzi Ondelettes multidimensionnelles et applications agrave lrsquoanalyse drsquoimages
Thegravese de Doctorat Univ Cath Louvain Louvain-la-Neuve 1990[vNe55] J von Neumann Mathematical Foundations of Quantum Mechanics (Princeton
University Press Princeton NJ 1955) (English translated by RT Byer)[Pap02] A Papoulis SU Pillai Probability Random Variables and Stochastic Processes 4th
edn (McGraw Hill New York 2002)[Par05] KR Parthasarathy Probability Measures on Metric Spaces (AMS Chelsea Publish-
ing Providence RI 2005)
References 545
[Pau85] T Paul Ondelettes et Meacutecanique Quantique Thegravese de doctorat Univ drsquoAix-MarseilleII 1985
[Per86] AM Perelomov Generalized Coherent States and Their Applications (SpringerBerlin 1986)
[Per05] G Peyreacute Geacuteomeacutetrie multi-eacutechelles pour les images et les textures Thegravese de doctoratEcole Polytechnique Palaiseau 2005
[Pru86] E Prugovecki Stochastic Quantum Mechanics and Quantum Spacetime (ReidelDordrecht 1986)
[Rau04] H Rauhut Time-frequency and wavelet analysis of functions with symmetry proper-ties PhD thesis TU Muumlnich 2004
[Ree80] M Reed B Simon Methods of Modern Mathematical Physics I Functional Analysis(Academic New York 1980)
[Rud62] W Rudin Fourier Analysis on Groups (Interscience New York 1962)[Sch96] FE Schroeck Jr Quantum Mechanics on Phase Space (Kluwer Dordrecht 1996)[Sch61] L Schwartz Meacutethodes matheacutematiques pour les sciences physiques (Hermann Paris
1961)[Scu97] MO Scully MS Zubairy Quantum Optics (Cambridge University Press Cam-
bridge 1997)[Sho50] JA Shohat JD Tamarkin The Problem of Moments (American Mathematical
Society Providence RI 1950)[Ste71] EM Stein G Weiss Introduction to Fourier Analysis on Euclidean Spaces (Prince-
ton University Press Princeton NJ 1971)[Str64] RF Streater AS Wightman PCT Spin and Statistics and All That (Benjamin New
York 1964)[Sug90] M Sugiura Unitary Representations and Harmonic Analysis An Introduction
(North-HollandKodansha Ltd Tokyo 1990)[Suv11] A Suvichakorn C Lemke A Schuck Jr J-P Antoine The continuous wavelet
transform in MRS Tutorial text Marie Curie Research Training Network FAST(2011) httpwwwfast-mariecurie-rtn-projecteuWavelet
[Tak79] M Takesaki Theory of Operator Algebras I (Springer New York 1979)[Ter88] A Terras Harmonic Analysis on Symmetric Spaces and Applications II (Springer
Berlin 1988)[Tho98] G Thonet New aspects of time-frequency analysis for biomedical signal processing
Thegravese de Doctorat EPFL Lausanne 1998[Tor95] B Torreacutesani Analyse continue par ondelettes (InterEacuteditionsCNRS Eacuteditions Paris
1995)[Unt87] A Unterberger Analyse harmonique et analyse pseudo-diffeacuterentielle du cocircne de
lumiegravere Asteacuterisque 156 1ndash201 (1987)[Unt91] A Unterberger Quantification relativiste Meacutem Soc Math France 44ndash45 1ndash215
(1991)[Van98] P Vandergheynst Ondelettes directionnelles et ondelettes sur la sphegravere Thegravese de
Doctorat Univ Cath Louvain Louvain-la-Neuve 1998[Var85] VS Varadarajan Geometry of Quantum Theory 2nd edn (Springer New York 1985)[Vet95] M Vetterli J Kovacevic Wavelets and Subband Coding (Prentice Hall Englewood
Cliffs NJ 1995)[Vil69] NJ Vilenkin Fonctions speacuteciales et theacuteorie de la repreacutesentation des groupes (Dunod
Paris 1969)[Wel03] GV Welland Beyond Wavelets (Academic New York 2003)[vWe86] C von Westenholz Differential Forms in Mathematical Physics (North-Holland
Amsterdam 1986)[Wey28] H Weyl Gruppentheorie und Quantenmechanik (Hirzel Leipzig 1928)[Wey31] H Weyl The Theory of Groups and Quantum Mechanics (Dover New York 1931)[Wic94] MV Wickerhauser Adapted Wavelet Analysis from Theory to Software (A K Peters
Wellesley MA 1994)
546 References
[Wis93] W Wisnoe Utilisation de la meacutethode de transformeacutee en ondelettes 2D pour lrsquoanalysede visualisation drsquoeacutecoulements Thegravese de Doctorat ENSAE Toulouse 1993
[Woj97] P Wojtaszczyk A Mathematical Introduction to Wavelets (Cambridge UniversityPress Cambridge 1997)
[Zac06] C Zachos D Fairlie T Curtright Quantum Mechanics in Phase Space An OverviewWith Selected Papers (World Scientific Publishing Singapore 2006)
B Articles
[1] P Abry R Baraniuk P Flandrin R Riedi D Veitch Multiscale nature of network trafficIEEE Signal Process Mag 19 28ndash46 (2002)
[2] MD Adams The JPEG-2000 still image compression standardhttpwwweceuvicca~frodopublicationsjpeg2000pdf
[3] SL Adler AC Millard Coherent states in quaternionic quantum mechanics J MathPhys 38 2117ndash2126 (1997)
[4] GS Agarwal K Tara Nonclassical properties of states generated by the excitation on acoherent state Phys Rev A 43 492ndash497 (1991)
[5] GS Agarwal E Wolf Calculus for functions of noncommuting operators and generalphase-space methods in quantum mechanics I Mapping theorems and ordering of func-tions of noncommuting operators Phys Rev D 2 2161ndash2186 (1970)
[6] GS Agarwal E Wolf Calculus for functions of noncommuting operators and generalphase-space methods in quantum mechanics II Quantum mechanics in phase space PhysRev D 2 2187ndash2205 (1970)
[7] GS Agarwal E Wolf Calculus for functions of noncommuting operators and generalphase-space methods in quantum mechanics III A generalized Wick theorem and multi-time mapping Phys Rev D 2 2206ndash2225 (1970)
[8] V Aldaya J Guerrero G Marmo Quantization on a Lie group Higher-order polariza-tions in Symmetry in Sciences X ed by B Gruber M Ramek (Plenum Press Nerw York1998) pp 1ndash36
[9] M Alexandrescu D Gibert G Hulot J-L Le Mouel G Saracco Worldwide waveletanalysis of geomagnetic jerks J Geophys Res B 101 21975ndash21994 (1996)
[10] G Alexanian A Pinzul A Stern Generalized coherent state approach to star productsand applications to the fuzzy sphere Nucl Phys B 600 531ndash547 (2001)
[11] ST Ali A geometrical property of POV-measures and systems of covariance in Differ-ential Geometric Methods in Mathematical Physics ed by HD Doebner SI AnderssonHR Petry Lecture Notes in Mathematics vol 905 (Springer Berlin 1982) pp 207ndash22
[12] ST Ali Commutative systems of covariance and a generalization of Mackeyrsquos imprimi-tivity theorem Canad Math Bull 27 390ndash397 (1984)
[13] ST Ali Stochastic localisation quantum mechanics on phase space and quantum space-time Riv Nuovo Cim 8(11) 1ndash128 (1985)
[14] ST Ali A general theorem on square-integrability Vector coherent states J Math Phys39 3954ndash3964 (1998)
[15] ST Ali J-P Antoine Coherent states of 1+1 dimensional Poincareacute group Squareintegrability and a relativistic Weyl transform Ann Inst H Poincareacute 51 23ndash44 (1989)
[16] ST Ali S De Biegravevre Coherent states and quantization on homogeneous spaces in GroupTheoretical Methods in Physics ed by H-D Doebner et al Lecture Notes in Mathematicsvol 313 (Springer Berlin 1988) pp 201ndash207
References 547
[17] ST Ali H-D Doebner Ordering problem in quantum mechanics Prime quantization anda physical interpretation Phys Rev A 41 1199ndash1210 (1990)
[18] ST Ali GG Emch Geometric quantization Modular reduction theory and coherentstates J Math Phys 27 2936ndash2943 (1986)
[19] ST Ali M Engliš J-P Gazeau Vector coherent states from Plancherelrsquos theorem andClifford algebras J Phys A 37 6067ndash6089 (2004)
[20] ST Ali MEH Ismail Some orthogonal polynomials arising from coherent states JPhys A 45 125203 (2012) (16pp)
[21] ST Ali UA Mueller Quantization of a classical system on a coadjoint orbit of thePoincareacute group in 1+1 dimensions J Math Phys 35 4405ndash4422 (1994)
[22] ST Ali E Prugovecki Systems of imprimitivity and representations of quantum mechan-ics on fuzzy phase spaces J Math Phys 18 219ndash228 (1977)
[23] ST Ali E Prugovecki Mathematical problems of stochastic quantum mechanics Har-monic analysis on phase space and quantum geometry Acta Appl Math 6 1ndash18 (1986)
[24] ST Ali E Prugovecki Extended harmonic analysis of phase space representation for theGalilei group Acta Appl Math 6 19ndash45 (1986)
[25] ST Ali E Prugovecki Harmonic analysis and systems of covariance for phase spacerepresentation of the Poincareacute group Acta Appl Math 6 47ndash62 (1986)
[26] ST Ali J-P Antoine J-P Gazeau De Sitter to Poincareacute contraction and relativisticcoherent states Ann Inst H Poincareacute 52 83ndash111 (1990)
[27] ST Ali J-P Antoine J-P Gazeau Square integrability of group representations onhomogeneous spaces I Reproducing triples and frames Ann Inst H Poincareacute 55 829ndash855 (1991)
[28] ST Ali J-P Antoine J-P Gazeau Square integrability of group representations onhomogeneous spaces II Coherent and quasi-coherent states The case of the Poincareacutegroup Ann Inst H Poincareacute 55 857ndash890 (1991)
[29] ST Ali J-P Antoine J-P Gazeau Continuous frames in Hilbert space Ann Phys(NY)222 1ndash37 (1993)
[30] ST Ali J-P Antoine J-P Gazeau Relativistic quantum frames Ann Phys(NY) 222 38ndash88 (1993)
[31] ST Ali J-P Antoine J-P Gazeau UA Mueller Coherent states and their generalizationsA mathematical overview Rev Math Phys 7 1013ndash1104 (1995)
[32] ST Ali J-P Gazeau MR Karim Frames the β -duality in Minkowski space and spincoherent states J Phys A Math Gen 29 5529ndash5549 (1996)
[33] ST Ali M Engliš Quantization methods A guide for physicists and analysts Rev MathPhys 17 391ndash490 (2005)
[34] ST Ali J-P Gazeau B Heller Coherent states and Bayesian duality J Phys A MathTheor 41 365302 (2008)
[35] ST Ali L Balkovaacute EMF Curado J-P Gazeau MA Rego-Monteiro LMCSRodrigues K Sekimoto Non-commutative reading of the complex plane through Delonesequences J Math Phys 50 043517 (2009)
[36] ST Ali C Carmeli T Heinosaari A Toigo Commutative POVMS and fuzzy observ-ables Found Phys 39 593ndash612 (2009)
[37] ST Ali T Bhattacharyya SS Roy Coherent states on Hilbert modules J Phys A MathTheor 44 275202 (2011)
[38] ST Ali J-P Antoine F Bagarello J-P Gazeau (Guest Editors) Coherent states Acontemporary panorama preface to a special issue on Coherent states Mathematical andphysical aspects J Phys A Math Gen 45(24) (2012)
[39] ST Ali F Bagarello J-P Gazeau Quantizations from reproducing kernel spaces AnnPhys (NY) 332 127ndash142 (2013)
[40] STAli K Goacuterska A Horzela F Szafraniec Squeezed states and Hermite polynomials ina complex variable Preprint (2013) arXiv13084730v1 [quant-phy]
[41] P Aniello G Cassinelli E De Vito A Levrero Square-integrability of induced represen-tations of semidirect products Rev Math Phys 10 301ndash313 (1998)
548 References
[42] P Aniello G Cassinelli E De Vito A Levrero Wavelet transforms and discrete framesassociated to semidirect products J Math Phys 39 3965ndash3973 (1998)
[43] J-P Antoine Remarques sur le vecteur de Runge-Lenz Ann Soc Scient Bruxelles 80160ndash168 (1966)
[44] J-P Antoine Etude de la deacutegeacuteneacuterescence orbitale du potentiel coulombien en theacuteorie desgroupes I II Ann Soc Scient Bruxelles 80 169ndash184 (1966)
[45] J-P Antoine Etude de la deacutegeacuteneacuterescence orbitale du potentiel coulombien en theacuteorie desgroupes I II Ann Soc Scient Bruxelles 81 49ndash68 (1967)
[46] J-P Antoine Dirac formalism and symmetry problems in quantum mechanics I Generaldirac formalism J Math Phys 10 53ndash69 (1969)
[47] J-P Antoine Dirac formalism and symmetry problems in quantum mechanics II Symme-try problems J Math Phys 10 2276ndash2290 (1969)
[48] J-P Antoine Quantum mechanics beyond Hilbert space in Irreversibility and Causality mdashSemigroups and Rigged Hilbert Spaces ed by A Boumlhm H-D Doebner P KielanowskiLecture Notes in Physics vol 504 (Springer Berlin 1998) pp 3ndash33
[49] J-P Antoine Discrete wavelets on abelian locally compact groups Rev Cien Math(Habana) 19 3ndash21 (2003)
[50] J-P Antoine Introduction to precursors in physics Affine coherent states in FundamentalPapers in Wavelet Theory ed by C Heil D Walnut (Princeton University Press PrincetonNJ 2006) pp 113ndash116
[51] J-P Antoine F Bagarello Wavelet-like orthonormal bases for the lowest Landau levelJ Phys A Math Gen 27 2471ndash2481 (1994)
[52] J-P Antoine P Balazs Frames and semi-frames J Phys A Math Theor 44 205201(2011) (25 pages) Corrigendum J-P Antoine P Balazs Frames and semi-frames J PhysA Math Theor 44 479501 (2011) (2 pages)
[53] J-P Antoine P Balazs Frames semi-frames and Hilbert scales Numer Funct AnalOptim 33 736ndash769 (2012)
[54] J-P Antoine A Coron Time-frequency and time-scale approach to magnetic resonancespectroscopy J Comput Methods Sci Eng (JCMSE) 1 327ndash352 (2001)
[55] J-P Antoine AL Hohoueacuteto Discrete frames of Poincareacute coherent states in 1+3 dimen-sions J Fourier Anal Appl 9 141ndash173 (2003)
[56] J-P Antoine I Mahara Galilean wavelets Coherent states for the affine Galilei groupJ Math Phys 40 5956ndash5971 (1999)
[57] J-P Antoine U Moschella Poincareacute coherent states The two-dimensional massless caseJ Phys A Math Gen 26 591ndash607 (1993)
[58] J-P Antoine R Murenzi Two-dimensional directional wavelets and the scale-anglerepresentation Signal Process 52 259ndash281 (1996)
[59] J-P Antoine R Murenzi Two-dimensional continuous wavelet transform as linear phasespace representation of two-dimensional signals in Wavelet Applications IV SPIE Pro-ceedings vol 3078 (SPIE Bellingham WA 1997) pp 206ndash217
[60] J-P Antoine D Rosca The wavelet transform on the two-sphere and related manifolds mdashA review in Optical and Digital Image Processing SPIE Proceedings vol 7000 (2008)pp 70000B-1ndash15
[61] J-P Antoine D Speiser Characters of irreducible representations of simple Lie groupsJ Math Phys 5 1226ndash1234 (1964)
[62] J-P Antoine P Vandergheynst Wavelets on the n-sphere and related manifolds J MathPhys 39 3987ndash4008 (1998)
[63] J-P Antoine P Vandergheynst Wavelets on the 2-sphere A group-theoretical approachAppl Comput Harmon Anal 7 262ndash291 (1999)
[64] J-P Antoine P Vandergheynst Wavelets on the two-sphere and other conic sections JFourier Anal Appl 13 369ndash386 (2007)
[65] J-P Antoine M Duval-Destin R Murenzi B Piette Image analysis with 2D wavelettransform Detection of position orientation and visual contrast of simple objects inWavelets and Applications (Proc Marseille 1989) ed by Y Meyer (Masson and SpringerParis and Berlin 1991) pp144ndash159
References 549
[66] J-P Antoine P Carrette R Murenzi B Piette Image analysis with 2D continuous wavelettransform Signal Process 31 241ndash272 (1993)
[67] J-P Antoine P Vandergheynst K Bouyoucef R Murenzi Alternative representations ofan image via the 2D wavelet transform Application to character recognition in VisualInformation Processing IV SPIE Proceedings vol 2488 (SPIE Bellingham WA 1995)pp 486ndash497
[68] J-P Antoine R Murenzi P Vandergheynst Two-dimensional directional wavelets inimage processing Int J Imaging Syst Tech 7 152ndash165 (1996)
[69] J-P Antoine D Barache RM Cesar Jr LF Costa Shape characterization with thewavelet transform Signal Process 62 265ndash290 (1997)
[70] J-P Antoine P Antoine B Piraux Wavelets in atomic physics in Spline Functions andthe Theory of Wavelets ed by S Dubuc G Deslauriers CRM Proceedings and LectureNotes vol 18 (AMS Providence RI 1999) pp261ndash276
[71] J-P Antoine P Antoine B Piraux Wavelets in atomic physics and in solid state physicsin Wavelets in Physics Chap 8 ed by JC van den Berg (Cambridge University PressCambridge 1999)
[72] J-P Antoine R Murenzi P Vandergheynst Directional wavelets revisited Cauchywavelets and symmetry detection in patterns Appl Comput Harmon Anal 6 314ndash345(1999)
[73] J-P Antoine L Jacques R Twarock Wavelet analysis of a quasiperiodic tiling withfivefold symmetry Phys Lett A 261 265ndash274 (1999)
[74] J-P Antoine L Jacques P Vandergheynst Penrose tilings quasicrystals and wavelets inWavelet Applications in Signal and Image Processing VII SPIE Proceedings vol 3813(SPIE Bellingham WA 1999) pp 28ndash39
[75] J-P Antoine YB Kouagou D Lambert B Torreacutesani An algebraic approach to discretedilations Application to discrete wavelet transforms J Fourier Anal Appl 6 113ndash141(2000)
[76] J-P Antoine A Coron J-M Dereppe Water peak suppression Time-frequency vs time-scale approach J Magn Reson 144 189ndash194 (2000)
[77] J-P Antoine J-P Gazeau P Monceau J R Klauder K Penson Temporally stablecoherent states for infinite well and Poumlschl-Teller potentials J Math Phys 42 2349ndash2387(2001)
[78] J-P Antoine A Coron C Chauvin Wavelets and related time-frequency techniques inmagnetic resonance spectroscopy NMR Biomed 14 265ndash270 (2001)
[79] J-P Antoine L Demanet J-F Hochedez L Jacques R Terrier E Verwichte Applicationof the 2-D wavelet transform to astrophysical images Phys Mag 24 93ndash116 (2002)
[80] J-P Antoine L Demanet L Jacques P Vandergheynst Wavelets on the sphere Imple-mentation and approximations Appl Comput Harmon Anal 13 177ndash200 (2002)
[81] J-P Antoine I Bogdanova P Vandergheynst The continuous wavelet transform on conicsections Int J Wavelets Multires Inform Proc 6 137ndash156 (2007)
[82] J-P Antoine D Rosca P Vandergheynst Wavelet transform on manifolds Old and newapproaches Appl Comput Harmon Anal 28 189ndash202 (2010)
[83] P Antoine B Piraux A Maquet Time profile of harmonics generated by a single atom ina strong electromagnetic field Phys Rev A 51 R1750ndashR1753 (1995)
[84] P Antoine B Piraux DB Miloševic M Gajda Generation of ultrashort pulses ofharmonics Phys Rev A 54 R1761ndashR1764 (1996)
[85] P Antoine B Piraux DB Miloševic M Gajda Temporal profile and time control ofharmonic generation Laser Phys 7 594ndash601 (1997)
[86] Apollonius see Wikipedia httpenwikipediaorgwikiApollonius_of_Perga[87] FT Arecchi E Courtens R Gilmore H Thomas Atomic coherent states in quantum
optics Phys Rev A 6 2211ndash2237 (1972)[88] I Aremua J-P Gazeau MN Hounkonnou Action-angle coherent states for quantum
systems with cylindric phase space J Phys A Math Theor 45 335302 (2012)
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[90] F Argoul A Arneacuteodo J Elezgaray G Grasseau R Murenzi Wavelet analysis of theself-similarity of diffusion-limited aggregates and electrodeposition clusters Phys Rev A41 5537ndash5560 (1990)
[91] TA Arias Multiresolution analysis of electronic structure Semicardinal and waveletbases Rev Mod Phys 71 267ndash312 (1999)
[92] A Arneacuteodo F Argoul E Bacry J Elezgaray E Freysz G Grasseau JF Muzy BPouligny Wavelet transform of fractals in Wavelets and Applications (Proc Marseille1989) ed by Y Meyer (Masson and Springer Paris and Berlin 1991) pp 286ndash352
[93] A Arneacuteodo E Bacry JF Muzy The thermodynamics of fractals revisited with waveletsPhysica A 213 232ndash275 (1995)
[94] A Arneacuteodo E Bacry JF Muzy Oscillating singularities in locally self-similar functionsPhys Rev Lett 74 4823ndash4826 (1995)
[95] A Arneacuteodo E Bacry PV Graves JF Muzy Characterizing long-range correlations inDNA sequences from wavelet analysis Phys Rev Lett 74 3293ndash3296 (1996)
[96] A Arneacuteodo Y drsquoAubenton E Bacry PV Graves JF Muzy C Thermes Wavelet basedfractal analysis of DNA sequences Physica D 96 291ndash320 (1996)
[97] A Arneacuteodo E Bacry S Jaffard JF Muzy Oscillating singularities on Cantor sets Agrand canonical multifractal formalism J Stat Phys 87 179ndash209 (1997)
[98] A Arneacuteodo E Bacry S Jaffard JF Muzy Singularity spectrum of multifractal functionsinvolving oscillating singularities J Fourier Anal Appl 4 159ndash174 (1998)
[99] N Aronszajn Theory of reproducing kernels Trans Amer Math Soc 66 337ndash404 (1950)[100] A Ashtekar J Lewandowski D Marolf J Mouratildeo T Thiemann Coherent state
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[105] PW Atkins JC Dobson Angular momentum coherent states Proc Roy Soc London A321 321ndash340 (1971)
[106] BW Atkinson DO Bruff JS Geronimo D P Hardin Wavelets centered on a knotsequence Piecewise polynomial wavelets on a quasi-crystal lattice preprint (2011)arXiv11024246v1 [mathNA]
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[108] H Bacry J-M Leacutevy-Leblond Possible kinematics J Math Phys 9 1605ndash1614 (1968)[109] H Bacry A Grossmann J Zak Proof of the completeness of lattice states in kq
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Amer Math Soc 72 593ndash600 (1978)[111] VG Bagrov J-P Gazeau D Gitman A Levine Coherent states and related quantizations
for unbounded motions J Phys A Math Theor 45 125306 (2012) arXiv12010955v2[quant-ph]
[112] P Balazs J-P Antoine A Grybos Weighted and controlled frames Mutual relationshipand first numerical properties Int J Wavelets Multires Inform Proc 8 109ndash132 (2010)
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[115] P Baldi G Kerkyacharian D Marinucci D Picard High frequency asymptotics forwavelet-based tests for Gaussianity and isotropy on the torus J Multivar Anal 99 606ndash636 (2008)
[116] P Baldi G Kerkyacharian D Marinucci D Picard Asymptotics for spherical needletsAnn of Stat 37 1150ndash1171 (2009)
[117] MC Baldiotti J-P Gazeau DM Gitman Coherent states of a particle in magnetic fieldand Stieltjes moment problem Phys Lett A 373 1916ndash1920 (2009) Erratum Phys LettA 373 2600 (2009)
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[121] D Barache S De Biegravevre J-P Gazeau Affine symmetry semigroups for quasicrystalsEurophys Lett 25 435ndash440 (1994)
[122] D Barache J-P Antoine J-M Dereppe The continuous wavelet transform a tool for NMRspectroscopy J Magn Reson 128 1ndash11 (1997)
[123] V Bargmann On a Hilbert space of analytic functions and an associated integral transformPart I Commun Pure Appl Math 14 187ndash214 (1961)
[124] V Bargmann On a Hilbert space of analytic functions and an associated integral transformPart II A family of related function spaces Application to distribution theory CommunPure Appl Math 20 1ndash101 (1967)
[125] V Bargmann P Butera L Girardello JR Klauder On the completeness of coherentstates Reports Math Phys 2 221ndash228 (1971)
[126] AO Barut L Girardello New ldquocoherentrdquo states associated with non compact groupsCommun Math Phys 21 41ndash55 (1971)
[127] AO Barut H Kleinert Transition probabilities of the hydrogen atom from noncompactdynamical groups Phys Rev 156 1541ndash1545 (1967)
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[131] J Ben Geloun J R Klauder Ladder operators and coherent states for continuous spectraJ Phys A Math Theor 42 375209 (2009)
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[134] JJ Benedetto A Teolis A wavelet auditory model and data compression Appl ComputHarmon Anal 1 3ndash28 (1993)
[135] FA Berezin Quantization Math USSR Izvestija 8 1109ndash1165 (1974)[136] FA Berezin General concept of quantization Commun Math Phys 40 153ndash174 (1975)[137] H Bergeron From classical to quantum mechanics How to translate physical ideas into
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[141] H Bergeron J-P Gazeau P Siegl A Youssef Semi-classical behavior of Poumlschl-Tellercoherent states Eur Phys Lett 92 60003 (2010)
[142] H Bergeron P Siegl A Youssef New SUSYQM coherent states for Poumlschl-Tellerpotentials A detailed mathematical analysis J Phys A Math Theor 45 244028 (2012)
[143] H Bergeron J-P Gazeau A Youssef Are the Weyl and coherent state descriptionsphysically equivalent Phys Lett A 377 598ndash605 (2013)
[144] H Bergeron A Dapor J-P Gazeau P Małkiewicz Wavelet quantum cosmology preprint(2013) arXiv13050653 [gr-qc]
[145] S Bergman Uumlber die Kernfunktion eines Bereiches und ihr Verhalten am Rande I ReineAngw Math 169 1ndash42 (1933)
[146] D Bernier KF Taylor Wavelets from square-integrable representations SIAM J MathAnal 27 594ndash608 (1996)
[147] G Bernuau Wavelet bases associated to a self-similar quasicrystal J Math Phys 394213ndash4225 (1998)
[148] A Bertrand Deacuteveloppements en base de Pisot et reacutepartition modulo 1 C R Acad SciParis 285 419ndash421 (1977)
[149] J Bertrand P Bertrand Classification of affine Wigner functions via an extendedcovariance principle in Group Theoretical Methods in Physics (Proc Sainte-Adegravele 1988)ed by Y Saint-Aubin L Vinet (World Scientific Singapore 1989) pp 1380ndash1383
[150] Z Białynicka-Birula I Białynicki-Birula Space-time description of squeezing J OptSoc Am B4 1621ndash1626 (1987)
[151] E Bianchi E Magliaro C Perini Coherent spin-networks Phys Rev D 82 024012(2010)
[152] S Biskri J-P Antoine B Inhester F Mekideche Extraction of Solar coronal magneticloops with the 2-D Morlet wavelet transform Solar Phys 262 373ndash385 (2010)
[153] R Bluhm VA Kostelecky JA Porter The evolution and revival structure of localizedquantum wave packets Am J Phys 64 944ndash953 (1996)
[154] I Bogdanova P Vandergheynst J-P Antoine L Jacques M Morvidone Stereographicwavelet frames on the sphere Appl Comput Harmon Anal 19 223ndash252 (2005)
[155] I Bogdanova X Bresson J-P Thiran P Vandergheynst Scale space analysis and activecontours for omnidirectional images IEEE Trans Image Process 16 1888ndash1901 (2007)
[156] I Bogdanova P Vandergheynst J-P Gazeau Continuous wavelet transform on thehyperboloid Appl Comput Harmon Anal 23 (2007) 286ndash306 (2007)
[157] P Boggiatto E Cordero Anti-Wick quantization of tempered distributions in Progress inAnalysis Berlin (2001) vol I II (World Sci Publ River Edge NJ 2003) pp 655ndash662
[158] P Boggiatto E Cordero K Groumlchenig Generalized Anti-Wick operators with symbols indistributional Sobolev spaces Int Equ Oper Theory 48 427ndash442 (2004)
[159] A Boumlhm The Rigged Hilbert Space in quantum mechanics in Lectures in TheoreticalPhysics vol IX A ed by WA Brittin et al (Gordon amp Breach New York 1967) pp255ndash315
[160] G Bohnkeacute Treillis drsquoondelettes associeacutes aux groupes de Lorentz Ann Inst H Poincareacute54 245ndash259 (1991)
[161] WR Bomstad JR Klauder Linearized quantum gravity using the projection operatorformalism Class Quantum Grav 23 5961ndash5981 (2006)
[162] VV Borzov Orthogonal polynomials and generalized oscillator algebras Int TransformSpec Funct 12 115ndash138 (2001)
[163] VV Borzov EV Damaskinsky Generalized coherent states for classical orthogonalpolynomials Day on Diffraction (2002) arXivmathQA0209181v1 (SPb 2002)
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[165] A Bouzouina S De Biegravevre Equipartition of the eigenfunctions of quantized ergodic mapson the torus Commun Math Phys 178 83ndash105 (1996)
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[167] A Briguet S Cavassila D Graveron-Demilly Suppression of huge signals using theCadzow enhancement procedure The NMR Newslett 440 26 (1995)
[168] CM Brislawn Fingerprints go digital Notices Amer Math Soc 42 1278ndash1283 (1995)[169] CM Brislawn On the group-theoretic structure of lifted filter banks in Excursions in
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[170] F Bruhat Sur les repreacutesentations induites des groupes de Lie Bull Soc Math France 8497ndash205 (1956)
[171] T Buumllow Multiscale image processing on the sphere in DAGM-Symposium (2002) pp609ndash617
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[173] KE Cahill Coherent-state representations for the photon density Phys Rev 138 B1566ndash1576 (1965)
[174] KE Cahill R Glauber Density operators and quasiprobability distributions Phys Rev177 1882ndash1902 (1969)
[175] KE Cahill R Glauber Ordered expansions in boson amplitude operators Phys Rev 1771857ndash1881 (1969)
[176] AR Calderbank I Daubechies W Sweldens BL Yeo Wavelets that map integers tointegers Appl Comput Harmon Anal 5 332ndash369 (1998)
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[180] EJ Candegraves Harmonic analysis of neural networks Appl Comput Harmon Anal 6 197ndash218 (1999)
[181] EJ Candegraves Ridgelets and the representation of mutilated Sobolev functions SIAM JMath Anal 33 347ndash368 (2001)
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[184] EJ Candegraves L Demanet The curvelet representation of wave propagators is optimallysparse Commun Pure Appl Math 58 1472ndash1528 (2005)
[185] EJ Candegraves DL Donoho Curvelets ndash A surprisingly effective nonadaptive representationfor objects with edges in Curves and Surfaces ed by LL Schumaker et al (VanderbiltUniversity Press Nashville TN 1999)
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[191] EJ Candegraves F Guo New multiscale transforms minimum total variationsynthesisApplications to edge-preserving image reconstruction Signal Proc 82 1519ndash1543 (2002)
[192] EJ Candegraves L Demanet D Donoho L Ying Fast discrete curvelet transforms MultiscaleModel Simul 5 861ndash899 (2006)
[193] AL Carey Square integrable representations of non-unimodular groups Bull AustrMath Soc 15 1ndash12 (1976)
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[195] P Carruthers MM Nieto Phase and angle variables in quantum mechanics Rev ModPhys 40 411ndash440 (1968)
[196] PG Casazza G Kutyniok Frames of subspaces in Wavelets Frames and Operator The-ory Contemporary Mathematics vol 345 (American Mathematical Society ProvidenceRI 2004) pp 87ndash113
[197] PG Casazza D Han DR Larson Frames for Banach spaces Contemp Math 247 149ndash182 (1999)
[198] P Casazza O Christensen S Li A Lindner Riesz-Fischer sequences and lower framebounds Z Anal Anwend 21 305ndash314 (2002)
[199] PG Casazza G Kutyniok S Li Fusion frames and distributed processing ApplComputHarmon Anal 25 114ndash132 (2008)
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dimensional numerical potentials Preprint (2013) arXiv13036439v2[203] S-J Chang K-J Shi Evolution and exact eigenstates of a resonant quantum system Phys
Rev A 34 7ndash22 (1986)[204] SHH Chowdhury ST Ali All the groups of signal analysis from the (1+1) affine Galilei
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10 1ndash4 (2012)[206] C Cishahayo S De Biegravevre On the contraction of the discrete series of SU(11) Ann Inst
Fourier (Grenoble) 43 551ndash567 (1993)[207] M Clerc and S Mallat Shape from texture and shading with wavelets in Dynamical
Systems Control Coding Computer Vision Progress in Systems and Control Theory 25393ndash417 (1999)
[208] L Cohen General phase-space distribution functions J Math Phys 7 781ndash786 (1966)[209] A Cohen I Daubechies J-C Feauveau Biorthogonal bases of compactly supported
wavelets Commun Pure Appl Math 45 485ndash560 (1992)[210] R Coifman Y Meyer MV Wickerhauser Wavelet analysis and signal processing
in Wavelets and Their Applications ed by MB Ruskai G Beylkin R CoifmanI Daubechies S Mallat Y Meyer L Raphael (Jones and Bartlett Boston 1992)pp 153ndash178
[211] R Coifman Y Meyer MV Wickerhauser Entropy-based algorithms for best basisselection IEEE Trans Inform Theory 38 713ndash718 (1992)
[212] R Coquereaux A Jadczyk Conformal theories curved spaces relativistic wavelets andthe geometry of complex domains Rev Math Phys 2 1ndash44 (1990)
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[214] N Cotfas J-P Gazeau Finite tight frames and some applications (topical review) J PhysA Math Theor 43 193001 (2010)
[215] N Cotfas J-P Gazeau K Goacuterska Complex and real Hermite polynomials and relatedquantizations J Phys A Math Theor 43 305304 (2010)
[216] N Cotfas J-P Gazeau A Vourdas Finite-dimensional Hilbert space and frame quantiza-tion J Phys A Math Gen 44 175303 (2011)
[217] EMF Curado MA Rego-Monteiro LMCS Rodrigues Y Hassouni Coherent statesfor a degenerate system The hydrogen atom Physica A 371 16ndash19 (2006)
[218] S Dahlke P Maass The affine uncertainty principle in one and two dimensions CompMath Appl 30 293ndash305 (1995)
[219] S Dahlke W Dahmen E Schmidt I Weinreich Multiresolution analysis and wavelets onS
2 and S3 Numer Funct Anal Optim 16 19ndash41 (1995)
[220] S Dahlke V Lehmann G Teschke Applications of wavelet methods to the analysis ofmeteorological radar data - An overview Arabian J Sci Eng 28 3ndash44 (2003)
[221] S Dahlke G Kutyniok P Maass C Sagiv H-G Stark G Teschke The uncertaintyprinciple associated with the continuous shearlet transform Int J Wavelets MultiresolutInf Process 6 157ndash181 (2008)
[222] S Dahlke G Kutyniok G Steidl G Teschke Shearlet coorbit spaces and associatedBanach frames Appl Comput Harmon Anal 27 195ndash214 (2009)
[223] S Dahlke G Steidl G Teschke The continuous shearlet transform in arbitrary spacedimensions J Fourier Anal Appl 16 340ndash364 (2010)
[224] S Dahlke G Steidl G Teschke Shearlet coorbit spaces Compactly supported analyzingshearlets traces and embeddings J Fourier Anal Appl 17 1232ndash1355 (2011)
[225] T Dallard GR Spedding 2-D wavelet transforms Generalisation of the Hardy space andapplication to experimental studies Eur J Mech BFluids 12 107ndash134 (1993)
[226] C Daskaloyannis Generalized deformed oscillator and nonlinear algebras J Phys AMath Gen 24 L789ndashL794 (1991)
[227] C Daskaloyannis K Ypsilantis A deformed oscillator with Coulomb energy spectrumJ Phys A Math Gen 25 4157ndash4166 (1992)
[228] I Daubechies On the distributions corresponding to bounded operators in the Weylquantization Commun Math Phys 75 229ndash238 (1980)
[229] I Daubechies and A Grossmann An integral transform related to quantization I J MathPhys 21 2080ndash2090 (1980)
[230] I Daubechies A Grossmann J Reignier An integral transform related to quantization IIJ Math Phys 24 239ndash254 (1983)
[231] I Daubechies Orthonormal bases of compactly supported wavelets Commun Pure ApplMath 41 909ndash996 (1988)
[232] I Daubechies The wavelet transform time-frequency localisation and signal analysisIEEE Trans Inform Theory 36 961ndash1005 (1990)
[233] I Daubechies S Maes A nonlinear squeezing of the continuous wavelet transform basedon auditory nerve models in Wavelets in Medicine and Biology ed by A Aldroubi MUnser (CRC Press Boca Raton 1996) pp 527ndash546
[234] I Daubechies A Grossmann Y Meyer Painless nonorthogonal expansions J Math Phys27 1271ndash1283 (1986)
[235] ER Davies Introduction to texture analysis in Handbook of texture analysis ed by MMirmehdi X Xie J Suri (World Scientific Singapore 2008) pp 1ndash31
[236] R De Beer D van Ormondt FTAW Wajer S Cavassila D Graveron-Demilly S VanHuffel SVD-based modelling of medical NMR signals in SVD and Signal ProcessingIII Algorithms Architectures and Applications ed by M Moonen B De Moor (Elsevier(North-Holland) Amsterdam 1995) pp 467ndash474
[237] S De Biegravevre Coherent states over symplectic homogeneous spaces J Math Phys 301401ndash1407 (1989)
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[239] S De Biegravevre JA Gonzaacutelez Semiclassical behaviour of coherent states on the circle inQuantization and Coherent States Methods in Physics ed by A Odzijewicz et al (WorldScientific Singapore 1993)
[240] S De Biegravevre AE Gradechi Quantum mechanics and coherent states on the anti-de Sitterspace-time and their Poincareacute contraction Ann Inst H Poincareacute 57 403ndash428 (1992)
[241] J Deenen C Quesne Dynamical group of collective states I II III J Math Phys 23878ndash889 2004ndash2015 (1982)
[242] J Deenen C Quesne Dynamical group of collective states I II III J Math Phys 251638ndash1650 (1984)
[243] J Deenen C Quesne Partially coherent states of the real symplectic group J Math Phys25 2354ndash2366 (1984)
[244] J Deenen C Quesne Boson representations of the real symplectic group and theirapplication to the nuclear collective model J Math Phys 26 2705ndash2716 (1985)
[245] R Delbourgo Minimal uncertainty states for the rotation and allied groups J Phys AMath Gen 10 1837ndash1846 (1977)
[246] R Delbourgo J R Fox Maximum weight vectors possess minimal uncertainty J PhysA Math Gen 10 L233ndashL235 (1977)
[247] V Delouille J de Patoul J-F Hochedez L Jacques J-P Antoine Wavelet spectrumanalysis of EITSoHO images Solar Phys 228 301ndash321 (2005)
[248] N Delprat B Escudieacute P Guillemain R Kronland-Martinet P Tchamitchian B Tor-reacutesani Asymptotic wavelet and Gabor analysis Extraction of instantaneous frequenciesIEEE Trans Inform Theory 38 644ndash664 (1992)
[249] Th Deutsch L Genovese Wavelets for electronic structure calculations Collection SocFr Neut 12 33ndash76 (2011)
[250] B Dewitt Quantum theory of gravity I The canonical theory Phys Rev 160 1113ndash1148(1967)
[251] RH Dicke Coherence in spontaneous radiation processes Phys Rev 93 99ndash110 (1954)[252] AN Dinkelaker AL MacKinnon Wavelets intermittency and solar flare hard X-rays 1
Local intermittency measure in cascade and avalanche scenarios Solar Phys 282 471ndash481(2013)
[253] AN Dinkelaker AL MacKinnon Wavelets intermittency and solar flare hard X-rays 2LIM analysis of high time resolution BATSE data Solar Phys 282 483ndash501 (2013)
[254] MN Do M Vetterli Contourlets in Beyond Wavelets ed by GV Welland (AcademicSan Diego 2003) pp 83ndash105
[255] MN Do M Vetterli The contourlet transform An efficient directional multiresolutionimage representation IEEE Trans Image Process 14 2091ndash2106 (2005)
[256] VV Dodonov Nonclassical states in quantum optics A ldquosqueezedrdquo review of the first 75years J Opt B Quant Semiclass Opot 4 R1ndashR33 (2002)
[257] DL Donoho Nonlinear wavelet methods for recovery of signals densities and spectrafrom indirect and noisy data in Different Perspectives on Wavelets Proceedings ofSymposia in Applied Mathematics vol 38 ed by I Daubechies (American MathematicalSociety Providence RI 1993) pp 173ndash205
[258] DL Donoho Wedgelets Nearly minimax estimation of edges Ann Stat 27 859ndash897(1999)
[259] DL Donoho X Huo Beamlet pyramids A new form of multiresolution analysis suitedfor extracting lines curves and objects from very noisy image data in SPIE Proceedingsvol 5914 (SPIE Bellingham WA 2005) pp 1ndash12
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[260] AH Dooley Contractions of Lie groups and applications to analysis in Topics in ModernHarmonic Analysis vol I (Istituto Nazionale di Alta Matematica Francesco Severi Roma1983) pp 483ndash515
[261] AH Dooley JW Rice Contractions of rotation groups and their representations MathProc Camb Phil Soc 94 509ndash517 (1983)
[262] AH Dooley JW Rice On contractions of semisimple Lie groups Trans Amer MathSoc 289 185ndash202 (1985)
[263] JR Driscoll DM Healy Computing Fourier transforms and convolutions on the 2-sphereAdv Appl Math 15 202ndash250 (1994)
[264] H Drissi F Regragui J-P Antoine M Bennouna Wavelet transform analysis of visualevoked potentials Some preliminary results ITBM-RBM 21 84ndash91 (2000)
[265] RJ Duffin AC Schaeffer A class of nonharmonic Fourier series Trans Amer MathSoc 72 341ndash366 (1952)
[266] M Duflo CC Moore On the regular representation of a nonunimodular locally compactgroup J Funct Anal 21 209ndash243 (1976)
[267] M Duval-Destin R Murenzi Spatio-temporal wavelets Application to the analysis ofmoving patterns in Progress in Wavelet Analysis and Applications (Proc Toulouse 1992)ed by Y Meyer S Roques (Ed Frontiegraveres Gif-sur-Yvette 1993) pp 399ndash408
[268] M Duval-Destin M-A Muschietti B Torreacutesani Continuous wavelet decompositionsmultiresolution and contrast analysis SIAM J Math Anal 24 739ndash755 (1993)
[269] SJL van Eindhoven JLH Meyers New orthogonality relations for the Hermitepolynomials and related Hilbert spaces J Math Anal Appl 146 89ndash98 (1990)
[270] M ElBaz R Fresneda J-P Gazeau Y Hassouni Coherent state quantization of para-grassmann algebras J Phys A Math Theor 43 385202 (2010) Corrigendum J PhysA Math Theor 45 (2012)
[271] A Elkharrat J-P Gazeau F Deacutenoyer Multiresolution of quasicrystal diffraction spectraActa Cryst A65 466ndash489 (2009)
[272] Q Fan Phase space analysis of the identity decompositions J Math Phys 34 3471ndash3477(1993)
[273] M Fanuel S Zonetti Affine quantization and the initial cosmological singularity Euro-phys Lett 101 10001 (2013)
[274] M Farge Wavelet transforms and their applications to turbulence Annu Rev Fluid Mech24 395ndash457 (1992)
[275] M Farge N Kevlahan V Perrier E Goirand Wavelets and turbulence Proc IEEE 84639ndash669 (1996)
[276] M Farge NK-R Kevlahan V Perrier K Schneider Turbulence analysis modellingand computing using wavelets in Wavelets in Physics Chap 4 ed by JC van den Berg(Cambridge University Press Cambridge 1999)
[277] HG Feichtinger Coherent frames and irregular sampling in Recent Advances in FourierAnalysis and Its applications ed by JS Byrnes JL Byrnes (Kluwer Dordrecht 1990)pp 427ndash440
[278] HG Feichtinger KH Groumlchenig Banach spaces related to integrable group representa-tions and their atomic decompositions I J Funct Anal 86 307ndash340 (1989)
[279] HG Feichtinger KH Groumlchenig Banach spaces related to integrable group representa-tions and their atomic decompositions II Mh Math 108 129ndash148 (1989)
[280] M Flensted-Jensen Discrete series for semisimple symmetric spaces Ann of Math 111253ndash311 (1980)
[281] K Flornes A Grossmann M Holschneider B Torreacutesani Wavelets on discrete fieldsAppl Comput Harmon Anal 1 137ndash146 (1994)
[282] V Fock Zur Theorie der Wasserstoffatoms Zs f Physik 98 145ndash54 (1936)[283] M Fornasier H Rauhut Continuous frames function spaces and the discretization
problem J Fourier Anal Appl 11 245ndash287 (2005)
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[284] W Freeden M Schreiner Orthogonal and non-orthogonal multiresolution analysis scalediscrete and exact fully discrete wavelet transform on the sphere Constr Approx 14 493ndash515 (1997)
[285] W Freeden U Windheuser Combined spherical harmonic and wavelet expansion mdash Afuture concept in Earthrsquos gravitational determination Appl Comput Harmon Anal 4 1ndash37 (1997)
[286] W Freeden T Maier S Zimmermann A survey on wavelet methods for (geo)applicationsRevista Mathematica Complutense 16 (2003) 277ndash310
[287] W Freeden M Schreiner Biorthogonal locally supported wavelets on the sphere based onzonal kernel functions J Fourier Anal Appl 13 693ndash709 (2007)
[288] WT Freeman EH Adelson The design and use of steerable filters IEEE Trans PatternAnal Machine Intell 13 891ndash906 (1991)
[289] L Freidel ER Livine U(N) coherent states for loop quantum gravity J Math Phys 52052502 (2011)
[290] J Froment S Mallat Arbitrary low bit rate image compression using wavelets in Progressin Wavelet Analysis and Applications (Proc Toulouse 1992) ed by Y Meyer S Roques(Ed Frontiegraveres Gif-sur-Yvette 1993) pp 413ndash418 and references therein
[291] L Freidel S Speziale Twisted geometries A geometric parameterisation of SU(2) phasespace Phys Rev D 82 084040 (2010)
[292] H Fuumlhr Wavelet frames and admissibility in higher dimensions J Math Phys 37 6353ndash6366 (1996)
[293] H Fuumlhr M Mayer Continuous wavelet transforms from semidirect products Cyclicrepresentations and Plancherel measure J Fourier Anal Appl 8 375ndash396 (2002)
[294] D Gabor Theory of communication J Inst Electr Engrg(London) 93 429ndash457 (1946)[295] J-P Gabardo D Han Frames associated with measurable spaces Adv Comput Math 18
127ndash147 (2003)[296] E Galapon Paulirsquos theorem and quantum canonical pairs The consistency of a bounded
self-adjoint time operator canonically conjugate to a Hamiltonian with non-empty pointspectrum Proc R Soc Lond A 458 451ndash472 (2002)
[297] PL Garciacutea de Leacuteon J-P Gazeau Coherent state quantization and phase operator PhysLett A 361 301ndash304 (2007)
[298] L Garciacutea de Leoacuten J-P Gazeau J Queacuteva The infinite well revisited Coherent states andquantization Phys Lett A 372 3597ndash3607 (2008)
[299] T Garidi J-P Gazeau E Huguet M Lachiegraveze Rey J Renaud Fuzzy spheres frominequivalent coherent states quantization J Phys A Math Theor 40 10225ndash10249 (2007)
[300] J-P Gazeau Four Euclidean conformal group in atomic calculations Exact analyticalexpressions for the bound-bound two-photon transition matrix elements in the H atomJ Math Phys 19 1041ndash1048 (1978)
[301] J-P Gazeau On the four Euclidean conformal group structure of the sturmian operatorLett Math Phys 3 285ndash292 (1979)
[302] J-P Gazeau Technique Sturmienne pour le spectre discret de lrsquoeacutequation de SchroumldingerJ Phys A Math Gen 13 3605ndash3617 (1980)
[303] J-P Gazeau Four Euclidean conformal group approach to the multiphoton processes in theH atom J Math Phys 23 156ndash164 (1982)
[304] J-P Gazeau A remarkable duality in one particle quantum mechanics between someconfining potentials and (R+Linfin
ε ) potentials Phys Lett 75A 159ndash163 (1980)[305] J-P Gazeau SL(2R)-coherent states and integrable systems in classical and quantum
physics in Quantization Coherent States and Complex Structures ed by J-P AntoineST Ali W Lisiecki IM Mladenov A Odzijewicz (Plenum Press New York and London1995) pp 147ndash158
[306] J-P Gazeau S Graffi Quantum harmonic oscillator A relativistic and statistical point ofview Boll Unione Mat Ital 11-A 815ndash839 (1997)
[307] J-P Gazeau V Hussin Poincareacute contraction of SU(11) Fock-Bargmann structure J PhysA Math Gen 25 1549ndash1573 (1992)
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[309] J-P Gazeau JR Klauder Coherent states for systems with discrete and continuousspectrum J Phys A Math Gen 32 123ndash132 (1999)
[310] J-P Gazeau P Monceau Generalized coherent states for arbitrary quantum systems inColloquium M Flato (Dijon Sept 99) vol II (Kluumlwer Dordrecht 2000) pp 131ndash144
[311] J-P Gazeau M Novello The question of mass in (Anti-) de Sitter space-times J Phys AMath Theor 41 304008 (2008)
[312] J-P Gazeau M del Olmo q-coherent states quantization of the harmonic oscillator AnnPhys (NY) 330 220ndash245 (2013) arXiv12071200 [quant-ph]
[313] J-P Gazeau J Patera Tau-wavelets of Haar J Phys A Math Gen 29 4549ndash4559 (1996)[314] J-P Gazeau W Piechocki Coherent states quantization of a particle in de Sitter space
J Phys A Math Gen 37 6977ndash6986 (2004)[315] J-P Gazeau J Renaud Lie algorithm for an interacting SU(11) elementary system and its
contraction Ann Phys (NY) 222 89ndash121 (1993)[316] J-P Gazeau J Renaud Relativistic harmonic oscillator and space curvature Phys Lett A
179 67ndash71 (1993)[317] J-P Gazeau V Spiridonov Toward discrete wavelets with irrational scaling factor J Math
plane J Phys A Math Theor 44 495201 (2011)[319] J-P Gazeau J Patera E Pelantovaacute Tau-wavelets in the plane J Math Phys 39 4201ndash
4212 (1998)[320] J-P Gazeau M Andrle C Burdiacutek R Krejcar Wavelet multiresolutions for the Fibonacci
chain J Phys A Math Gen 33 L47ndashL51 (2000)[321] J-P Gazeau M Andrle C Burdiacutek Bernuau spline wavelets and sturmian sequences
J Fourier Anal Appl 10 269ndash300 (2004)[322] J-P Gazeau F-X Josse-Michaux P Monceau Finite dimensional quantizations of the
(q p) plane new space and momentum inequalities Int J Modern Phys B 20 1778ndash1791 (2006)
[323] J-P Gazeau J Mourad J Queacuteva Fuzzy de Sitter space-times via coherent statesquantization in Proceedings of the XXVIth Colloquium on Group Theoretical Methodsin Physics New York 2006 ed by J Birman S Catto B Nicolescu (Canopus PublishingLimited London 2009)
[324] D Geller A Mayeli Continuous wavelets on compact manifolds Math Z 262 895ndash927(2009)
[325] D Geller A Mayeli Nearly tight frames and space-frequency analysis on compactmanifolds Math Z 263 235ndash264 (2009)
[326] L Genovese B Videau M Ospici Th Deutsch S Goedecker J-F Mhaut Daubechieswavelets for high performance electronic structure calculations The BigDFT project CR Mecanique 339 149ndash164 (2011)
[327] G Gentili C Stoppato Power series and analyticity over the quaternions Math Ann 352113ndash131 (2012)
[328] G Gentili DC Struppa A new theory of regular functions of a quaternionic variable AdvMath 216 279ndash301 (2007)
[329] C Geyer K Daniilidis Catadioptric projective geometry Int J Comput Vision 45 223ndash243 (2001)
[330] R Gilmore Geometry of symmetrized states Ann Phys (NY) 74 391ndash463 (1972)[331] R Gilmore On properties of coherent states Rev Mex Fis 23 143ndash187 (1974)[332] J Ginibre Statistical ensembles of complex quaternion and real matrices J Math Phys
6 440ndash449 (1965)[333] RJ Glauber The quantum theory of optical coherence Phys Rev 130 2529ndash2539 (1963)
560 References
[334] RJ Glauber Coherent and incoherent states of radiation field Phys Rev 131 2766ndash2788(1963)
[335] J Glimm Locally compact transformation groups Trans Amer Math Soc 101 124ndash138(1961)
[336] R Godement Sur les relations drsquoorthogonaliteacute de V Bargmann C R Acad Sci Paris 255521ndash523 657ndash659 (1947)
[337] C Gonnet B Torreacutesani Local frequency analysis with two-dimensional wavelet trans-form Signal Proc 37 389ndash404 (1994)
[338] JA Gonzalez MA del Olmo Coherent states on the circle J Phys A Math Gen 318841ndash8857 (1998)
[339] XGonze B Amadon et al ABINIT First-principles approach to material and nanosystemproperties Computer Physics Comm 180 2582ndash2615 (2009)
[340] KM Gograverski E Hivon AJ Banday BD Wandelt FK Hansen M Reinecke MBartelmann HEALPix A framework for high-resolution discretization and fast analysisof data distributed on the sphere Astrophys J 622 759ndash771 (2005)
[341] P Goupillaud A Grossmann J Morlet Cycle-octave and related transforms in seismicsignal analysis Geoexploration 23 85ndash102 (1984)
[342] KH Groumlchenig A new approach to irregular sampling of band-limited functions in RecentAdvances in Fourier Analysis and Its applications ed by JS Byrnes JL Byrnes (KluwerDordrecht 1990) pp 251ndash260
[343] KH Groumlchenig Gabor analysis over LCA groups in Gabor Analysis and Algorithms ndashTheory and Applications ed by HG Feichtinger T Strohmer (Birkhaumluser Boston-Basel-Berlin 1998) pp 211ndash231
[344] HJ Groenewold On the principles of elementary quantum mechanics Physica 12 405ndash460 (1946)
[345] P Grohs Continuous shearlet tight frames J Fourier Anal Appl 17 506ndash518 (2011)[346] P Grohs G Kutyniok Parabolic molecules preprint TU Berlin (2012)[347] M Grosser A note on distribution spaces on manifolds Novi Sad J Math 38 121ndash128
(2008)[348] A Grossmann Parity operator and quantization of δ -functions Commun Math Phys 48
191ndash194 (1976)[349] A Grossmann J Morlet Decomposition of Hardy functions into square integrable
wavelets of constant shape SIAM J Math Anal 15 723ndash736 (1984)[350] A Grossmann J Morlet Decomposition of functions into wavelets of constant shape and
related transforms in Mathematics + Physics Lectures on recent results I ed by L Streit(World Scientific Singapore 1985) pp 135ndash166
[351] A Grossmann J Morlet T Paul Integral transforms associated to square integrablerepresentations I General results J Math Phys 26 2473ndash2479 (1985)
[352] A Grossmann J Morlet T Paul Integral transforms associated to square integrablerepresentations II Examples Ann Inst H Poincareacute 45 293ndash309 (1986)
[353] A Grossmann R Kronland-Martinet J Morlet Reading and understanding the contin-uous wavelet transform in Wavelets Time-Frequency Methods and Phase Space (ProcMarseille 1987) ed by J-M Combes A Grossmann P Tchamitchian 2nd edn (SpringerBerlin 1990) pp 2ndash20
[354] P Guillemain R Kronland-Martinet B Martens Estimation of spectral lines with helpof the wavelet transform Application in NMR spectroscopy in Wavelets and Applications(Proc Marseille 1989) ed by Y Meyer (Masson and Springer Paris and Berlin 1991) pp38ndash60
[355] H de Guise M Bertola Coherent state realizations of su(n+ 1) on the n-torus J MathPhys 43 3425ndash3444 (2002)
[356] K Guo D Labate Representation of Fourier Integral Operators using shearlets J FourierAnal Appl 14 327ndash371 (2008)
References 561
[357] K Guo G Kutyniok D Labate Sparse multidimensional representations usinganisotropic dilation and shear operators in Wavelets and Spines (Athens GA 2005)(Nashboro Press Nashville TN 2006) pp 189ndash201
[358] K Guo D Labate W-Q Lim G Weiss E Wilson Wavelets with composite dilationsand their MRA properties Appl Comput Harmon Anal 20 202ndash236 (2006)
[359] EA Gutkin Overcomplete subspace systems and operator symbols Funct Anal Appl 9260ndash261 (1975)
[360] G Gyoumlrgyi Integration of the dynamical symmetry groups for the 1r potential Acta PhysAcad Sci Hung 27 435ndash439 (1969)
[361] BC Hall The Segal-Bargmann ldquoCoherent Staterdquo transform for compact Lie groups JFunct Analysis 122 103ndash151 (1994)
[362] B Hall JJ Mitchell Coherent states on spheres J Math Phys 43 1211ndash1236 (2002)[363] DK Hammond P Vandergheynst R Gribonval Wavelets on graphs via spectral theory
Appl Comput Harmon Anal 30 129ndash150 (2011)[364] Y Hassouni EMF Curado MA Rego-Monteiro Construction of coherent states for
physical algebraic system Phys Rev A 71 022104 (2005)[365] J He H Liu Admissible wavelets associated with the affine automorphism group of the
Siegel upper half-plane J Math Anal Appl 208 58ndash70 (1997)[366] J He H Liu Admissible wavelets associated with the classical domain of type one
Approx Appl 14 (1998) 89ndash105[367] J He L Peng Wavelet transform on the symmetric matrix space preprint Beijing (1997)
(unpublished)[368] J He L Peng Admissible wavelets on the unit disk Complex Variables 35 109ndash119
(1998)[369] DM Healy Jr FE Schroeck Jr On informational completeness of covariant localization
observables and Wigner coefficients J Math Phys 36 453ndash507 (1995)[370] C Heil D Walnut Continuous and discrete wavelet transforms SIAM Review 31 628ndash
666 (1989)[371] K Hepp EH Lieb On the superradiant phase transition for molecules in a quantized
radiation field The Dicke maser model Ann Phys (NY) 76 360ndash404 (1973)[372] K Hepp EH Lieb Equilibrium statistical mechanics of matter interacting with the
quantized radiation field Phys Rev A 8 2517ndash2525 (1973)[373] JA Hogan JD Lakey Extensions of the Heisenberg group by dilations and frames Appl
Comput Harmon Anal 2 174ndash199 (1995)[374] AL Hohoueacuteto K Thirulogasanthar ST Ali J-P Antoine Coherent states lattices and
square integrability of representations J Phys A Math Gen36 11817ndash11835 (2003)[375] M Holschneider On the wavelet transformation of fractal objects J Stat Phys 50 963ndash
993 (1988)[376] M Holschneider Wavelet analysis on the circle J Math Phys 31 39ndash44 (1990)[377] M Holschneider Inverse Radon transforms through inverse wavelet transforms Inv Probl
7 853ndash861 (1991)[378] M Holschneider Localization properties of wavelet transforms J Math Phys 34 3227ndash
3244 (1993)[379] M Holschneider General inversion formulas for wavelet transforms J Math Phys 34
4190ndash4198 (1993)[380] M Holschneider Wavelet analysis over abelian groups Applied Comput Harmon Anal
2 52ndash60 (1995)[381] M Holschneider Continuous wavelet transforms on the sphere J Math Phys 37 4156ndash
4165 (1996)[382] M Holschneider I Iglewska-Nowak Poisson wavelets on the sphere J Fourier Anal
Appl 13 405ndash419 (2007)
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[383] M Holschneider R Kronland-Martinet J Morlet P Tchamitchian A real-time algorithmfor signal analysis with the help of wavelet transform in Wavelets Time-FrequencyMethods and Phase Space (Proc Marseille 1987) ed by J-M Combes A Grossmann PTchamitchian 2nd edn (Springer Berlin 1990) pp 286ndash297
[384] M Holschneider P Tchamitchian Pointwise analysis of Riemannrsquos ldquonondifferentiablerdquofunction Invent Math 105 157ndash175 (1991)
[385] GR Honarasa MK Tavassoly M Hatami R Roknizadeh Nonclassical properties ofcoherent states and excited coherent states for continuous spectra J Phys A Math Theor44 085303 (2011)
[386] M Hongoh Coherent states associated with the continuous spectrum of noncompactgroups J Math Phys 18 2081ndash2085 (1977)
[387] A Horzela FH Szafraniec A measure free approach to coherent states J Phys A MathGen 45 244018 (2012)
[388] W-L Hwang S Mallat Characterization of self-similar multifractals with waveletmaxima Appl Comput Harmon Anal 1 316ndash328 (1994)
[389] W-L Hwang C-S Lu P-C Chung Shape from texture Estimation of planar surfaceorientation through the ridge surfaces of continuous wavelet transform IEEE Trans ImageProc 7 773ndash780 (1998)
[390] I Iglewska-Nowak M Holschneider Frames of Poisson wavelets on the sphere ApplComput Harmon Anal 28 227ndash248 (2010)
[391] E Inoumlnuuml EP Wigner On the contraction of groups and their representations Proc NatAcad Sci U S 39 510ndash524 (1953)
[392] S Iqbal F Saif Generalized coherent states and their statistical characteristics in power-law potentials J Math Phys 52 082105 (2011)
[393] CJ Isham JR Klauder Coherent states for n-dimensional Euclidean groups E(n) andtheir application J MathPhys 32 607ndash620 (1991)
[394] L Jacques J-P Antoine Multiselective pyramidal decomposition of images Wavelets withadaptive angular selectivity Int J Wavelets Multires Inform Proc 5 785ndash814 (2007)
[395] L Jacques L Duval C Chaux G Peyreacute A panorama on multiscale geometric rep-resentations intertwining spatial directional and frequency selectivity Signal Proc 912699ndash2730 (2011)
[396] HR Jalali M K Tavassoly On the ladder operators and nonclassicality of generalizedcoherent state associated with a particle in an infinite square well preprint (2013)arXiv13034100v1 [quant-ph]
[397] C Johnston On the pseudo-dilation representations of Flornes Grossmann Holschneiderand Torreacutesani Appl Comput Harmon Anal 3 377ndash385 (1997)
[398] G Kaiser Phase-space approach to relativistic quantum mechanics I Coherent staterepresentation for massive scalar particles J MathPhys 18 952ndash959 (1977)
[399] G Kaiser Phase-space approach to relativistic quantum mechanics II Geometrical aspectsJ MathPhys 19 502ndash507 (1978)
[400] C Kalisa B Torreacutesani N-dimensional affine Weyl-Heisenberg wavelets Ann Inst HPoincareacute 59 201ndash236 (1993)
[401] W Kaminski J Lewandowski T Pawłowski Quantum constraints Dirac observables andevolution group averaging versus the Schroumldinger picture in LQC Class Quant Grav 26245016 (2009)
[402] MR Karim ST Ali A relativistic windowed Fourier transform preprint ConcordiaUniversity Montreacuteal (1997) (unpublished)
[403] M R Karim ST Ali M Bodruzzaman A relativistic windowed Fourier transform inProceedings of IEEE SoutheastCon 2000 Nashville Tennessee pp 253ndash260 (2000)
[404] T Kawazoe Wavelet transforms associated to a principal series representation of semisim-ple Lie groups I II Proc Japan Acad Ser A ndash Math Sci 71 154ndash157 158ndash160 (1995)
[405] T Kawazoe Wavelet transform associated to an induced representation of SL(n+ 2R)Ann Inst H Poincareacute 65 1ndash13 (1996)
References 563
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[407] P Kittipoom G Kutyniok W-Q Lim Construction of compactly supported shearletframes Constr Approx 35 21ndash72 (2012)
[408] J Kiukas P Lahti K Ylinenc Phase space quantization and the operator moment problemJ Math Phys 47 072104 (2006)
[409] JR Klauder Continuous-representation theory I Postulates of continuous-representationtheory J Math Phys 4 1055ndash1058 (1963)
[410] JR Klauder Continuous-representation theory II Generalized relation between quantumand classical dynamics J Math Phys 4 1058ndash1073 (1963)
[411] JR Klauder Path integrals for affine variables in Functional Integration Theory andApplications ed by J-P Antoine E Tirapegui (Plenum Press New York and London1980) pp 101ndash119
[412] JR Klauder Are coherent states the natural language of quantum mechanics inFundamental Aspects of Quantum Theory ed by V Gorini A Frigerio NATO ASI Seriesvol B 144 (Plenum Press New York 1986) pp 1ndash12
[413] JR Klauder Quantization without quantization Ann Phys (NY) 237 147ndash160 (1995)[414] JR Klauder Coherent states for the hydrogen atom J Phys A Math Gen 29 L293ndash
L296 (1996)[415] JR Klauder An affinity for affine quantum gravity Proc Steklov Inst Math 272 169ndash176
(2011) and references therein[416] JR Klauder RF Streater A wavelet transform for the Poincareacute group J Math Phys 32
1609ndash1611 (1991)[417] JR Klauder RF Streater Wavelets and the Poincareacute half-plane J Math Phys 35 471ndash
478 (1994)[418] JR Klauder K Penson J-M Sixdeniers Constructing coherent states through solutions
of Stieltjes and Hausdorff moment problems Phys Rev A 64 013817 (2001)[419] A Kleppner RL Lipsman The Plancherel formula for group extensions Ann Ec Norm
Sup 5 459ndash516 (1972)[420] AB Klimov C Muntildeoz Coherent isotropic and squeezed states in a N-qubit system Phys
Scr 87 038110 (2013)[421] A Klyashko Dynamical symmetry approach to entanglement in Physics and Theoretical
Computer Science From Numbers and Languages to (Quantum) Cryptography - NATOSecurity through Science Series D - Information and Communication Security vol 7 edby J-P Gazeau J Nesetril B Rovan (IOS Press Washington DC 2007) pp 25ndash54
[422] S Kobayashi Irreducibility of certain unitary representations J Math Soc Japan 20 638ndash642 (1968)
[423] K Kowalski J Rembielinski LC Papaloucas Coherent states for a quantum particle ona circle J Phys A Math Gen 29 4149ndash4167 (1996)
[424] K Kowalski J Rembielinski Quantum mechanics on a sphere and coherent states J PhysA Math Gen 33 6035ndash6048 (2000)
[425] K Kowalski J Rembielinski The Bargmann representation for the quantum mechanicson a sphere J Math Phys 42 4138ndash4147 (2001)
[426] C Kristjansen J Plefka GW Semenoff M Staudacher A new double-scaling limit ofN = 4 super-Yang-Mills theory and pp-wave strings Nuclear Phys B 643 3ndash30 (2002)
[427] M Kulesh M Holschneider MS Diallo Geophysical wavelet library Applications ofthe continuous wavelet transform to the polarization and dispersion analysis of signalsComput Geosci 34 1732ndash1752 (2008)
[428] R Kunze On the Frobenius reciprocity theorem for square integrable representationsPacific J Math 53 465ndash471 (1974)
[429] Y Kuroda A Wada T Yamazaki K Nagayama Postacquisition data processing methodfor suppression of the solvent signal I J Magn Reson 84 604ndash610 (1989)
564 References
[430] Y Kuroda A Wada T Yamazaki K Nagayama Postacquisition data processing methodfor suppression of the solvent signal II The weighted first derivative J Magn Reson 88141ndash145 (1990)
[431] G Kutyniok D Labate Resolution of the wavefront set using continuous shearlets TransAmer Math Soc 361 2719ndash2754 (2009)
[432] G Kutyniok W-Q Lim Compactly supported shearlets are optimally sparse J ApproxTheory 163 1564ndash1589 (2011)
[433] D Labate W-Q Lim G Kutyniok G Weiss Sparse multidimensional representationusing shearlets in Wavelets XI (San Diego CA 2005) ed by M Papadakis A Laine MUnser SPIE Proceedings vol 5914 (SPIE Bellingham WA 2005) pp 254ndash262
[434] P Lahti J-P Pellonpaumlauml Continuous variable tomographic measurements Phys Lett A373 3435ndash3438 (2009)
[435] Lambertrsquos projection see WikipediahttpenwikipediaorgwikiLambert_azimuthal_equal-area_projection
[436] J-P Leduc F Mujica R Murenzi MJT Smith Missile-tracking algorithm using target-adapted spatio-temporal wavelets in Automatic Object Recognition VII SPIE Proceedingsvol 5914 (SPIE Bellingham WA 1997) pp 400ndash411
[437] J-P Leduc F Mujica R Murenzi MJT Smith Spatio-temporal wavelet transforms formotion tracking in IEEE ICASSP 1997 vol 4 (1997) pp 3013ndash3016
[438] J-P Leduc F Mujica R Murenzi MJT Smith Spatio-temporal continuous waveletsapplied to missile warhead detection and tracking in SPIE VCIP rsquo97 vol 3024 ed byJ Biemond EJ Delp (1997) pp 787ndash798
[439] B Leistedt JD McEwen Exact wavelets on the ball IEEE Trans Signal Proc 60 1564ndash1589 (2012)
[440] PG Lemarieacute Y Meyer Ondelettes et bases hilbertiennes Rev Math Iberoamer 2 1ndash18(1986)
[441] C Lemke A Schuck Jr J-P Antoine D Sima Metabolite-sensitive analysis of magneticresonance spectroscopic signals using the continuous wavelet transform Meas SciTechnol 22 (2011) Art 114013
[442] J-M Leacutevy-Leblond Galilei group and non-relativistic quantum mechanics J Math Phys4 776-788 (1963)
[443] J-M Leacutevy-Leblond Galilei group and Galilean invariance in Group Theory and ItsApplications vol II ed by EM Loebl (Academic New York 1971) pp 221ndash299
[444] J-M Leacutevy-Leblond On the conceptual nature of the physical constants Riv Nuovo Cim7 187ndash214 (1977)
[445] EH Lieb The classical limit of quantum spin systems Commun Math Phys 31 327ndash340(1973)
[446] G Lindblad B Nagel Continuous bases for unitary irreducible representations of SU(11)Ann Inst H Poincareacute 13 27ndash56 (1970)
[447] W Lisiecki Kaumlhler coherent states orbits for representations of semisimple Lie groupsAnn Inst H Poincareacute 53 857ndash890 (1990)
[448] A Lisowska Moment-based fast wedgelet transform J Math Imaging Vis 39 180ndash192(2011)
[449] H Liu L Peng Admissible wavelets associated with the Heisenberg group Pacific JMath 180 101ndash123 (1997)
[450] E Livine S Speziale Physical boundary state for the quantum tetrahedron Class QuantGrav 25 085003 (2008)
[451] F Low Complete sets of wave packets in A Passion for Physics ndash Essay in Honor ofGeoffrey Chew ed by C DeTar (World Scientific Singapore 1985) pp 17ndash22
[452] G Mack All unitary ray representations of the conformal group SU(22) with positiveenergy Commun Math Phys 55 1ndash28 (1977)
[453] GW Mackey Imprimitivity for representations of locally compact groups I Proc NatAcad Sci 35 537ndash545 (1949)
References 565
[454] S Majid M Rodriguez-Plaza Random walk and the heat equation on superspace andanyspace J Math Phys 35 3753ndash3760 (1994)
[455] M Mallalieu CR Stroud Jr Rydberg wave packets fractional revivals and classicalorbits in Coherent States Past Present and Future (Proc Oak Ridge 1993) ed by DHFeng JR Klauder M Strayer (World Scientific Singapore 1994) pp 301ndash314
[456] SG Mallat Multifrequency channel decompositions of images and wavelet models IEEETrans Acoust Speech Signal Proc 37 2091ndash2110 (1989)
[457] SG Mallat A theory for multiresolution signal decomposition The wavelet representa-tion IEEE Trans Pattern Anal Machine Intell 11 674ndash693 (1989)
[458] S Mallat W-L Hwang Singularity detection and processing with wavelets IEEE TransInform Theory 38 617ndash643 (1992)
[459] S Mallat Z Zhang Matching pursuits with time frequency dictionaries IEEE TransSignal Proc 41 3397ndash3415 (1993)
[460] S Mallat S Zhong Wavelet maxima representation in Wavelets and Applications (ProcMarseille 1989) ed by Y Meyer (Masson and Springer Paris and Berlin 1991) pp 207ndash284
[461] VI Manrsquoko G Marmo ECG Sudarshan F Zaccaria f -oscillators and non-linearcoherent states Phys Scr 55 528ndash541 (1997)
[462] D Marinucci D Pietrobon A Baldi P Baldi P Cabella G Kerkyacharian P Natoli DPicard N Vittorio Spherical needlets for CMB data analysis Mon Not R Astron Soc383 539ndash545 (2008)
[463] D Marion M Ikura A Bax Improved solvent suppression in one- and two-dimensionalNMR spectra by convolution of time-domain data J Magn Reson 84 425ndash430 (1989)
[464] Y Meyer Principe drsquoincertitude bases hilbertiennes et algegravebres drsquoopeacuterateurs SeacuteminaireBourbaki 662 (1985ndash1986)
[465] Y Meyer Principe drsquoincertitude bases hilbertiennes et algegravebres drsquoopeacuterateurs Asteacuterisque145ndash146 209ndash223 (1987)
[466] Y Meyer H Xu Wavelet analysis and chirps Appl Comput Harmon Anal 4 366ndash379(1997)
[467] L Michel Invariance in quantum mechanics and group extensions in Group TheoreticalConcepts and Methods in Elementary Particle Physics ed by F Guumlrsey (Gordon andBreach New York and London 1964) pp 135ndash200
[468] J Mickelsson J Niederle Contractions of representations of the de Sitter groupsCommun Math Phys 27 167ndash180 (1972)
[469] MM Miller Convergence of the Sudarshan expansion for the diagonal coherent-stateweight functional J Math Phys 9 1270ndash1274 (1968)
[470] V F Molchanov Harmonic analysis on homogeneous spaces in Representation Theoryand Noncommutative Harmonic Analysis II ed by AA Kirillov (Springer Berlin 1995)
[471] MI Monastyrsky AM Perelomov Coherent states and symmetric spaces II Ann InstH Poincareacute 23 23ndash48 (1975)
[472] B Moran S Howard D Cochran Positive-operator-valued measures A general settingfor frames in Excursions in Harmonic Analysis vol 1 2 ed by TD Andrews R BalanJJ Benedetto W Czaja KA Okoudjou (Birkhaumluser Boston 2013) pp 49ndash64
[473] H Moscovici Coherent states representations of nilpotent Lie groups Commun MathPhys 54 63ndash68 (1977)
[474] H Moscovici A Verona Coherent states and square integrable representations Ann InstH Poincareacute 29 139ndash156 (1978)
[475] F Mujica R Murenzi MJT Smith J-P Leduc Robust tracking in compressed imagesequences J Electr Imaging 7 746ndash754 (1998)
[476] R Murenzi Wavelet transforms associated to the n-dimensional Euclidean group withdilations Signals in more than one dimension in Wavelets Time-Frequency Methodsand Phase Space (Proc Marseille 1987) ed by J-M Combes A Grossmann PTchamitchian 2nd edn (Springer Berlin 1990) pp 239ndash246
566 References
[477] MA Muschietti B Torreacutesani Pyramidal algorithms for LittlewoodndashPaley decomposi-tions SIAM J Math Anal 26 925ndash943 (1995)
[478] B Nagel Generalized eigenvectors in group representations in Studies in MathematicalPhysics (Proc Istanbul 1970) ed by AO Barut (Reidel Dordrecht and Boston 1970)pp 135ndash154
[479] MA Naımark Dokl Akad Nauk SSSR 41 359ndash361 (1943) see also B Sz-NagyExtensions of linear transformations in Hilbert space which extend beyond this spaceAppendix to F Riesz B Sz-Nagy Functional Analysis (Frederick Ungar New York 1960)
[480] FJ Narcowich P Petrushev JD Ward Localized tight frames on spheres SIAM J MathAnal 38 574ndash594 (2006)
[481] M Nauenberg Quantum wave packets on Kepler elliptic orbits Phys Rev A 40 1133ndash1136 (1989)
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[483] H Neumann Transformation properties of observables Helv Phys Acta 45 811ndash819(1972)
[484] U Niederer The maximal kinematical invariance group of the free Schroumldinger equationHelv Phys Acta 45 802ndash881 (1972)
[485] MM Nieto LM Simmons Jr Coherent states for general potentials I Formalism IIConfining one-dimensional examples III Nonconfining one-dimensional examples PhysRev D 20 1321ndash1331 1332ndash1341 1342ndash1350 (1979)
[486] MM Nieto LM Simmons Jr Coherent states for general potentials Phys Rev Lett 41207ndash210 (1987)
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Wavelets Multiresolut Inf Process 6 209ndash222 (2008)[531] D Rosca On a norm equivalence on L2(S2) Results Math 53 399ndash405 (2009)[532] D Rosca New uniform grids on the sphere Astron Astrophys 520 (2010) Art A63[533] D Rosca Uniform and refinable grids on elliptic domains and on some surfaces of
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sphere in Recent Advances in Signal Processing ed by S Miron (IN-TECH ViennaAustria and Rijeka Croatia 2010) pp 59ndash76
[537] D Rosca G Plonka Uniform spherical grids via area preserving projection from the cubeto the sphere J Comput Appl Math 236 1033ndash1041 (2011)
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[540] DJ Rotenberg Application of Sturmian functions to the Schroedinger three-body prob-lem Elastic e+ndashH scattering Ann Phys (NY) 19 262ndash278 (1962)
[541] C Rovelli Zakopane lectures on loop gravity in Proceedings of 3rd Quantum Gravityand Quantum Geometry School 28 Febndash13 March 2011 (Zakopane Poland 2011)arXiv11023660v5
[542] C Rovelli S Speziale A semiclassical tetrahedron Class Quant Grav 23 5861ndash5870(2006)
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[546] DJ Rowe J Repka Vector-coherent-state theory as a theory of induced representationsJ Math Phys 32 2614ndash2634 (1991)
[547] DJ Rowe G Rosensteel R Gilmore Vector coherent state representation theory J MathPhys 26 2787ndash2791 (1985)
[548] A Royer Phase states and phase operators for the quantum harmonic oscillator Phys RevA 53 70ndash108 (1996)
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[551] P Schroumlder W Sweldens Spherical wavelets Efficiently representing functions on thesphere in Computer Graphics Proceedings (SIGGRAPH95) (ACM Siggraph Los Angeles1995) pp 161ndash175
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[554] H Scutaru Coherent states and induced representations Lett Math Phys 2 101ndash107(1977)
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[579] T Thiemann Gauge field theory coherent states (GCS) 1 General properties Class QuantGrav 18 2025ndash2064 (2001)
[580] T Thiemann O Winkler Gauge field theory coherent states (GCS) 2 Peakednessproperties Class Quant Grav 18 2561ndash2636 (2001)
[581] T Thiemann O Winkler Gauge field theory coherent states (GCS) 3 Ehrenfest theoremsClass Quant Grav 18 4629ndash4682 (2001)
[582] T Thiemann O Winkler Gauge field theory coherent states (GCS) 4 Infinite tensorproduct and thermodynamical limit Class Quant Grav 18 4997ndash5054 (2001)
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simulation of an impact test using wavelets analytical and finite element models Int JSolids Struct 38 5481ndash5508 (2001)
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[610] K Woacutedkiewicz On the quantum mechanics of squeezed states J Modern Optics 34 941ndash948(1987)
[611] JA Yeazell M Mallalieu CR Stroud Jr Observation of the collapse and revival of aRydberg electronic wave packet Phys Rev Lett 64 2007ndash2010 (1990)
[612] JA Yeazell CR Stroud Jr Observation of fractional revivals in the evolution of aRydberg atomic wave packet Phys Rev A 43 5153ndash5156 (1991)
[613] HP Yuen Two-photon coherent states of the radiation field Phys Rev A 13 2226ndash2243(1976)
[614] J Zak Balian-Low theorem for Landau levels Phys Rev Lett 79 533ndash536 (1997)[615] J Zak Orthonormal sets of localized functions for a Landau level J Math Phys 39 4195ndash
4200 (1998) and references quoted there[616] AA Zakharova On the properties of generalized frames Math Notes 83 190ndash200 (2008)[617] W-M Zhang DH Feng R Gilmore Coherent states Theory and some applications Rev
Mod Phys 26 867ndash927 (1990)[618] I Zlatev W-M Zhang DH Feng Possibility that Schroumldingerrsquos conjecture for the
hydrogen atom coherent states is not attainable Phys Rev A 50 R1973ndashR1975 (1994)[619] WH Zurek Decoherence einselection and the quantum origins of the classical Rev Mod
Phys 75 715ndash775 (2003)[620] WH Zurek S Habib JP Paz Coherent states via decoherence Phys Rev Lett 70 1187ndash
1190 (1993)[621] K Zyczkowski Squeezed states in a quantum chaotic system J Phys A Math Theor 22
of SU(11) 81 296 297HilbertClowast-modules 164holomorphic 140nonholomorphic 151nonlinear 146of affine Galilei group 505of affine Poincareacute group 509of affine Weyl-Heisenberg group GaWH
497of compact semisimple Lie groups 174of Euclidean group E(n) 266of Galilei group G (11) 290of isochronous Galilei group 237of non-semisimple Lie groups 179of noncompact semisimple Lie groups 177of Poincareacute group Puarr
+(11) 283massless case 288
of Poincareacute group Puarr+(13) 279
of Schroumldinger group 508quasi-coherent states 186quaternionic 164
ST Ali et al Coherent States Wavelets and Their Generalizations Theoreticaland Mathematical Physics DOI 101007978-1-4614-8535-3copy Springer Science+Business Media New York 2014
573
574 Index
coherent states (CS) (cont)spin or SU(2) 175square integrable covariant 166 180 264vector (VCS) 73 108 112 170weighted 184 523
of affine Weyl-Heisenberg group GaWH497
of Poincareacute group Puarr+(11) 284
cohomology group 393 403coboundaries 403cochains 402cocycle 403
algebraic 387Cauchy 418Cauchy-Paul 354 419 425conical 418difference 417 462directional 416 440kinematical 499local 488metabolite-based 355 374minimal uncertainty 425multiselective 440on a graph 493on the sphere S
2 458on the sphere S
n 479on the torus T2 481steerable 439von Mises 440
wedgelet transform 455Wigner function 322Wigner-Ville transform 349Windowed Fourier or Gabor transform 349
ZZak transform 518
References
A Books and Theses
B Articles
Index
542 References
[Ber99] JC van den Berg (ed) Wavelets in Physics (Cambridge University Press Cambridge1999)
[Ber98] G Bernuau Proprieacuteteacutes spectrales et geacuteomeacutetriques des quasicristaux Ondelettesadapteacutees aux quasicristaux Thegravese de Doctorat CEREMADE Universiteacute Paris IXDauphine France 1998
[Bie81] L Biedenharn JD Louck The Racah-Wigner Algebra in Quantum Theory Ency-clopaedia of Mathematics vol 9 (Addison-Wesley Reading MA 1981)
[Bis10] S Biskri Deacutetection et analyse des boucles magneacutetiques solaires par traitementdrsquoimages Thegravese de Doctorat UST Houari Boumediegravene Alger 2010
[Bog05] I Bogdanova Wavelets on non-Euclidean manifolds PhD thesis EPFL 2005[Bog74] J Bognar Indefinite Inner Product Spaces (Springer Berlin 1974)[Bor72] A Borel Repreacutesentations des groupes localement compacts Lecture Notes in
Mathematics vol 276 (Springer Berlin 1972)[Bou93] K Bouyoucef Sur des aspects multireacutesolution en reconstruction drsquoimages Applica-
tion au Teacutelescope Spatial de Hubble Thegravese de Doctorat Univ P Sabatier Toulouse1993
[Bou97] A Bouzouina Comportement semi-classique de symplectomorphismes du tore quan-tifieacutes Thegravese de Doctorat Univ Paris-Dauphine 1997
[Bus91] P Busch PJ Lahti P Mittelstaedt The Quantum Theory of Measurement (SpringerBerlin and Heidelberg 1991)
[Can98] EJ Candegraves Ridgelets Theory and applications PhD thesis Department of Statis-tics Stanford University 1998
[Chr03] O Christensen An Introduction to Frames and Riesz Bases (Birkhaumluser BaselBoston Berlin 2003)
[Chu92] CK Chui An Introduction to Wavelets (Academic San Diego 1992)[Coh77] C Cohen-Tannoudji B Diu F Laloeuml Meacutecanique Quantique Tome I (Hermann
Paris 1977)[Com90] J-M Combes A Grossmann P Tchamitchian (eds) Wavelets Time-Frequency
Methods and Phase Space (Proc Marseille 1987) 2nd edn (Springer Berlin 1990)[Com12] M Combescure D Robert Shape Analysis and Classification Theory and Practice
(Springer Dordrecht Heidelberg 2012)[Cos01] LF Costa RM Cesar Jr Coherent States and Applications in Mathematical Physics
(CRC Press Boca Raton FL 2001)[Dau92] I Daubechies Ten Lectures on Wavelets (SIAM Philadelphia 1992)[Dav90] EB Davies Heat Kernels and Spectral Theory (Cambridge University Press Cam-
bridge 1990)[DeV88] R De Valois K De Valois Spatial Vision (Oxford University Press New York 1988)
[Dir01] PAM Dirac Lectures on Quantum Mechanics (Dover New York 2001)[Dix64] J Dixmier Les C-algegravebres et leurs repreacutesentations (Gauthier-Villars Paris 1964)[Dod03] VV Dodonov VI Manrsquoko (eds) Theory of Nonclassical States of Light (Taylor and
Francis London New York 2003)[Duv91] M Duval-Destin Analyse spatiale et spatio-temporelle de la stimulation visuelle agrave
lrsquoaide de la transformeacutee en ondelettes Thegravese de Doctorat Universiteacute drsquoAix-MarseilleII 1991
[Fea90] J-C Feauveau Analyse multireacutesolution par ondelettes non orthogonales et bancs defiltres numeacuteriques Thegravese de Doctorat Universiteacute Paris-Sud 1990
[Fei98] HG Feichtinger T Strohmer (eds) Gabor Analysis and Algorithms ndash Theory andApplications (Birkhaumluser Boston-Basel-Berlin 1998)
[Fei01] HG Feichtinger T Strohmer (eds) Advances in Gabor Analysis (BirkhaumluserBoston 2001)
[Fen94] DH Feng JR Klauder M Strayer (eds) Coherent States Past Present and Future(Proc Oak Ridge 1993) (World Scientific Singapore 1994)
[Fla98] P Flandrin Temps-Freacutequence (Hermegraves Paris 1993) Engliah translation Time-FrequencyTime-Scale Analysis (Academic New York 1998)
References 543
[Fol95] GB Folland A Course in Abstract Harmonic Analysis (CRC Press Boca Raton FL1995)
[Fre97] W Freeden M Schreiner T Gervens Constructive Approximation on the Spherewith Applications to Geomathematics (Clarendon Press Oxford 1997)
[Fue05] H Fuumlhr Abstract Harmonic Analysis of Continuous Wavelet Transforms LectureNotes in Mathematics vol 1863 (Springer Berlin Heidelberg 2005)
[Gaa73] SA Gaal Linear Analysis and Representation Theory (Springer Berlin 1973)[Gaz09] J-P Gazeau Coherent States in Quantum Physics (Wiley-VCH Berlin 2009)[Gel64] IM Gelfand NY Vilenkin Generalized Functions vol 4 (Academic New York
1964)[Gen13] G Gentili C Stoppato DC Struppa Regular Functions for a Quaternionic Variable
Springer Monographs in Mathematics (Springer Berlin 2013)[Gol81] H Goldstein C Poole J Safko Classical Mechanics 3rd edn (Addison-Wesley
Reading MA 1981)[Got66] K Gottfried Quantum Mechanics Fundamentals vol I (Benjamin New York and
Amsterdam 1966)[Grouml01] K Groumlchenig Foundations of Time-Frequency Analysis (Birkhaumluser Boston 2001)[Gun94] H Guumlnther NMR Spectroscopy 2nd edn (Wiley Chichester New York 1994)[Gui84] V Guillemin S Sternberg Symplectic Techniques in Physics (Cambridge University
Press Cambridge 1984)[Hei06] C Heil D Walnut (eds) Fundamental Papers in Wavelet Theory (Princeton Univer-
sity Press Princeton NJ 2006)[Hel78] S Helgason Differential Geometry Lie Groups and Symmetric Spaces (Academic
New York 1978)[Hel76] CW Helstrom Quantum Detection and Estimation Theory (Academic New York
1976)[Her89] G Herzberg Molecular Spectra and Molecular Structure Spectra of Diatomic
Molecules 2nd edn (Krieger Pub Malabar FL 1989)[Hil71] P Hilton U Stammbach A Course in Homological Algebra (Springer Berlin 1971)[H0l01] AS Holevo Statistical Structure of Quantum Theory (Springer Berlin 2001)[Hol95] M Holschneider Wavelets An Analysis Tool (Oxford University Press Oxford 1995)[Hon07] G Honnouvo Gabor analysis and wavelet transforms on some non-Euclidean 2-
dimensional manifolds PhD thesis Concordia University Montreal PQ Canada2007
[Hua63] LK Hua Harmonic Analysis of Functions of Several Complex Variables in the Clas-sical Domains Translations of Mathematical Monographs (American MathematicalSociety Providence RI 1963)
[Hum72] JE Humphreys Introduction to Lie Algebras and Representation Theory (SpringerBerlin 1972)
[Inouml54] E Inoumlnuuml A study of the unitary representations of the Galilei group in relation toquantum mechanics PhD thesis University of Ankara 1954
[Ino92] A Inomata H Kuratsuji CC Gerry Path Integrals and Coherent States of SU(2)and SU(11) (World Scientific Singapore 1992)
[Jac62] N Jacobson Lie Algebras (Interscience New York and London 1962)[Jac04] L Jacques Ondelettes repegraveres et couronne solaire Thegravese de Doctorat Univ Cath
Louvain Louvain-la-Neuve 2004[Jaf96] S Jaffard Y Meyer Wavelet Methods for Pointwise Regularity and Local Oscillations
of Functions Memoirs of the American Mathematical Society vol 143 (AmericanMathematical Society Providence RI 1996)
[Kah98] J-P Kahane PG Lemarieacute-Rieusset Fourier Series and Wavelets (Gordon and BreachLuxembourg 1995) French translation Seacuteries de Fourier et ondelettes (Cassini Paris1998)
[Kai94] G Kaiser A Friendly Guide to Wavelets (Birkhaumluser Boston 1994)[Kat76] T Kato Perturbation Theory for Linear Operators (Springer Berlin 1976)
544 References
[Kem37] EC Kemble Fundamental Principles of Quantum Mechanics (McGraw Hill NewYork 1937)
[Kir76] AA Kirillov Elements of the Theory of Representations (Springer Berlin 1976)[Kla68] JR Klauder ECG Sudarshan Fundamentals of Quantum Optics (Benjamin New
York 1968)[Kla85] JR Klauder BS Skagerstam Coherent States ndash Applications in Physics and
Mathematical Physics (World Scientific Singapore 1985)[Kla00] JR Klauder Beyond Conventional Quantization (Cambridge University Press Cam-
bridge 2000)[Kla11] JR Klauder A Modern Approach to Functional Integration (BirkhaumluserSpringer
New York 2011)[Kna96] AW Knapp Lie Groups Beyond an Introduction (Birkhaumluser Basel 1996 2nd edn
2002)[Kut12] G Kutyniok D Labate (eds) Shearlets Multiscale Analysis for Multivariate Data
(Birkhaumluser Boston 2012)[Lan81] L Landau E Lifchitz Mechanics 3rd edn (Pergamon Oxford1981)[Lan93] S Lang Algebra 3rd edn (Addison-Wesley Reading MA 1993)[Lie97] EH Lieb M Loss Analysis (American Mathematical Society Providence RI 1997)[Lip74] RL Lipsman Group Representations Lecture Notes in Mathematics vol 388
(Springer Berlin 1974)[Lyn82] PA Lynn An Introduction to the Analysis and Processing of Signals 2nd edn
(MacMillan London 1982)[Mac68] GW Mackey Induced Representations of Groups and Quantum Mechanics (Ben-
jamin New York 1968)[Mac76] GW Mackey Theory of Unitary Group Representations (University of Chicago
Press Chicago 1976)[Mad95] J Madore An Introduction to Noncommutative Differential Geometry and Its Physical
Applications (Cambridge University Press Cambridge 1995)[Mae94] S Maes The wavelet transform in signal processing with application to the extraction
of the speech modulation model features Thegravese de Doctorat Univ Cath LouvainLouvain-la-Neuve 1994
[Mag66] W Magnus F Oberhettinger RP Soni Formulas and Theorems for the SpecialFunctions of Mathematical Physics (Springer Berlin 1966)
[Mal99] SG Mallat A Wavelet Tour of Signal Processing 2nd edn (Academic San Diego1999)
[Mar82] D Marr Vision (Freeman San Francisco 1982)[Mes62] H Meschkowsky Hilbertsche Raumlume mit Kernfunktionen (Springer Berlin 1962)[Mey91] Y Meyer (ed) Wavelets and Applications (Proc Marseille 1989) (Masson and
Springer Paris and Berlin 1991)[Mey92] Y Meyer Les Ondelettes Algorithmes et Applications (Armand Colin Paris 1992)
English translation Wavelets Algorithms and Applications (SIAM Philadelphia1993)
[Mey00] CD Meyer Matrix Analysis and Applied Linear Algebra (SIAM Philadelphia 2000)[Mey93] Y Meyer S Roques (eds) Progress in Wavelet Analysis and Applications (Proc
Toulouse 1992) (Ed Frontiegraveres Gif-sur-Yvette 1993)[Mur90] R Murenzi Ondelettes multidimensionnelles et applications agrave lrsquoanalyse drsquoimages
Thegravese de Doctorat Univ Cath Louvain Louvain-la-Neuve 1990[vNe55] J von Neumann Mathematical Foundations of Quantum Mechanics (Princeton
University Press Princeton NJ 1955) (English translated by RT Byer)[Pap02] A Papoulis SU Pillai Probability Random Variables and Stochastic Processes 4th
edn (McGraw Hill New York 2002)[Par05] KR Parthasarathy Probability Measures on Metric Spaces (AMS Chelsea Publish-
ing Providence RI 2005)
References 545
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[Per05] G Peyreacute Geacuteomeacutetrie multi-eacutechelles pour les images et les textures Thegravese de doctoratEcole Polytechnique Palaiseau 2005
[Pru86] E Prugovecki Stochastic Quantum Mechanics and Quantum Spacetime (ReidelDordrecht 1986)
[Rau04] H Rauhut Time-frequency and wavelet analysis of functions with symmetry proper-ties PhD thesis TU Muumlnich 2004
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[Rud62] W Rudin Fourier Analysis on Groups (Interscience New York 1962)[Sch96] FE Schroeck Jr Quantum Mechanics on Phase Space (Kluwer Dordrecht 1996)[Sch61] L Schwartz Meacutethodes matheacutematiques pour les sciences physiques (Hermann Paris
1961)[Scu97] MO Scully MS Zubairy Quantum Optics (Cambridge University Press Cam-
bridge 1997)[Sho50] JA Shohat JD Tamarkin The Problem of Moments (American Mathematical
Society Providence RI 1950)[Ste71] EM Stein G Weiss Introduction to Fourier Analysis on Euclidean Spaces (Prince-
ton University Press Princeton NJ 1971)[Str64] RF Streater AS Wightman PCT Spin and Statistics and All That (Benjamin New
York 1964)[Sug90] M Sugiura Unitary Representations and Harmonic Analysis An Introduction
(North-HollandKodansha Ltd Tokyo 1990)[Suv11] A Suvichakorn C Lemke A Schuck Jr J-P Antoine The continuous wavelet
transform in MRS Tutorial text Marie Curie Research Training Network FAST(2011) httpwwwfast-mariecurie-rtn-projecteuWavelet
[Tak79] M Takesaki Theory of Operator Algebras I (Springer New York 1979)[Ter88] A Terras Harmonic Analysis on Symmetric Spaces and Applications II (Springer
Berlin 1988)[Tho98] G Thonet New aspects of time-frequency analysis for biomedical signal processing
Thegravese de Doctorat EPFL Lausanne 1998[Tor95] B Torreacutesani Analyse continue par ondelettes (InterEacuteditionsCNRS Eacuteditions Paris
1995)[Unt87] A Unterberger Analyse harmonique et analyse pseudo-diffeacuterentielle du cocircne de
lumiegravere Asteacuterisque 156 1ndash201 (1987)[Unt91] A Unterberger Quantification relativiste Meacutem Soc Math France 44ndash45 1ndash215
(1991)[Van98] P Vandergheynst Ondelettes directionnelles et ondelettes sur la sphegravere Thegravese de
Doctorat Univ Cath Louvain Louvain-la-Neuve 1998[Var85] VS Varadarajan Geometry of Quantum Theory 2nd edn (Springer New York 1985)[Vet95] M Vetterli J Kovacevic Wavelets and Subband Coding (Prentice Hall Englewood
Cliffs NJ 1995)[Vil69] NJ Vilenkin Fonctions speacuteciales et theacuteorie de la repreacutesentation des groupes (Dunod
Paris 1969)[Wel03] GV Welland Beyond Wavelets (Academic New York 2003)[vWe86] C von Westenholz Differential Forms in Mathematical Physics (North-Holland
Amsterdam 1986)[Wey28] H Weyl Gruppentheorie und Quantenmechanik (Hirzel Leipzig 1928)[Wey31] H Weyl The Theory of Groups and Quantum Mechanics (Dover New York 1931)[Wic94] MV Wickerhauser Adapted Wavelet Analysis from Theory to Software (A K Peters
Wellesley MA 1994)
546 References
[Wis93] W Wisnoe Utilisation de la meacutethode de transformeacutee en ondelettes 2D pour lrsquoanalysede visualisation drsquoeacutecoulements Thegravese de Doctorat ENSAE Toulouse 1993
[Woj97] P Wojtaszczyk A Mathematical Introduction to Wavelets (Cambridge UniversityPress Cambridge 1997)
[Zac06] C Zachos D Fairlie T Curtright Quantum Mechanics in Phase Space An OverviewWith Selected Papers (World Scientific Publishing Singapore 2006)
B Articles
[1] P Abry R Baraniuk P Flandrin R Riedi D Veitch Multiscale nature of network trafficIEEE Signal Process Mag 19 28ndash46 (2002)
[2] MD Adams The JPEG-2000 still image compression standardhttpwwweceuvicca~frodopublicationsjpeg2000pdf
[3] SL Adler AC Millard Coherent states in quaternionic quantum mechanics J MathPhys 38 2117ndash2126 (1997)
[4] GS Agarwal K Tara Nonclassical properties of states generated by the excitation on acoherent state Phys Rev A 43 492ndash497 (1991)
[5] GS Agarwal E Wolf Calculus for functions of noncommuting operators and generalphase-space methods in quantum mechanics I Mapping theorems and ordering of func-tions of noncommuting operators Phys Rev D 2 2161ndash2186 (1970)
[6] GS Agarwal E Wolf Calculus for functions of noncommuting operators and generalphase-space methods in quantum mechanics II Quantum mechanics in phase space PhysRev D 2 2187ndash2205 (1970)
[7] GS Agarwal E Wolf Calculus for functions of noncommuting operators and generalphase-space methods in quantum mechanics III A generalized Wick theorem and multi-time mapping Phys Rev D 2 2206ndash2225 (1970)
[8] V Aldaya J Guerrero G Marmo Quantization on a Lie group Higher-order polariza-tions in Symmetry in Sciences X ed by B Gruber M Ramek (Plenum Press Nerw York1998) pp 1ndash36
[9] M Alexandrescu D Gibert G Hulot J-L Le Mouel G Saracco Worldwide waveletanalysis of geomagnetic jerks J Geophys Res B 101 21975ndash21994 (1996)
[10] G Alexanian A Pinzul A Stern Generalized coherent state approach to star productsand applications to the fuzzy sphere Nucl Phys B 600 531ndash547 (2001)
[11] ST Ali A geometrical property of POV-measures and systems of covariance in Differ-ential Geometric Methods in Mathematical Physics ed by HD Doebner SI AnderssonHR Petry Lecture Notes in Mathematics vol 905 (Springer Berlin 1982) pp 207ndash22
[12] ST Ali Commutative systems of covariance and a generalization of Mackeyrsquos imprimi-tivity theorem Canad Math Bull 27 390ndash397 (1984)
[13] ST Ali Stochastic localisation quantum mechanics on phase space and quantum space-time Riv Nuovo Cim 8(11) 1ndash128 (1985)
[14] ST Ali A general theorem on square-integrability Vector coherent states J Math Phys39 3954ndash3964 (1998)
[15] ST Ali J-P Antoine Coherent states of 1+1 dimensional Poincareacute group Squareintegrability and a relativistic Weyl transform Ann Inst H Poincareacute 51 23ndash44 (1989)
[16] ST Ali S De Biegravevre Coherent states and quantization on homogeneous spaces in GroupTheoretical Methods in Physics ed by H-D Doebner et al Lecture Notes in Mathematicsvol 313 (Springer Berlin 1988) pp 201ndash207
References 547
[17] ST Ali H-D Doebner Ordering problem in quantum mechanics Prime quantization anda physical interpretation Phys Rev A 41 1199ndash1210 (1990)
[18] ST Ali GG Emch Geometric quantization Modular reduction theory and coherentstates J Math Phys 27 2936ndash2943 (1986)
[19] ST Ali M Engliš J-P Gazeau Vector coherent states from Plancherelrsquos theorem andClifford algebras J Phys A 37 6067ndash6089 (2004)
[20] ST Ali MEH Ismail Some orthogonal polynomials arising from coherent states JPhys A 45 125203 (2012) (16pp)
[21] ST Ali UA Mueller Quantization of a classical system on a coadjoint orbit of thePoincareacute group in 1+1 dimensions J Math Phys 35 4405ndash4422 (1994)
[22] ST Ali E Prugovecki Systems of imprimitivity and representations of quantum mechan-ics on fuzzy phase spaces J Math Phys 18 219ndash228 (1977)
[23] ST Ali E Prugovecki Mathematical problems of stochastic quantum mechanics Har-monic analysis on phase space and quantum geometry Acta Appl Math 6 1ndash18 (1986)
[24] ST Ali E Prugovecki Extended harmonic analysis of phase space representation for theGalilei group Acta Appl Math 6 19ndash45 (1986)
[25] ST Ali E Prugovecki Harmonic analysis and systems of covariance for phase spacerepresentation of the Poincareacute group Acta Appl Math 6 47ndash62 (1986)
[26] ST Ali J-P Antoine J-P Gazeau De Sitter to Poincareacute contraction and relativisticcoherent states Ann Inst H Poincareacute 52 83ndash111 (1990)
[27] ST Ali J-P Antoine J-P Gazeau Square integrability of group representations onhomogeneous spaces I Reproducing triples and frames Ann Inst H Poincareacute 55 829ndash855 (1991)
[28] ST Ali J-P Antoine J-P Gazeau Square integrability of group representations onhomogeneous spaces II Coherent and quasi-coherent states The case of the Poincareacutegroup Ann Inst H Poincareacute 55 857ndash890 (1991)
[29] ST Ali J-P Antoine J-P Gazeau Continuous frames in Hilbert space Ann Phys(NY)222 1ndash37 (1993)
[30] ST Ali J-P Antoine J-P Gazeau Relativistic quantum frames Ann Phys(NY) 222 38ndash88 (1993)
[31] ST Ali J-P Antoine J-P Gazeau UA Mueller Coherent states and their generalizationsA mathematical overview Rev Math Phys 7 1013ndash1104 (1995)
[32] ST Ali J-P Gazeau MR Karim Frames the β -duality in Minkowski space and spincoherent states J Phys A Math Gen 29 5529ndash5549 (1996)
[33] ST Ali M Engliš Quantization methods A guide for physicists and analysts Rev MathPhys 17 391ndash490 (2005)
[34] ST Ali J-P Gazeau B Heller Coherent states and Bayesian duality J Phys A MathTheor 41 365302 (2008)
[35] ST Ali L Balkovaacute EMF Curado J-P Gazeau MA Rego-Monteiro LMCSRodrigues K Sekimoto Non-commutative reading of the complex plane through Delonesequences J Math Phys 50 043517 (2009)
[36] ST Ali C Carmeli T Heinosaari A Toigo Commutative POVMS and fuzzy observ-ables Found Phys 39 593ndash612 (2009)
[37] ST Ali T Bhattacharyya SS Roy Coherent states on Hilbert modules J Phys A MathTheor 44 275202 (2011)
[38] ST Ali J-P Antoine F Bagarello J-P Gazeau (Guest Editors) Coherent states Acontemporary panorama preface to a special issue on Coherent states Mathematical andphysical aspects J Phys A Math Gen 45(24) (2012)
[39] ST Ali F Bagarello J-P Gazeau Quantizations from reproducing kernel spaces AnnPhys (NY) 332 127ndash142 (2013)
[40] STAli K Goacuterska A Horzela F Szafraniec Squeezed states and Hermite polynomials ina complex variable Preprint (2013) arXiv13084730v1 [quant-phy]
[41] P Aniello G Cassinelli E De Vito A Levrero Square-integrability of induced represen-tations of semidirect products Rev Math Phys 10 301ndash313 (1998)
548 References
[42] P Aniello G Cassinelli E De Vito A Levrero Wavelet transforms and discrete framesassociated to semidirect products J Math Phys 39 3965ndash3973 (1998)
[43] J-P Antoine Remarques sur le vecteur de Runge-Lenz Ann Soc Scient Bruxelles 80160ndash168 (1966)
[44] J-P Antoine Etude de la deacutegeacuteneacuterescence orbitale du potentiel coulombien en theacuteorie desgroupes I II Ann Soc Scient Bruxelles 80 169ndash184 (1966)
[45] J-P Antoine Etude de la deacutegeacuteneacuterescence orbitale du potentiel coulombien en theacuteorie desgroupes I II Ann Soc Scient Bruxelles 81 49ndash68 (1967)
[46] J-P Antoine Dirac formalism and symmetry problems in quantum mechanics I Generaldirac formalism J Math Phys 10 53ndash69 (1969)
[47] J-P Antoine Dirac formalism and symmetry problems in quantum mechanics II Symme-try problems J Math Phys 10 2276ndash2290 (1969)
[48] J-P Antoine Quantum mechanics beyond Hilbert space in Irreversibility and Causality mdashSemigroups and Rigged Hilbert Spaces ed by A Boumlhm H-D Doebner P KielanowskiLecture Notes in Physics vol 504 (Springer Berlin 1998) pp 3ndash33
[49] J-P Antoine Discrete wavelets on abelian locally compact groups Rev Cien Math(Habana) 19 3ndash21 (2003)
[50] J-P Antoine Introduction to precursors in physics Affine coherent states in FundamentalPapers in Wavelet Theory ed by C Heil D Walnut (Princeton University Press PrincetonNJ 2006) pp 113ndash116
[51] J-P Antoine F Bagarello Wavelet-like orthonormal bases for the lowest Landau levelJ Phys A Math Gen 27 2471ndash2481 (1994)
[52] J-P Antoine P Balazs Frames and semi-frames J Phys A Math Theor 44 205201(2011) (25 pages) Corrigendum J-P Antoine P Balazs Frames and semi-frames J PhysA Math Theor 44 479501 (2011) (2 pages)
[53] J-P Antoine P Balazs Frames semi-frames and Hilbert scales Numer Funct AnalOptim 33 736ndash769 (2012)
[54] J-P Antoine A Coron Time-frequency and time-scale approach to magnetic resonancespectroscopy J Comput Methods Sci Eng (JCMSE) 1 327ndash352 (2001)
[55] J-P Antoine AL Hohoueacuteto Discrete frames of Poincareacute coherent states in 1+3 dimen-sions J Fourier Anal Appl 9 141ndash173 (2003)
[56] J-P Antoine I Mahara Galilean wavelets Coherent states for the affine Galilei groupJ Math Phys 40 5956ndash5971 (1999)
[57] J-P Antoine U Moschella Poincareacute coherent states The two-dimensional massless caseJ Phys A Math Gen 26 591ndash607 (1993)
[58] J-P Antoine R Murenzi Two-dimensional directional wavelets and the scale-anglerepresentation Signal Process 52 259ndash281 (1996)
[59] J-P Antoine R Murenzi Two-dimensional continuous wavelet transform as linear phasespace representation of two-dimensional signals in Wavelet Applications IV SPIE Pro-ceedings vol 3078 (SPIE Bellingham WA 1997) pp 206ndash217
[60] J-P Antoine D Rosca The wavelet transform on the two-sphere and related manifolds mdashA review in Optical and Digital Image Processing SPIE Proceedings vol 7000 (2008)pp 70000B-1ndash15
[61] J-P Antoine D Speiser Characters of irreducible representations of simple Lie groupsJ Math Phys 5 1226ndash1234 (1964)
[62] J-P Antoine P Vandergheynst Wavelets on the n-sphere and related manifolds J MathPhys 39 3987ndash4008 (1998)
[63] J-P Antoine P Vandergheynst Wavelets on the 2-sphere A group-theoretical approachAppl Comput Harmon Anal 7 262ndash291 (1999)
[64] J-P Antoine P Vandergheynst Wavelets on the two-sphere and other conic sections JFourier Anal Appl 13 369ndash386 (2007)
[65] J-P Antoine M Duval-Destin R Murenzi B Piette Image analysis with 2D wavelettransform Detection of position orientation and visual contrast of simple objects inWavelets and Applications (Proc Marseille 1989) ed by Y Meyer (Masson and SpringerParis and Berlin 1991) pp144ndash159
References 549
[66] J-P Antoine P Carrette R Murenzi B Piette Image analysis with 2D continuous wavelettransform Signal Process 31 241ndash272 (1993)
[67] J-P Antoine P Vandergheynst K Bouyoucef R Murenzi Alternative representations ofan image via the 2D wavelet transform Application to character recognition in VisualInformation Processing IV SPIE Proceedings vol 2488 (SPIE Bellingham WA 1995)pp 486ndash497
[68] J-P Antoine R Murenzi P Vandergheynst Two-dimensional directional wavelets inimage processing Int J Imaging Syst Tech 7 152ndash165 (1996)
[69] J-P Antoine D Barache RM Cesar Jr LF Costa Shape characterization with thewavelet transform Signal Process 62 265ndash290 (1997)
[70] J-P Antoine P Antoine B Piraux Wavelets in atomic physics in Spline Functions andthe Theory of Wavelets ed by S Dubuc G Deslauriers CRM Proceedings and LectureNotes vol 18 (AMS Providence RI 1999) pp261ndash276
[71] J-P Antoine P Antoine B Piraux Wavelets in atomic physics and in solid state physicsin Wavelets in Physics Chap 8 ed by JC van den Berg (Cambridge University PressCambridge 1999)
[72] J-P Antoine R Murenzi P Vandergheynst Directional wavelets revisited Cauchywavelets and symmetry detection in patterns Appl Comput Harmon Anal 6 314ndash345(1999)
[73] J-P Antoine L Jacques R Twarock Wavelet analysis of a quasiperiodic tiling withfivefold symmetry Phys Lett A 261 265ndash274 (1999)
[74] J-P Antoine L Jacques P Vandergheynst Penrose tilings quasicrystals and wavelets inWavelet Applications in Signal and Image Processing VII SPIE Proceedings vol 3813(SPIE Bellingham WA 1999) pp 28ndash39
[75] J-P Antoine YB Kouagou D Lambert B Torreacutesani An algebraic approach to discretedilations Application to discrete wavelet transforms J Fourier Anal Appl 6 113ndash141(2000)
[76] J-P Antoine A Coron J-M Dereppe Water peak suppression Time-frequency vs time-scale approach J Magn Reson 144 189ndash194 (2000)
[77] J-P Antoine J-P Gazeau P Monceau J R Klauder K Penson Temporally stablecoherent states for infinite well and Poumlschl-Teller potentials J Math Phys 42 2349ndash2387(2001)
[78] J-P Antoine A Coron C Chauvin Wavelets and related time-frequency techniques inmagnetic resonance spectroscopy NMR Biomed 14 265ndash270 (2001)
[79] J-P Antoine L Demanet J-F Hochedez L Jacques R Terrier E Verwichte Applicationof the 2-D wavelet transform to astrophysical images Phys Mag 24 93ndash116 (2002)
[80] J-P Antoine L Demanet L Jacques P Vandergheynst Wavelets on the sphere Imple-mentation and approximations Appl Comput Harmon Anal 13 177ndash200 (2002)
[81] J-P Antoine I Bogdanova P Vandergheynst The continuous wavelet transform on conicsections Int J Wavelets Multires Inform Proc 6 137ndash156 (2007)
[82] J-P Antoine D Rosca P Vandergheynst Wavelet transform on manifolds Old and newapproaches Appl Comput Harmon Anal 28 189ndash202 (2010)
[83] P Antoine B Piraux A Maquet Time profile of harmonics generated by a single atom ina strong electromagnetic field Phys Rev A 51 R1750ndashR1753 (1995)
[84] P Antoine B Piraux DB Miloševic M Gajda Generation of ultrashort pulses ofharmonics Phys Rev A 54 R1761ndashR1764 (1996)
[85] P Antoine B Piraux DB Miloševic M Gajda Temporal profile and time control ofharmonic generation Laser Phys 7 594ndash601 (1997)
[86] Apollonius see Wikipedia httpenwikipediaorgwikiApollonius_of_Perga[87] FT Arecchi E Courtens R Gilmore H Thomas Atomic coherent states in quantum
optics Phys Rev A 6 2211ndash2237 (1972)[88] I Aremua J-P Gazeau MN Hounkonnou Action-angle coherent states for quantum
systems with cylindric phase space J Phys A Math Theor 45 335302 (2012)
550 References
[89] F Argoul A Arneacuteodo G Grasseau Y Gagne EJ Hopfinger Wavelet analysis ofturbulence reveals the multifractal nature of the Richardson cascade Nature 338 51ndash53(1989)
[90] F Argoul A Arneacuteodo J Elezgaray G Grasseau R Murenzi Wavelet analysis of theself-similarity of diffusion-limited aggregates and electrodeposition clusters Phys Rev A41 5537ndash5560 (1990)
[91] TA Arias Multiresolution analysis of electronic structure Semicardinal and waveletbases Rev Mod Phys 71 267ndash312 (1999)
[92] A Arneacuteodo F Argoul E Bacry J Elezgaray E Freysz G Grasseau JF Muzy BPouligny Wavelet transform of fractals in Wavelets and Applications (Proc Marseille1989) ed by Y Meyer (Masson and Springer Paris and Berlin 1991) pp 286ndash352
[93] A Arneacuteodo E Bacry JF Muzy The thermodynamics of fractals revisited with waveletsPhysica A 213 232ndash275 (1995)
[94] A Arneacuteodo E Bacry JF Muzy Oscillating singularities in locally self-similar functionsPhys Rev Lett 74 4823ndash4826 (1995)
[95] A Arneacuteodo E Bacry PV Graves JF Muzy Characterizing long-range correlations inDNA sequences from wavelet analysis Phys Rev Lett 74 3293ndash3296 (1996)
[96] A Arneacuteodo Y drsquoAubenton E Bacry PV Graves JF Muzy C Thermes Wavelet basedfractal analysis of DNA sequences Physica D 96 291ndash320 (1996)
[97] A Arneacuteodo E Bacry S Jaffard JF Muzy Oscillating singularities on Cantor sets Agrand canonical multifractal formalism J Stat Phys 87 179ndash209 (1997)
[98] A Arneacuteodo E Bacry S Jaffard JF Muzy Singularity spectrum of multifractal functionsinvolving oscillating singularities J Fourier Anal Appl 4 159ndash174 (1998)
[99] N Aronszajn Theory of reproducing kernels Trans Amer Math Soc 66 337ndash404 (1950)[100] A Ashtekar J Lewandowski D Marolf J Mouratildeo T Thiemann Coherent state
transforms for spaces of connections J Funct Analysis 135 519ndash551 (1996)[101] A Askari-Hemmat MA Dehghan M Radjabalipour Generalized frames and their
redundancy Proc Amer Math Soc 129 1143ndash1147 (2001)[102] EW Aslaksen JR Klauder Unitary representations of the affine group J Math Phys 9
206ndash211 (1968)[103] EW Aslaksen JR Klauder Continuous representation theory using the affine group
J Math Phys 10 2267ndash2275 (1969)[104] D Astruc L Plantieacute R Murenzi Y Lebret D Vandromme On the use of the 3D
wavelet transform for the analysis of computational fluid dynamics results in Progressin Wavelet Analysis and Applications (Proc Toulouse 1992) ed by Y Meyer S Roques(Ed Frontiegraveres Gif-sur-Yvette 1993) pp 463ndash470
[105] PW Atkins JC Dobson Angular momentum coherent states Proc Roy Soc London A321 321ndash340 (1971)
[106] BW Atkinson DO Bruff JS Geronimo D P Hardin Wavelets centered on a knotsequence Piecewise polynomial wavelets on a quasi-crystal lattice preprint (2011)arXiv11024246v1 [mathNA]
[107] IS Averbuch NF Perelman Fractional revivals Universality in the long-term evolutionof quantum wave packets beyond the correspondence principle dynamics Phys Lett A139 449ndash453 (1989)
[108] H Bacry J-M Leacutevy-Leblond Possible kinematics J Math Phys 9 1605ndash1614 (1968)[109] H Bacry A Grossmann J Zak Proof of the completeness of lattice states in kq
representation Phys Rev B 12 1118ndash1120 (1975)[110] L Baggett KF Taylor Groups with completely reducible regular representation Proc
Amer Math Soc 72 593ndash600 (1978)[111] VG Bagrov J-P Gazeau D Gitman A Levine Coherent states and related quantizations
for unbounded motions J Phys A Math Theor 45 125306 (2012) arXiv12010955v2[quant-ph]
[112] P Balazs J-P Antoine A Grybos Weighted and controlled frames Mutual relationshipand first numerical properties Int J Wavelets Multires Inform Proc 8 109ndash132 (2010)
References 551
[113] P Balazs DT Stoeva J-P Antoine Classification of general sequences by frame-relatedoperators Sampling Theory Signal Image Proc (STSIP) 10 151ndash170 (2011)
[114] P Balazs D Bayer A Rahimi Multipliers for continuous frames in Hilbert spaces JPhys A Math Gen 45 244023 (2012)
[115] P Baldi G Kerkyacharian D Marinucci D Picard High frequency asymptotics forwavelet-based tests for Gaussianity and isotropy on the torus J Multivar Anal 99 606ndash636 (2008)
[116] P Baldi G Kerkyacharian D Marinucci D Picard Asymptotics for spherical needletsAnn of Stat 37 1150ndash1171 (2009)
[117] MC Baldiotti J-P Gazeau DM Gitman Coherent states of a particle in magnetic fieldand Stieltjes moment problem Phys Lett A 373 1916ndash1920 (2009) Erratum Phys LettA 373 2600 (2009)
[118] MC Baldiotti J-P Gazeau DM Gitman Semiclassical and quantum description ofmotion on the noncommutative plane Phys Lett A 373 3937ndash3943 (2009)
[119] R Balian Un principe drsquoincertitude fort en theacuteorie du signal ou en meacutecanique quantiqueCR Acad Sci(Paris) 292 1357ndash1362 (1981)
[120] M Bander C Itzykson Group theory and the hydrogen atom I II Rev Mod Phys 38330ndash345 346ndash358 (1966)
[121] D Barache S De Biegravevre J-P Gazeau Affine symmetry semigroups for quasicrystalsEurophys Lett 25 435ndash440 (1994)
[122] D Barache J-P Antoine J-M Dereppe The continuous wavelet transform a tool for NMRspectroscopy J Magn Reson 128 1ndash11 (1997)
[123] V Bargmann On a Hilbert space of analytic functions and an associated integral transformPart I Commun Pure Appl Math 14 187ndash214 (1961)
[124] V Bargmann On a Hilbert space of analytic functions and an associated integral transformPart II A family of related function spaces Application to distribution theory CommunPure Appl Math 20 1ndash101 (1967)
[125] V Bargmann P Butera L Girardello JR Klauder On the completeness of coherentstates Reports Math Phys 2 221ndash228 (1971)
[126] AO Barut L Girardello New ldquocoherentrdquo states associated with non compact groupsCommun Math Phys 21 41ndash55 (1971)
[127] AO Barut H Kleinert Transition probabilities of the hydrogen atom from noncompactdynamical groups Phys Rev 156 1541ndash1545 (1967)
[128] AO Barut BW Xu Non-spreading coherent states riding on Kepler orbits Helv PhysActa 66 711ndash720 (1993)
[129] G Battle Wavelets A renormalization group point of view in Wavelets and TheirApplications ed by MB Ruskai G Beylkin R Coifman I Daubechies S Mallat YMeyer L Raphael (Jones and Bartlett Boston 1992) pp 323ndash349
[130] P Bellomo CR Stroud Jr Dispersion of Klauderrsquos temporally stable coherent states forthe hydrogen atom J Phys A Math Gen 31 L445ndashL450 (1998)
[131] J Ben Geloun J R Klauder Ladder operators and coherent states for continuous spectraJ Phys A Math Theor 42 375209 (2009)
[132] J Ben Geloun J Hnybida JR Klauder Coherent states for continuous spectrum operatorswith non-normalizable fiducial states J Phys A Math Theor 45 085301 (2012)
[133] JJ Benedetto TD Andrews Intrinsic wavelet and frame applications in IndependentComponent Analyses Wavelets Neural Networks Biosystems and Nanoengineering IXed by H Szu L Dai SPIE Proceedings vol 8058 (SPIE Bellingham WA 2011) p805802
[134] JJ Benedetto A Teolis A wavelet auditory model and data compression Appl ComputHarmon Anal 1 3ndash28 (1993)
[135] FA Berezin Quantization Math USSR Izvestija 8 1109ndash1165 (1974)[136] FA Berezin General concept of quantization Commun Math Phys 40 153ndash174 (1975)[137] H Bergeron From classical to quantum mechanics How to translate physical ideas into
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[139] H Bergeron and J-P Gazeau Integral quantization with two basic examples Preprint(2013) arXiv13082348v1
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[141] H Bergeron J-P Gazeau P Siegl A Youssef Semi-classical behavior of Poumlschl-Tellercoherent states Eur Phys Lett 92 60003 (2010)
[142] H Bergeron P Siegl A Youssef New SUSYQM coherent states for Poumlschl-Tellerpotentials A detailed mathematical analysis J Phys A Math Theor 45 244028 (2012)
[143] H Bergeron J-P Gazeau A Youssef Are the Weyl and coherent state descriptionsphysically equivalent Phys Lett A 377 598ndash605 (2013)
[144] H Bergeron A Dapor J-P Gazeau P Małkiewicz Wavelet quantum cosmology preprint(2013) arXiv13050653 [gr-qc]
[145] S Bergman Uumlber die Kernfunktion eines Bereiches und ihr Verhalten am Rande I ReineAngw Math 169 1ndash42 (1933)
[146] D Bernier KF Taylor Wavelets from square-integrable representations SIAM J MathAnal 27 594ndash608 (1996)
[147] G Bernuau Wavelet bases associated to a self-similar quasicrystal J Math Phys 394213ndash4225 (1998)
[148] A Bertrand Deacuteveloppements en base de Pisot et reacutepartition modulo 1 C R Acad SciParis 285 419ndash421 (1977)
[149] J Bertrand P Bertrand Classification of affine Wigner functions via an extendedcovariance principle in Group Theoretical Methods in Physics (Proc Sainte-Adegravele 1988)ed by Y Saint-Aubin L Vinet (World Scientific Singapore 1989) pp 1380ndash1383
[150] Z Białynicka-Birula I Białynicki-Birula Space-time description of squeezing J OptSoc Am B4 1621ndash1626 (1987)
[151] E Bianchi E Magliaro C Perini Coherent spin-networks Phys Rev D 82 024012(2010)
[152] S Biskri J-P Antoine B Inhester F Mekideche Extraction of Solar coronal magneticloops with the 2-D Morlet wavelet transform Solar Phys 262 373ndash385 (2010)
[153] R Bluhm VA Kostelecky JA Porter The evolution and revival structure of localizedquantum wave packets Am J Phys 64 944ndash953 (1996)
[154] I Bogdanova P Vandergheynst J-P Antoine L Jacques M Morvidone Stereographicwavelet frames on the sphere Appl Comput Harmon Anal 19 223ndash252 (2005)
[155] I Bogdanova X Bresson J-P Thiran P Vandergheynst Scale space analysis and activecontours for omnidirectional images IEEE Trans Image Process 16 1888ndash1901 (2007)
[156] I Bogdanova P Vandergheynst J-P Gazeau Continuous wavelet transform on thehyperboloid Appl Comput Harmon Anal 23 (2007) 286ndash306 (2007)
[157] P Boggiatto E Cordero Anti-Wick quantization of tempered distributions in Progress inAnalysis Berlin (2001) vol I II (World Sci Publ River Edge NJ 2003) pp 655ndash662
[158] P Boggiatto E Cordero K Groumlchenig Generalized Anti-Wick operators with symbols indistributional Sobolev spaces Int Equ Oper Theory 48 427ndash442 (2004)
[159] A Boumlhm The Rigged Hilbert Space in quantum mechanics in Lectures in TheoreticalPhysics vol IX A ed by WA Brittin et al (Gordon amp Breach New York 1967) pp255ndash315
[160] G Bohnkeacute Treillis drsquoondelettes associeacutes aux groupes de Lorentz Ann Inst H Poincareacute54 245ndash259 (1991)
[161] WR Bomstad JR Klauder Linearized quantum gravity using the projection operatorformalism Class Quantum Grav 23 5961ndash5981 (2006)
[162] VV Borzov Orthogonal polynomials and generalized oscillator algebras Int TransformSpec Funct 12 115ndash138 (2001)
[163] VV Borzov EV Damaskinsky Generalized coherent states for classical orthogonalpolynomials Day on Diffraction (2002) arXivmathQA0209181v1 (SPb 2002)
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[165] A Bouzouina S De Biegravevre Equipartition of the eigenfunctions of quantized ergodic mapson the torus Commun Math Phys 178 83ndash105 (1996)
[166] P Brault J-P Antoine A spatio-temporal Gaussian-Conical wavelet with high apertureselectivity for motion and speed analysis Appl Comput Harmon Anal 34 148ndash161(2012)
[167] A Briguet S Cavassila D Graveron-Demilly Suppression of huge signals using theCadzow enhancement procedure The NMR Newslett 440 26 (1995)
[168] CM Brislawn Fingerprints go digital Notices Amer Math Soc 42 1278ndash1283 (1995)[169] CM Brislawn On the group-theoretic structure of lifted filter banks in Excursions in
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[170] F Bruhat Sur les repreacutesentations induites des groupes de Lie Bull Soc Math France 8497ndash205 (1956)
[171] T Buumllow Multiscale image processing on the sphere in DAGM-Symposium (2002) pp609ndash617
[172] C Burdik C Frougny J-P Gazeau R Krejcar Beta-integers as natural counting systemsfor quasicrystals J Phys A Math Gen 31 6449ndash6472 (1998)
[173] KE Cahill Coherent-state representations for the photon density Phys Rev 138 B1566ndash1576 (1965)
[174] KE Cahill R Glauber Density operators and quasiprobability distributions Phys Rev177 1882ndash1902 (1969)
[175] KE Cahill R Glauber Ordered expansions in boson amplitude operators Phys Rev 1771857ndash1881 (1969)
[176] AR Calderbank I Daubechies W Sweldens BL Yeo Wavelets that map integers tointegers Appl Comput Harmon Anal 5 332ndash369 (1998)
[177] M Calixto J Guerrero Wavelet transform on the circle and the real line A unified group-theoretical treatment Appl Comput Harmon Anal 21 204ndash229 (2006)
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[179] M Calixto J Guerrero D Rosca Wavelet transform on the torus A group-theoreticalapproach preprint (2013)
[180] EJ Candegraves Harmonic analysis of neural networks Appl Comput Harmon Anal 6 197ndash218 (1999)
[181] EJ Candegraves Ridgelets and the representation of mutilated Sobolev functions SIAM JMath Anal 33 347ndash368 (2001)
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[183] EJ Candegraves L Demanet The curvelet representation of wave propagators is optimallysparse Commun Pure Appl Math 58 1472ndash1528 (2004)
[184] EJ Candegraves L Demanet The curvelet representation of wave propagators is optimallysparse Commun Pure Appl Math 58 1472ndash1528 (2005)
[185] EJ Candegraves DL Donoho Curvelets ndash A surprisingly effective nonadaptive representationfor objects with edges in Curves and Surfaces ed by LL Schumaker et al (VanderbiltUniversity Press Nashville TN 1999)
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[191] EJ Candegraves F Guo New multiscale transforms minimum total variationsynthesisApplications to edge-preserving image reconstruction Signal Proc 82 1519ndash1543 (2002)
[192] EJ Candegraves L Demanet D Donoho L Ying Fast discrete curvelet transforms MultiscaleModel Simul 5 861ndash899 (2006)
[193] AL Carey Square integrable representations of non-unimodular groups Bull AustrMath Soc 15 1ndash12 (1976)
[194] AL Carey Group representations in reproducing kernel Hilbert spaces Rep Math Phys14 247ndash259 (1978)
[195] P Carruthers MM Nieto Phase and angle variables in quantum mechanics Rev ModPhys 40 411ndash440 (1968)
[196] PG Casazza G Kutyniok Frames of subspaces in Wavelets Frames and Operator The-ory Contemporary Mathematics vol 345 (American Mathematical Society ProvidenceRI 2004) pp 87ndash113
[197] PG Casazza D Han DR Larson Frames for Banach spaces Contemp Math 247 149ndash182 (1999)
[198] P Casazza O Christensen S Li A Lindner Riesz-Fischer sequences and lower framebounds Z Anal Anwend 21 305ndash314 (2002)
[199] PG Casazza G Kutyniok S Li Fusion frames and distributed processing ApplComputHarmon Anal 25 114ndash132 (2008)
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Rev A 34 7ndash22 (1986)[204] SHH Chowdhury ST Ali All the groups of signal analysis from the (1+1) affine Galilei
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Fourier (Grenoble) 43 551ndash567 (1993)[207] M Clerc and S Mallat Shape from texture and shading with wavelets in Dynamical
Systems Control Coding Computer Vision Progress in Systems and Control Theory 25393ndash417 (1999)
[208] L Cohen General phase-space distribution functions J Math Phys 7 781ndash786 (1966)[209] A Cohen I Daubechies J-C Feauveau Biorthogonal bases of compactly supported
wavelets Commun Pure Appl Math 45 485ndash560 (1992)[210] R Coifman Y Meyer MV Wickerhauser Wavelet analysis and signal processing
in Wavelets and Their Applications ed by MB Ruskai G Beylkin R CoifmanI Daubechies S Mallat Y Meyer L Raphael (Jones and Bartlett Boston 1992)pp 153ndash178
[211] R Coifman Y Meyer MV Wickerhauser Entropy-based algorithms for best basisselection IEEE Trans Inform Theory 38 713ndash718 (1992)
[212] R Coquereaux A Jadczyk Conformal theories curved spaces relativistic wavelets andthe geometry of complex domains Rev Math Phys 2 1ndash44 (1990)
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[214] N Cotfas J-P Gazeau Finite tight frames and some applications (topical review) J PhysA Math Theor 43 193001 (2010)
[215] N Cotfas J-P Gazeau K Goacuterska Complex and real Hermite polynomials and relatedquantizations J Phys A Math Theor 43 305304 (2010)
[216] N Cotfas J-P Gazeau A Vourdas Finite-dimensional Hilbert space and frame quantiza-tion J Phys A Math Gen 44 175303 (2011)
[217] EMF Curado MA Rego-Monteiro LMCS Rodrigues Y Hassouni Coherent statesfor a degenerate system The hydrogen atom Physica A 371 16ndash19 (2006)
[218] S Dahlke P Maass The affine uncertainty principle in one and two dimensions CompMath Appl 30 293ndash305 (1995)
[219] S Dahlke W Dahmen E Schmidt I Weinreich Multiresolution analysis and wavelets onS
2 and S3 Numer Funct Anal Optim 16 19ndash41 (1995)
[220] S Dahlke V Lehmann G Teschke Applications of wavelet methods to the analysis ofmeteorological radar data - An overview Arabian J Sci Eng 28 3ndash44 (2003)
[221] S Dahlke G Kutyniok P Maass C Sagiv H-G Stark G Teschke The uncertaintyprinciple associated with the continuous shearlet transform Int J Wavelets MultiresolutInf Process 6 157ndash181 (2008)
[222] S Dahlke G Kutyniok G Steidl G Teschke Shearlet coorbit spaces and associatedBanach frames Appl Comput Harmon Anal 27 195ndash214 (2009)
[223] S Dahlke G Steidl G Teschke The continuous shearlet transform in arbitrary spacedimensions J Fourier Anal Appl 16 340ndash364 (2010)
[224] S Dahlke G Steidl G Teschke Shearlet coorbit spaces Compactly supported analyzingshearlets traces and embeddings J Fourier Anal Appl 17 1232ndash1355 (2011)
[225] T Dallard GR Spedding 2-D wavelet transforms Generalisation of the Hardy space andapplication to experimental studies Eur J Mech BFluids 12 107ndash134 (1993)
[226] C Daskaloyannis Generalized deformed oscillator and nonlinear algebras J Phys AMath Gen 24 L789ndashL794 (1991)
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[228] I Daubechies On the distributions corresponding to bounded operators in the Weylquantization Commun Math Phys 75 229ndash238 (1980)
[229] I Daubechies and A Grossmann An integral transform related to quantization I J MathPhys 21 2080ndash2090 (1980)
[230] I Daubechies A Grossmann J Reignier An integral transform related to quantization IIJ Math Phys 24 239ndash254 (1983)
[231] I Daubechies Orthonormal bases of compactly supported wavelets Commun Pure ApplMath 41 909ndash996 (1988)
[232] I Daubechies The wavelet transform time-frequency localisation and signal analysisIEEE Trans Inform Theory 36 961ndash1005 (1990)
[233] I Daubechies S Maes A nonlinear squeezing of the continuous wavelet transform basedon auditory nerve models in Wavelets in Medicine and Biology ed by A Aldroubi MUnser (CRC Press Boca Raton 1996) pp 527ndash546
[234] I Daubechies A Grossmann Y Meyer Painless nonorthogonal expansions J Math Phys27 1271ndash1283 (1986)
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[236] R De Beer D van Ormondt FTAW Wajer S Cavassila D Graveron-Demilly S VanHuffel SVD-based modelling of medical NMR signals in SVD and Signal ProcessingIII Algorithms Architectures and Applications ed by M Moonen B De Moor (Elsevier(North-Holland) Amsterdam 1995) pp 467ndash474
[237] S De Biegravevre Coherent states over symplectic homogeneous spaces J Math Phys 301401ndash1407 (1989)
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[239] S De Biegravevre JA Gonzaacutelez Semiclassical behaviour of coherent states on the circle inQuantization and Coherent States Methods in Physics ed by A Odzijewicz et al (WorldScientific Singapore 1993)
[240] S De Biegravevre AE Gradechi Quantum mechanics and coherent states on the anti-de Sitterspace-time and their Poincareacute contraction Ann Inst H Poincareacute 57 403ndash428 (1992)
[241] J Deenen C Quesne Dynamical group of collective states I II III J Math Phys 23878ndash889 2004ndash2015 (1982)
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[243] J Deenen C Quesne Partially coherent states of the real symplectic group J Math Phys25 2354ndash2366 (1984)
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[245] R Delbourgo Minimal uncertainty states for the rotation and allied groups J Phys AMath Gen 10 1837ndash1846 (1977)
[246] R Delbourgo J R Fox Maximum weight vectors possess minimal uncertainty J PhysA Math Gen 10 L233ndashL235 (1977)
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[248] N Delprat B Escudieacute P Guillemain R Kronland-Martinet P Tchamitchian B Tor-reacutesani Asymptotic wavelet and Gabor analysis Extraction of instantaneous frequenciesIEEE Trans Inform Theory 38 644ndash664 (1992)
[249] Th Deutsch L Genovese Wavelets for electronic structure calculations Collection SocFr Neut 12 33ndash76 (2011)
[250] B Dewitt Quantum theory of gravity I The canonical theory Phys Rev 160 1113ndash1148(1967)
[251] RH Dicke Coherence in spontaneous radiation processes Phys Rev 93 99ndash110 (1954)[252] AN Dinkelaker AL MacKinnon Wavelets intermittency and solar flare hard X-rays 1
Local intermittency measure in cascade and avalanche scenarios Solar Phys 282 471ndash481(2013)
[253] AN Dinkelaker AL MacKinnon Wavelets intermittency and solar flare hard X-rays 2LIM analysis of high time resolution BATSE data Solar Phys 282 483ndash501 (2013)
[254] MN Do M Vetterli Contourlets in Beyond Wavelets ed by GV Welland (AcademicSan Diego 2003) pp 83ndash105
[255] MN Do M Vetterli The contourlet transform An efficient directional multiresolutionimage representation IEEE Trans Image Process 14 2091ndash2106 (2005)
[256] VV Dodonov Nonclassical states in quantum optics A ldquosqueezedrdquo review of the first 75years J Opt B Quant Semiclass Opot 4 R1ndashR33 (2002)
[257] DL Donoho Nonlinear wavelet methods for recovery of signals densities and spectrafrom indirect and noisy data in Different Perspectives on Wavelets Proceedings ofSymposia in Applied Mathematics vol 38 ed by I Daubechies (American MathematicalSociety Providence RI 1993) pp 173ndash205
[258] DL Donoho Wedgelets Nearly minimax estimation of edges Ann Stat 27 859ndash897(1999)
[259] DL Donoho X Huo Beamlet pyramids A new form of multiresolution analysis suitedfor extracting lines curves and objects from very noisy image data in SPIE Proceedingsvol 5914 (SPIE Bellingham WA 2005) pp 1ndash12
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[265] RJ Duffin AC Schaeffer A class of nonharmonic Fourier series Trans Amer MathSoc 72 341ndash366 (1952)
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[268] M Duval-Destin M-A Muschietti B Torreacutesani Continuous wavelet decompositionsmultiresolution and contrast analysis SIAM J Math Anal 24 739ndash755 (1993)
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[275] M Farge N Kevlahan V Perrier E Goirand Wavelets and turbulence Proc IEEE 84639ndash669 (1996)
[276] M Farge NK-R Kevlahan V Perrier K Schneider Turbulence analysis modellingand computing using wavelets in Wavelets in Physics Chap 4 ed by JC van den Berg(Cambridge University Press Cambridge 1999)
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[280] M Flensted-Jensen Discrete series for semisimple symmetric spaces Ann of Math 111253ndash311 (1980)
[281] K Flornes A Grossmann M Holschneider B Torreacutesani Wavelets on discrete fieldsAppl Comput Harmon Anal 1 137ndash146 (1994)
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problem J Fourier Anal Appl 11 245ndash287 (2005)
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[286] W Freeden T Maier S Zimmermann A survey on wavelet methods for (geo)applicationsRevista Mathematica Complutense 16 (2003) 277ndash310
[287] W Freeden M Schreiner Biorthogonal locally supported wavelets on the sphere based onzonal kernel functions J Fourier Anal Appl 13 693ndash709 (2007)
[288] WT Freeman EH Adelson The design and use of steerable filters IEEE Trans PatternAnal Machine Intell 13 891ndash906 (1991)
[289] L Freidel ER Livine U(N) coherent states for loop quantum gravity J Math Phys 52052502 (2011)
[290] J Froment S Mallat Arbitrary low bit rate image compression using wavelets in Progressin Wavelet Analysis and Applications (Proc Toulouse 1992) ed by Y Meyer S Roques(Ed Frontiegraveres Gif-sur-Yvette 1993) pp 413ndash418 and references therein
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[292] H Fuumlhr Wavelet frames and admissibility in higher dimensions J Math Phys 37 6353ndash6366 (1996)
[293] H Fuumlhr M Mayer Continuous wavelet transforms from semidirect products Cyclicrepresentations and Plancherel measure J Fourier Anal Appl 8 375ndash396 (2002)
[294] D Gabor Theory of communication J Inst Electr Engrg(London) 93 429ndash457 (1946)[295] J-P Gabardo D Han Frames associated with measurable spaces Adv Comput Math 18
127ndash147 (2003)[296] E Galapon Paulirsquos theorem and quantum canonical pairs The consistency of a bounded
self-adjoint time operator canonically conjugate to a Hamiltonian with non-empty pointspectrum Proc R Soc Lond A 458 451ndash472 (2002)
[297] PL Garciacutea de Leacuteon J-P Gazeau Coherent state quantization and phase operator PhysLett A 361 301ndash304 (2007)
[298] L Garciacutea de Leoacuten J-P Gazeau J Queacuteva The infinite well revisited Coherent states andquantization Phys Lett A 372 3597ndash3607 (2008)
[299] T Garidi J-P Gazeau E Huguet M Lachiegraveze Rey J Renaud Fuzzy spheres frominequivalent coherent states quantization J Phys A Math Theor 40 10225ndash10249 (2007)
[300] J-P Gazeau Four Euclidean conformal group in atomic calculations Exact analyticalexpressions for the bound-bound two-photon transition matrix elements in the H atomJ Math Phys 19 1041ndash1048 (1978)
[301] J-P Gazeau On the four Euclidean conformal group structure of the sturmian operatorLett Math Phys 3 285ndash292 (1979)
[302] J-P Gazeau Technique Sturmienne pour le spectre discret de lrsquoeacutequation de SchroumldingerJ Phys A Math Gen 13 3605ndash3617 (1980)
[303] J-P Gazeau Four Euclidean conformal group approach to the multiphoton processes in theH atom J Math Phys 23 156ndash164 (1982)
[304] J-P Gazeau A remarkable duality in one particle quantum mechanics between someconfining potentials and (R+Linfin
ε ) potentials Phys Lett 75A 159ndash163 (1980)[305] J-P Gazeau SL(2R)-coherent states and integrable systems in classical and quantum
physics in Quantization Coherent States and Complex Structures ed by J-P AntoineST Ali W Lisiecki IM Mladenov A Odzijewicz (Plenum Press New York and London1995) pp 147ndash158
[306] J-P Gazeau S Graffi Quantum harmonic oscillator A relativistic and statistical point ofview Boll Unione Mat Ital 11-A 815ndash839 (1997)
[307] J-P Gazeau V Hussin Poincareacute contraction of SU(11) Fock-Bargmann structure J PhysA Math Gen 25 1549ndash1573 (1992)
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[308] J-P Gazeau R Kanamoto Action-angle coherent states and related quantization inProceedings of QTS7 Colloquium Prague 2011 Journal of Physics Conference Seriesvol 343 (2012) p 012038-1-9
[309] J-P Gazeau JR Klauder Coherent states for systems with discrete and continuousspectrum J Phys A Math Gen 32 123ndash132 (1999)
[310] J-P Gazeau P Monceau Generalized coherent states for arbitrary quantum systems inColloquium M Flato (Dijon Sept 99) vol II (Kluumlwer Dordrecht 2000) pp 131ndash144
[311] J-P Gazeau M Novello The question of mass in (Anti-) de Sitter space-times J Phys AMath Theor 41 304008 (2008)
[312] J-P Gazeau M del Olmo q-coherent states quantization of the harmonic oscillator AnnPhys (NY) 330 220ndash245 (2013) arXiv12071200 [quant-ph]
[313] J-P Gazeau J Patera Tau-wavelets of Haar J Phys A Math Gen 29 4549ndash4559 (1996)[314] J-P Gazeau W Piechocki Coherent states quantization of a particle in de Sitter space
J Phys A Math Gen 37 6977ndash6986 (2004)[315] J-P Gazeau J Renaud Lie algorithm for an interacting SU(11) elementary system and its
contraction Ann Phys (NY) 222 89ndash121 (1993)[316] J-P Gazeau J Renaud Relativistic harmonic oscillator and space curvature Phys Lett A
179 67ndash71 (1993)[317] J-P Gazeau V Spiridonov Toward discrete wavelets with irrational scaling factor J Math
plane J Phys A Math Theor 44 495201 (2011)[319] J-P Gazeau J Patera E Pelantovaacute Tau-wavelets in the plane J Math Phys 39 4201ndash
4212 (1998)[320] J-P Gazeau M Andrle C Burdiacutek R Krejcar Wavelet multiresolutions for the Fibonacci
chain J Phys A Math Gen 33 L47ndashL51 (2000)[321] J-P Gazeau M Andrle C Burdiacutek Bernuau spline wavelets and sturmian sequences
J Fourier Anal Appl 10 269ndash300 (2004)[322] J-P Gazeau F-X Josse-Michaux P Monceau Finite dimensional quantizations of the
(q p) plane new space and momentum inequalities Int J Modern Phys B 20 1778ndash1791 (2006)
[323] J-P Gazeau J Mourad J Queacuteva Fuzzy de Sitter space-times via coherent statesquantization in Proceedings of the XXVIth Colloquium on Group Theoretical Methodsin Physics New York 2006 ed by J Birman S Catto B Nicolescu (Canopus PublishingLimited London 2009)
[324] D Geller A Mayeli Continuous wavelets on compact manifolds Math Z 262 895ndash927(2009)
[325] D Geller A Mayeli Nearly tight frames and space-frequency analysis on compactmanifolds Math Z 263 235ndash264 (2009)
[326] L Genovese B Videau M Ospici Th Deutsch S Goedecker J-F Mhaut Daubechieswavelets for high performance electronic structure calculations The BigDFT project CR Mecanique 339 149ndash164 (2011)
[327] G Gentili C Stoppato Power series and analyticity over the quaternions Math Ann 352113ndash131 (2012)
[328] G Gentili DC Struppa A new theory of regular functions of a quaternionic variable AdvMath 216 279ndash301 (2007)
[329] C Geyer K Daniilidis Catadioptric projective geometry Int J Comput Vision 45 223ndash243 (2001)
[330] R Gilmore Geometry of symmetrized states Ann Phys (NY) 74 391ndash463 (1972)[331] R Gilmore On properties of coherent states Rev Mex Fis 23 143ndash187 (1974)[332] J Ginibre Statistical ensembles of complex quaternion and real matrices J Math Phys
6 440ndash449 (1965)[333] RJ Glauber The quantum theory of optical coherence Phys Rev 130 2529ndash2539 (1963)
560 References
[334] RJ Glauber Coherent and incoherent states of radiation field Phys Rev 131 2766ndash2788(1963)
[335] J Glimm Locally compact transformation groups Trans Amer Math Soc 101 124ndash138(1961)
[336] R Godement Sur les relations drsquoorthogonaliteacute de V Bargmann C R Acad Sci Paris 255521ndash523 657ndash659 (1947)
[337] C Gonnet B Torreacutesani Local frequency analysis with two-dimensional wavelet trans-form Signal Proc 37 389ndash404 (1994)
[338] JA Gonzalez MA del Olmo Coherent states on the circle J Phys A Math Gen 318841ndash8857 (1998)
[339] XGonze B Amadon et al ABINIT First-principles approach to material and nanosystemproperties Computer Physics Comm 180 2582ndash2615 (2009)
[340] KM Gograverski E Hivon AJ Banday BD Wandelt FK Hansen M Reinecke MBartelmann HEALPix A framework for high-resolution discretization and fast analysisof data distributed on the sphere Astrophys J 622 759ndash771 (2005)
[341] P Goupillaud A Grossmann J Morlet Cycle-octave and related transforms in seismicsignal analysis Geoexploration 23 85ndash102 (1984)
[342] KH Groumlchenig A new approach to irregular sampling of band-limited functions in RecentAdvances in Fourier Analysis and Its applications ed by JS Byrnes JL Byrnes (KluwerDordrecht 1990) pp 251ndash260
[343] KH Groumlchenig Gabor analysis over LCA groups in Gabor Analysis and Algorithms ndashTheory and Applications ed by HG Feichtinger T Strohmer (Birkhaumluser Boston-Basel-Berlin 1998) pp 211ndash231
[344] HJ Groenewold On the principles of elementary quantum mechanics Physica 12 405ndash460 (1946)
[345] P Grohs Continuous shearlet tight frames J Fourier Anal Appl 17 506ndash518 (2011)[346] P Grohs G Kutyniok Parabolic molecules preprint TU Berlin (2012)[347] M Grosser A note on distribution spaces on manifolds Novi Sad J Math 38 121ndash128
(2008)[348] A Grossmann Parity operator and quantization of δ -functions Commun Math Phys 48
191ndash194 (1976)[349] A Grossmann J Morlet Decomposition of Hardy functions into square integrable
wavelets of constant shape SIAM J Math Anal 15 723ndash736 (1984)[350] A Grossmann J Morlet Decomposition of functions into wavelets of constant shape and
related transforms in Mathematics + Physics Lectures on recent results I ed by L Streit(World Scientific Singapore 1985) pp 135ndash166
[351] A Grossmann J Morlet T Paul Integral transforms associated to square integrablerepresentations I General results J Math Phys 26 2473ndash2479 (1985)
[352] A Grossmann J Morlet T Paul Integral transforms associated to square integrablerepresentations II Examples Ann Inst H Poincareacute 45 293ndash309 (1986)
[353] A Grossmann R Kronland-Martinet J Morlet Reading and understanding the contin-uous wavelet transform in Wavelets Time-Frequency Methods and Phase Space (ProcMarseille 1987) ed by J-M Combes A Grossmann P Tchamitchian 2nd edn (SpringerBerlin 1990) pp 2ndash20
[354] P Guillemain R Kronland-Martinet B Martens Estimation of spectral lines with helpof the wavelet transform Application in NMR spectroscopy in Wavelets and Applications(Proc Marseille 1989) ed by Y Meyer (Masson and Springer Paris and Berlin 1991) pp38ndash60
[355] H de Guise M Bertola Coherent state realizations of su(n+ 1) on the n-torus J MathPhys 43 3425ndash3444 (2002)
[356] K Guo D Labate Representation of Fourier Integral Operators using shearlets J FourierAnal Appl 14 327ndash371 (2008)
References 561
[357] K Guo G Kutyniok D Labate Sparse multidimensional representations usinganisotropic dilation and shear operators in Wavelets and Spines (Athens GA 2005)(Nashboro Press Nashville TN 2006) pp 189ndash201
[358] K Guo D Labate W-Q Lim G Weiss E Wilson Wavelets with composite dilationsand their MRA properties Appl Comput Harmon Anal 20 202ndash236 (2006)
[359] EA Gutkin Overcomplete subspace systems and operator symbols Funct Anal Appl 9260ndash261 (1975)
[360] G Gyoumlrgyi Integration of the dynamical symmetry groups for the 1r potential Acta PhysAcad Sci Hung 27 435ndash439 (1969)
[361] BC Hall The Segal-Bargmann ldquoCoherent Staterdquo transform for compact Lie groups JFunct Analysis 122 103ndash151 (1994)
[362] B Hall JJ Mitchell Coherent states on spheres J Math Phys 43 1211ndash1236 (2002)[363] DK Hammond P Vandergheynst R Gribonval Wavelets on graphs via spectral theory
Appl Comput Harmon Anal 30 129ndash150 (2011)[364] Y Hassouni EMF Curado MA Rego-Monteiro Construction of coherent states for
physical algebraic system Phys Rev A 71 022104 (2005)[365] J He H Liu Admissible wavelets associated with the affine automorphism group of the
Siegel upper half-plane J Math Anal Appl 208 58ndash70 (1997)[366] J He H Liu Admissible wavelets associated with the classical domain of type one
Approx Appl 14 (1998) 89ndash105[367] J He L Peng Wavelet transform on the symmetric matrix space preprint Beijing (1997)
(unpublished)[368] J He L Peng Admissible wavelets on the unit disk Complex Variables 35 109ndash119
(1998)[369] DM Healy Jr FE Schroeck Jr On informational completeness of covariant localization
observables and Wigner coefficients J Math Phys 36 453ndash507 (1995)[370] C Heil D Walnut Continuous and discrete wavelet transforms SIAM Review 31 628ndash
666 (1989)[371] K Hepp EH Lieb On the superradiant phase transition for molecules in a quantized
radiation field The Dicke maser model Ann Phys (NY) 76 360ndash404 (1973)[372] K Hepp EH Lieb Equilibrium statistical mechanics of matter interacting with the
quantized radiation field Phys Rev A 8 2517ndash2525 (1973)[373] JA Hogan JD Lakey Extensions of the Heisenberg group by dilations and frames Appl
Comput Harmon Anal 2 174ndash199 (1995)[374] AL Hohoueacuteto K Thirulogasanthar ST Ali J-P Antoine Coherent states lattices and
square integrability of representations J Phys A Math Gen36 11817ndash11835 (2003)[375] M Holschneider On the wavelet transformation of fractal objects J Stat Phys 50 963ndash
993 (1988)[376] M Holschneider Wavelet analysis on the circle J Math Phys 31 39ndash44 (1990)[377] M Holschneider Inverse Radon transforms through inverse wavelet transforms Inv Probl
7 853ndash861 (1991)[378] M Holschneider Localization properties of wavelet transforms J Math Phys 34 3227ndash
3244 (1993)[379] M Holschneider General inversion formulas for wavelet transforms J Math Phys 34
4190ndash4198 (1993)[380] M Holschneider Wavelet analysis over abelian groups Applied Comput Harmon Anal
2 52ndash60 (1995)[381] M Holschneider Continuous wavelet transforms on the sphere J Math Phys 37 4156ndash
4165 (1996)[382] M Holschneider I Iglewska-Nowak Poisson wavelets on the sphere J Fourier Anal
Appl 13 405ndash419 (2007)
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[383] M Holschneider R Kronland-Martinet J Morlet P Tchamitchian A real-time algorithmfor signal analysis with the help of wavelet transform in Wavelets Time-FrequencyMethods and Phase Space (Proc Marseille 1987) ed by J-M Combes A Grossmann PTchamitchian 2nd edn (Springer Berlin 1990) pp 286ndash297
[384] M Holschneider P Tchamitchian Pointwise analysis of Riemannrsquos ldquonondifferentiablerdquofunction Invent Math 105 157ndash175 (1991)
[385] GR Honarasa MK Tavassoly M Hatami R Roknizadeh Nonclassical properties ofcoherent states and excited coherent states for continuous spectra J Phys A Math Theor44 085303 (2011)
[386] M Hongoh Coherent states associated with the continuous spectrum of noncompactgroups J Math Phys 18 2081ndash2085 (1977)
[387] A Horzela FH Szafraniec A measure free approach to coherent states J Phys A MathGen 45 244018 (2012)
[388] W-L Hwang S Mallat Characterization of self-similar multifractals with waveletmaxima Appl Comput Harmon Anal 1 316ndash328 (1994)
[389] W-L Hwang C-S Lu P-C Chung Shape from texture Estimation of planar surfaceorientation through the ridge surfaces of continuous wavelet transform IEEE Trans ImageProc 7 773ndash780 (1998)
[390] I Iglewska-Nowak M Holschneider Frames of Poisson wavelets on the sphere ApplComput Harmon Anal 28 227ndash248 (2010)
[391] E Inoumlnuuml EP Wigner On the contraction of groups and their representations Proc NatAcad Sci U S 39 510ndash524 (1953)
[392] S Iqbal F Saif Generalized coherent states and their statistical characteristics in power-law potentials J Math Phys 52 082105 (2011)
[393] CJ Isham JR Klauder Coherent states for n-dimensional Euclidean groups E(n) andtheir application J MathPhys 32 607ndash620 (1991)
[394] L Jacques J-P Antoine Multiselective pyramidal decomposition of images Wavelets withadaptive angular selectivity Int J Wavelets Multires Inform Proc 5 785ndash814 (2007)
[395] L Jacques L Duval C Chaux G Peyreacute A panorama on multiscale geometric rep-resentations intertwining spatial directional and frequency selectivity Signal Proc 912699ndash2730 (2011)
[396] HR Jalali M K Tavassoly On the ladder operators and nonclassicality of generalizedcoherent state associated with a particle in an infinite square well preprint (2013)arXiv13034100v1 [quant-ph]
[397] C Johnston On the pseudo-dilation representations of Flornes Grossmann Holschneiderand Torreacutesani Appl Comput Harmon Anal 3 377ndash385 (1997)
[398] G Kaiser Phase-space approach to relativistic quantum mechanics I Coherent staterepresentation for massive scalar particles J MathPhys 18 952ndash959 (1977)
[399] G Kaiser Phase-space approach to relativistic quantum mechanics II Geometrical aspectsJ MathPhys 19 502ndash507 (1978)
[400] C Kalisa B Torreacutesani N-dimensional affine Weyl-Heisenberg wavelets Ann Inst HPoincareacute 59 201ndash236 (1993)
[401] W Kaminski J Lewandowski T Pawłowski Quantum constraints Dirac observables andevolution group averaging versus the Schroumldinger picture in LQC Class Quant Grav 26245016 (2009)
[402] MR Karim ST Ali A relativistic windowed Fourier transform preprint ConcordiaUniversity Montreacuteal (1997) (unpublished)
[403] M R Karim ST Ali M Bodruzzaman A relativistic windowed Fourier transform inProceedings of IEEE SoutheastCon 2000 Nashville Tennessee pp 253ndash260 (2000)
[404] T Kawazoe Wavelet transforms associated to a principal series representation of semisim-ple Lie groups I II Proc Japan Acad Ser A ndash Math Sci 71 154ndash157 158ndash160 (1995)
[405] T Kawazoe Wavelet transform associated to an induced representation of SL(n+ 2R)Ann Inst H Poincareacute 65 1ndash13 (1996)
References 563
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[407] P Kittipoom G Kutyniok W-Q Lim Construction of compactly supported shearletframes Constr Approx 35 21ndash72 (2012)
[408] J Kiukas P Lahti K Ylinenc Phase space quantization and the operator moment problemJ Math Phys 47 072104 (2006)
[409] JR Klauder Continuous-representation theory I Postulates of continuous-representationtheory J Math Phys 4 1055ndash1058 (1963)
[410] JR Klauder Continuous-representation theory II Generalized relation between quantumand classical dynamics J Math Phys 4 1058ndash1073 (1963)
[411] JR Klauder Path integrals for affine variables in Functional Integration Theory andApplications ed by J-P Antoine E Tirapegui (Plenum Press New York and London1980) pp 101ndash119
[412] JR Klauder Are coherent states the natural language of quantum mechanics inFundamental Aspects of Quantum Theory ed by V Gorini A Frigerio NATO ASI Seriesvol B 144 (Plenum Press New York 1986) pp 1ndash12
[413] JR Klauder Quantization without quantization Ann Phys (NY) 237 147ndash160 (1995)[414] JR Klauder Coherent states for the hydrogen atom J Phys A Math Gen 29 L293ndash
L296 (1996)[415] JR Klauder An affinity for affine quantum gravity Proc Steklov Inst Math 272 169ndash176
(2011) and references therein[416] JR Klauder RF Streater A wavelet transform for the Poincareacute group J Math Phys 32
1609ndash1611 (1991)[417] JR Klauder RF Streater Wavelets and the Poincareacute half-plane J Math Phys 35 471ndash
478 (1994)[418] JR Klauder K Penson J-M Sixdeniers Constructing coherent states through solutions
of Stieltjes and Hausdorff moment problems Phys Rev A 64 013817 (2001)[419] A Kleppner RL Lipsman The Plancherel formula for group extensions Ann Ec Norm
Sup 5 459ndash516 (1972)[420] AB Klimov C Muntildeoz Coherent isotropic and squeezed states in a N-qubit system Phys
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Computer Science From Numbers and Languages to (Quantum) Cryptography - NATOSecurity through Science Series D - Information and Communication Security vol 7 edby J-P Gazeau J Nesetril B Rovan (IOS Press Washington DC 2007) pp 25ndash54
[422] S Kobayashi Irreducibility of certain unitary representations J Math Soc Japan 20 638ndash642 (1968)
[423] K Kowalski J Rembielinski LC Papaloucas Coherent states for a quantum particle ona circle J Phys A Math Gen 29 4149ndash4167 (1996)
[424] K Kowalski J Rembielinski Quantum mechanics on a sphere and coherent states J PhysA Math Gen 33 6035ndash6048 (2000)
[425] K Kowalski J Rembielinski The Bargmann representation for the quantum mechanicson a sphere J Math Phys 42 4138ndash4147 (2001)
[426] C Kristjansen J Plefka GW Semenoff M Staudacher A new double-scaling limit ofN = 4 super-Yang-Mills theory and pp-wave strings Nuclear Phys B 643 3ndash30 (2002)
[427] M Kulesh M Holschneider MS Diallo Geophysical wavelet library Applications ofthe continuous wavelet transform to the polarization and dispersion analysis of signalsComput Geosci 34 1732ndash1752 (2008)
[428] R Kunze On the Frobenius reciprocity theorem for square integrable representationsPacific J Math 53 465ndash471 (1974)
[429] Y Kuroda A Wada T Yamazaki K Nagayama Postacquisition data processing methodfor suppression of the solvent signal I J Magn Reson 84 604ndash610 (1989)
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[431] G Kutyniok D Labate Resolution of the wavefront set using continuous shearlets TransAmer Math Soc 361 2719ndash2754 (2009)
[432] G Kutyniok W-Q Lim Compactly supported shearlets are optimally sparse J ApproxTheory 163 1564ndash1589 (2011)
[433] D Labate W-Q Lim G Kutyniok G Weiss Sparse multidimensional representationusing shearlets in Wavelets XI (San Diego CA 2005) ed by M Papadakis A Laine MUnser SPIE Proceedings vol 5914 (SPIE Bellingham WA 2005) pp 254ndash262
[434] P Lahti J-P Pellonpaumlauml Continuous variable tomographic measurements Phys Lett A373 3435ndash3438 (2009)
[435] Lambertrsquos projection see WikipediahttpenwikipediaorgwikiLambert_azimuthal_equal-area_projection
[436] J-P Leduc F Mujica R Murenzi MJT Smith Missile-tracking algorithm using target-adapted spatio-temporal wavelets in Automatic Object Recognition VII SPIE Proceedingsvol 5914 (SPIE Bellingham WA 1997) pp 400ndash411
[437] J-P Leduc F Mujica R Murenzi MJT Smith Spatio-temporal wavelet transforms formotion tracking in IEEE ICASSP 1997 vol 4 (1997) pp 3013ndash3016
[438] J-P Leduc F Mujica R Murenzi MJT Smith Spatio-temporal continuous waveletsapplied to missile warhead detection and tracking in SPIE VCIP rsquo97 vol 3024 ed byJ Biemond EJ Delp (1997) pp 787ndash798
[439] B Leistedt JD McEwen Exact wavelets on the ball IEEE Trans Signal Proc 60 1564ndash1589 (2012)
[440] PG Lemarieacute Y Meyer Ondelettes et bases hilbertiennes Rev Math Iberoamer 2 1ndash18(1986)
[441] C Lemke A Schuck Jr J-P Antoine D Sima Metabolite-sensitive analysis of magneticresonance spectroscopic signals using the continuous wavelet transform Meas SciTechnol 22 (2011) Art 114013
[442] J-M Leacutevy-Leblond Galilei group and non-relativistic quantum mechanics J Math Phys4 776-788 (1963)
[443] J-M Leacutevy-Leblond Galilei group and Galilean invariance in Group Theory and ItsApplications vol II ed by EM Loebl (Academic New York 1971) pp 221ndash299
[444] J-M Leacutevy-Leblond On the conceptual nature of the physical constants Riv Nuovo Cim7 187ndash214 (1977)
[445] EH Lieb The classical limit of quantum spin systems Commun Math Phys 31 327ndash340(1973)
[446] G Lindblad B Nagel Continuous bases for unitary irreducible representations of SU(11)Ann Inst H Poincareacute 13 27ndash56 (1970)
[447] W Lisiecki Kaumlhler coherent states orbits for representations of semisimple Lie groupsAnn Inst H Poincareacute 53 857ndash890 (1990)
[448] A Lisowska Moment-based fast wedgelet transform J Math Imaging Vis 39 180ndash192(2011)
[449] H Liu L Peng Admissible wavelets associated with the Heisenberg group Pacific JMath 180 101ndash123 (1997)
[450] E Livine S Speziale Physical boundary state for the quantum tetrahedron Class QuantGrav 25 085003 (2008)
[451] F Low Complete sets of wave packets in A Passion for Physics ndash Essay in Honor ofGeoffrey Chew ed by C DeTar (World Scientific Singapore 1985) pp 17ndash22
[452] G Mack All unitary ray representations of the conformal group SU(22) with positiveenergy Commun Math Phys 55 1ndash28 (1977)
[453] GW Mackey Imprimitivity for representations of locally compact groups I Proc NatAcad Sci 35 537ndash545 (1949)
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[456] SG Mallat Multifrequency channel decompositions of images and wavelet models IEEETrans Acoust Speech Signal Proc 37 2091ndash2110 (1989)
[457] SG Mallat A theory for multiresolution signal decomposition The wavelet representa-tion IEEE Trans Pattern Anal Machine Intell 11 674ndash693 (1989)
[458] S Mallat W-L Hwang Singularity detection and processing with wavelets IEEE TransInform Theory 38 617ndash643 (1992)
[459] S Mallat Z Zhang Matching pursuits with time frequency dictionaries IEEE TransSignal Proc 41 3397ndash3415 (1993)
[460] S Mallat S Zhong Wavelet maxima representation in Wavelets and Applications (ProcMarseille 1989) ed by Y Meyer (Masson and Springer Paris and Berlin 1991) pp 207ndash284
[461] VI Manrsquoko G Marmo ECG Sudarshan F Zaccaria f -oscillators and non-linearcoherent states Phys Scr 55 528ndash541 (1997)
[462] D Marinucci D Pietrobon A Baldi P Baldi P Cabella G Kerkyacharian P Natoli DPicard N Vittorio Spherical needlets for CMB data analysis Mon Not R Astron Soc383 539ndash545 (2008)
[463] D Marion M Ikura A Bax Improved solvent suppression in one- and two-dimensionalNMR spectra by convolution of time-domain data J Magn Reson 84 425ndash430 (1989)
[464] Y Meyer Principe drsquoincertitude bases hilbertiennes et algegravebres drsquoopeacuterateurs SeacuteminaireBourbaki 662 (1985ndash1986)
[465] Y Meyer Principe drsquoincertitude bases hilbertiennes et algegravebres drsquoopeacuterateurs Asteacuterisque145ndash146 209ndash223 (1987)
[466] Y Meyer H Xu Wavelet analysis and chirps Appl Comput Harmon Anal 4 366ndash379(1997)
[467] L Michel Invariance in quantum mechanics and group extensions in Group TheoreticalConcepts and Methods in Elementary Particle Physics ed by F Guumlrsey (Gordon andBreach New York and London 1964) pp 135ndash200
[468] J Mickelsson J Niederle Contractions of representations of the de Sitter groupsCommun Math Phys 27 167ndash180 (1972)
[469] MM Miller Convergence of the Sudarshan expansion for the diagonal coherent-stateweight functional J Math Phys 9 1270ndash1274 (1968)
[470] V F Molchanov Harmonic analysis on homogeneous spaces in Representation Theoryand Noncommutative Harmonic Analysis II ed by AA Kirillov (Springer Berlin 1995)
[471] MI Monastyrsky AM Perelomov Coherent states and symmetric spaces II Ann InstH Poincareacute 23 23ndash48 (1975)
[472] B Moran S Howard D Cochran Positive-operator-valued measures A general settingfor frames in Excursions in Harmonic Analysis vol 1 2 ed by TD Andrews R BalanJJ Benedetto W Czaja KA Okoudjou (Birkhaumluser Boston 2013) pp 49ndash64
[473] H Moscovici Coherent states representations of nilpotent Lie groups Commun MathPhys 54 63ndash68 (1977)
[474] H Moscovici A Verona Coherent states and square integrable representations Ann InstH Poincareacute 29 139ndash156 (1978)
[475] F Mujica R Murenzi MJT Smith J-P Leduc Robust tracking in compressed imagesequences J Electr Imaging 7 746ndash754 (1998)
[476] R Murenzi Wavelet transforms associated to the n-dimensional Euclidean group withdilations Signals in more than one dimension in Wavelets Time-Frequency Methodsand Phase Space (Proc Marseille 1987) ed by J-M Combes A Grossmann PTchamitchian 2nd edn (Springer Berlin 1990) pp 239ndash246
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[478] B Nagel Generalized eigenvectors in group representations in Studies in MathematicalPhysics (Proc Istanbul 1970) ed by AO Barut (Reidel Dordrecht and Boston 1970)pp 135ndash154
[479] MA Naımark Dokl Akad Nauk SSSR 41 359ndash361 (1943) see also B Sz-NagyExtensions of linear transformations in Hilbert space which extend beyond this spaceAppendix to F Riesz B Sz-Nagy Functional Analysis (Frederick Ungar New York 1960)
[480] FJ Narcowich P Petrushev JD Ward Localized tight frames on spheres SIAM J MathAnal 38 574ndash594 (2006)
[481] M Nauenberg Quantum wave packets on Kepler elliptic orbits Phys Rev A 40 1133ndash1136 (1989)
[482] M Nauenberg C Stroud J Yeazell The classical limit of an atom Scient Amer 27024ndash29 (1994)
[483] H Neumann Transformation properties of observables Helv Phys Acta 45 811ndash819(1972)
[484] U Niederer The maximal kinematical invariance group of the free Schroumldinger equationHelv Phys Acta 45 802ndash881 (1972)
[485] MM Nieto LM Simmons Jr Coherent states for general potentials I Formalism IIConfining one-dimensional examples III Nonconfining one-dimensional examples PhysRev D 20 1321ndash1331 1332ndash1341 1342ndash1350 (1979)
[486] MM Nieto LM Simmons Jr Coherent states for general potentials Phys Rev Lett 41207ndash210 (1987)
[487] A Odzijewicz On reproducing kernels and quantization of states Commun Math Phys114 577ndash597 (1988)
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[489] A Odzijewicz Quantum algebras and q-special functions related to coherent states mapsof the disc Commun Math Phys 192 183ndash215 (1998)
[490] A Odzijewicz M Horowski A Tereszkiewicz Integrable multi-boson systems andorthogonal polynomials J Phys A Math Gen 34 4353ndash4376 (2001)
[491] G Oacutelafsson B Oslashrsted The holomorphic discrete series for affine symmetric spaces JFunct Anal 81 126ndash159 (1988)
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[494] E Onofri Dynamical quantization of the Kepler manifold J Math Phys 17 401ndash408(1976)
[495] D Oriti R Pereira L Sindoni Coherent states in quantum gravity A construction basedon the flux representation of loop quantum gravity J Phys A Math Theor 45 244004(2012)
[496] LC Papaloucas J Rembielinski W Tybor Vectorlike coherent states with noncompactstability group J Math Phys 30 2406ndash2410 (1989)
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[498] Z Pasternak-Winiarski On reproducing kernels for holomorphic vector bundles inQuantization and Infinite Dimensional Systems (Proc Białowieza Poland 1993) ed by J-P Antoine ST Ali W Lisiecki IM Mladenov A Odzijewicz (Plenum Press New Yorkand London 1994) pp 109ndash112
[499] T Paul Affine coherent states and the radial Schroumldinger equation I preprint CPT-84P1710 (1984) (unpublished)
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[501] AM Perelomov On the completeness of a system of coherent states Theor Math Phys6 156ndash164 (1971)
[502] AM Perelomov Coherent states for arbitrary Lie group Commun Math Phys 26 222ndash236 (1972)
[503] AM Perelomov Coherent states and symmetric spaces Commun Math Phys 44 197ndash210 (1975)
[504] M Perroud Projective representations of the Schroumldinger group Helv Phys Acta 50 233ndash252 (1977)
[505] J Phillips A note on square-integrable representations J Funct Anal 20 83ndash92 (1975)[506] D Pietrobon P Baldi D Marinucci Integrated Sachs-Wolfe effect from the cross
correlation of WMAP3 year and the NRAO VLA sky survey data New results andconstraints on dark energy Phys Rev D 74 043524 (2006)
[507] WWF Pijnappel A van den Boogaart R de Beer D van Ormondt SVD-basedquantification of magnetic resonance signals J Magn Reson 97 122ndash134 (1992)
[508] V Pop D Rosca Generalized piecewise constant orthogonal wavelet bases on 2D-domains Appl Anal 90 715ndash723 (2011)
[509] G Poumlschl E Teller Bemerkungen zur Quantenmechanik des anharmonischen OszillatorsZ Physik 83 143ndash151 (1933)
[510] D Potts G Steidl M Tasche Kernels of spherical harmonics and spherical frames inAdvanced Topics in Multivariate Approximation ed by F Fontanella K Jetter PJ Laurent(World Scientific Singapore 1996) pp 287ndash301
[511] E Prugovecki Consistent formulation of relativistic dynamics for massive spin-zeroparticles in external fields Phys Rev D 18 3655ndash3673 (1978) (Appendix C)
[512] E Prugovecki Relativistic quantum kinematics on stochastic phase space for massiveparticles J MathPhys 19 2261ndash2270 (1978)
[513] C Quesne Coherent states of the real symplectic group in a complex analytic parametriza-tion I II J Math Phys 27 428ndash441 869ndash878 (1986)
[514] C Quesne Generalized vector coherent states of sp(2NR) vector operators and ofsp(2NR) sup u(N) reduced Wigner coefficients J Phys A Math Gen 24 2697ndash2714(1991)
[515] JM Radcliffe Some properties of spin coherent states J Phys A Math Gen 4 313ndash323(1971)
[516] A Rahimi A Najati YN Dehghan Continuous frames in Hilbert spaces Methods FunctAnal Topol 12 170ndash182 (2006)
[517] H Rauhut M Roumlsler Radial multiresolution in dimension three Constr Approx 22 193ndash218 (2005)
[518] JH Rawnsley Coherent states and Kaumlhler manifolds Quart J Math Oxford 28(2) 403ndash415 (1977)
[519] J Renaud The contraction of the SU(11) discrete series of representations by means ofcoherent states J Math Phys 37 3168ndash3179 (1996)
[520] A Reacutenyi Representations for real numbers and their ergodic properties Acta Math AcadSci Hungary 8(3ndash4) 477ndash493 (1957)
[521] D Robert La coheacuterence dans tous ses eacutetats SMF Gazette 132 (2012)[522] JE Roberts The Dirac bra and ket formalism J Math Phys 7 1097ndash1104 (1966)[523] JE Roberts Rigged Hilbert spaces in quantum mechanics Commun Math Phys 3 98ndash
119 (1966)[524] S Roques F Bourzeix K Bouyoucef Soft-thresholding technique and restoration of
3C273 jet Astrophys Space Sci Nr 239 297ndash304 (1996)[525] D Rosca Haar wavelets on spherical triangulations in Advances in Multiresolution for
Geometric Modelling ed by NA Dogson MS Floater MA Sabin (Springer Berlin2005) pp 407ndash419
568 References
[526] D Rosca Locally supported rational spline wavelets on the sphere Math Comput 741803ndash1829 (2005)
[527] D Rosca Wavelets defined on closed surfaces J Comput Anal Appl 8 121ndash132 (2006)[528] D Rosca Weighted Haar wavelets on the sphere Int J Wavelets Multiresol Inf Proc 5
501ndash511 (2007)[529] D Rosca Wavelet bases on the sphere obtained by radial projection J Fourier Anal Appl
13 421ndash434 (2007)[530] D Rosca Piecewise constant wavelets on triangulations obtained by 1ndash3 splitting Int J
Wavelets Multiresolut Inf Process 6 209ndash222 (2008)[531] D Rosca On a norm equivalence on L2(S2) Results Math 53 399ndash405 (2009)[532] D Rosca New uniform grids on the sphere Astron Astrophys 520 (2010) Art A63[533] D Rosca Uniform and refinable grids on elliptic domains and on some surfaces of
revolution Appl Math Comput 217 7812ndash7817 (2011)[534] D Rosca Wavelet analysis on some surfaces of revolution via area preserving projection
Appl Comput Harmon Anal 30 262ndash272 (2011)[535] D Rosca J-P Antoine Locally supported orthogonal wavelet bases on the sphere via
stereographic projection Math Probl Eng 2009 124904 (2009)[536] D Rosca J-P Antoine Constructing wavelet frames and orthogonal wavelet bases on the
sphere in Recent Advances in Signal Processing ed by S Miron (IN-TECH ViennaAustria and Rijeka Croatia 2010) pp 59ndash76
[537] D Rosca G Plonka Uniform spherical grids via area preserving projection from the cubeto the sphere J Comput Appl Math 236 1033ndash1041 (2011)
[538] D Rosca G Plonka An area preserving projection from the regular octahedron to thesphere Results Math 63 429ndash444 (2012)
[539] H Rossi M Vergne Analytic continuation of the holomorphic discrete series for a semi-simple Lie group Acta Math 136 1ndash59 (1976)
[540] DJ Rotenberg Application of Sturmian functions to the Schroedinger three-body prob-lem Elastic e+ndashH scattering Ann Phys (NY) 19 262ndash278 (1962)
[541] C Rovelli Zakopane lectures on loop gravity in Proceedings of 3rd Quantum Gravityand Quantum Geometry School 28 Febndash13 March 2011 (Zakopane Poland 2011)arXiv11023660v5
[542] C Rovelli S Speziale A semiclassical tetrahedron Class Quant Grav 23 5861ndash5870(2006)
[543] DJ Rowe Coherent state theory of the noncompact symplectic group J Math Phys 252662ndash2271 (1984)
[544] DJ Rowe Microscopic theory of the nuclear collective model Rep Prog Phys 48 1419ndash1480 (1985)
[545] DJ Rowe Vector coherent state representations and their inner products J Phys A MathGen 45 244003 (2012) (This paper belongs to the special issue [38])
[546] DJ Rowe J Repka Vector-coherent-state theory as a theory of induced representationsJ Math Phys 32 2614ndash2634 (1991)
[547] DJ Rowe G Rosensteel R Gilmore Vector coherent state representation theory J MathPhys 26 2787ndash2791 (1985)
[548] A Royer Phase states and phase operators for the quantum harmonic oscillator Phys RevA 53 70ndash108 (1996)
[549] J Saletan Contraction of Lie groups J Math Phys 2 1ndash21 (1961)[550] G Saracco A Grossmann P Tchamitchian Use of wavelet transforms in the study of
propagation of transient acoustic signals across a plane interface between two homoge-neous media in Wavelets Time-Frequency Methods and Phase Space (Proc Marseille1987) ed by J-M Combes A Grossmann P Tchamitchian 2nd edn (Springer Berlin1990) pp 139ndash146
[551] P Schroumlder W Sweldens Spherical wavelets Efficiently representing functions on thesphere in Computer Graphics Proceedings (SIGGRAPH95) (ACM Siggraph Los Angeles1995) pp 161ndash175
References 569
[552] E Schroumldinger Der stetige Uumlbergang von der Mikro- zur Makromechanik Naturwiss 14664ndash666 (1926)
[553] S Scodeller Oslash Rudjord FK Hansen D Marinucci D Geller A Mayeli IntroducingMexican needlets for CMB analysis Issues for practical applications and comparison withstandard needlets Astrophys J 733 (2011) Art 121
[554] H Scutaru Coherent states and induced representations Lett Math Phys 2 101ndash107(1977)
[555] B Simon Distributions and their Hermite expansions J Math Phys 12 140ndash148 (1971)[556] B Simon The classical moment problem as a self-adjoint finite difference operator Adv
Math 137 82ndash203 (1998)[557] R Simon ECG Sudarshan N Mukunda Gaussian pure states in quantum mechanics
and the symplectic group Phys Rev A37 3028ndash3038 (1988)[558] S Sivakumar Studies on nonlinear coherent states J Opt B Quant Semiclass Opt 2
R61ndashR75 (2000)[559] E Slezak A Bijaoui G Mars Identification of structures from galaxy counts Use of the
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Geometric Methods in Physics XXXI Workshop 2012 (Trends in Mathematics ed byP Kielanowski et al Birkhaumluser Verlag Basel 2013) pp 47ndash63
[562] SB Sontz Paragrassmann algebras as quantum spaces Part II Toeplitz operators J OperTh (2013 to appear) arXiv12055493
[563] SB Sontz A reproducing kernel and Toeplitz operators in the quantum plane Preprint(2013) arXiv13056986 [math-ph]
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[567] J-L Starck DL Donoho E J Candegraves Astronomical image representation by the curvelettransform Astron Astroph 398 785ndash800 (2003)
[568] J-L Starck Y Moudden P Abrial M Nguyen Wavelets ridgelets and curvelets on thesphere Astron Astroph 446 1191ndash1204 (2006)
[569] MB Stenzel The Segal-Bargmann transform on a symmetric space of compact type JFunct Analysis 165 44ndash58 (1994)
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[571] A Suvichakorn H Ratiney A Bucur S Cavassila J-P Antoine Toward a quantitativeanalysis of in vivo magnetic resonance proton spectroscopic signals using the continuousMorlet wavelet transform Meas Sci Technol 20 (2009) Art 104029
[572] W Sweldens The lifting scheme A custom-design construction of biorthogonal waveletsApplied Comput Harmon Anal 3 1186ndash1200 (1996)
[573] W Sweldens The lifting scheme A construction of second generation wavelets SIAM JMath Anal 29 511ndash546 (1998)
[574] FH Szafraniec The reproducing kernel Hilbert space and its multiplication operatorsin Complex Analysis and Related Topics ed by E Ramirez de Arellano et al OperatorTheory Advances and Applications vol 114 (Birkhaumluser Basel 2000) pp 254ndash263
[575] FH Szafraniec Multipliers in the reproducing kernel Hilbert space subnormality andnoncommutative complex analysis in Reproducing Kernel Spaces and Applications edby D Alpay Operator Theory Advances and Applications vol 143 (Birkhaumluser Basel2003) pp 313ndash331
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[577] MC Teich BEA Saleh Squeezed states of light Quantum Opt 1 152ndash191 (1989)[578] R Terrier L Demanet IA Grenier J-P Antoine Wavelet analysis of EGRET data in
Proceedings of the 27th International Cosmic Ray Conference (ICRC 2001) (CopernicusGesellschaft DE 2001) pp 2923ndash2926
[579] T Thiemann Gauge field theory coherent states (GCS) 1 General properties Class QuantGrav 18 2025ndash2064 (2001)
[580] T Thiemann O Winkler Gauge field theory coherent states (GCS) 2 Peakednessproperties Class Quant Grav 18 2561ndash2636 (2001)
[581] T Thiemann O Winkler Gauge field theory coherent states (GCS) 3 Ehrenfest theoremsClass Quant Grav 18 4629ndash4682 (2001)
[582] T Thiemann O Winkler Gauge field theory coherent states (GCS) 4 Infinite tensorproduct and thermodynamical limit Class Quant Grav 18 4997ndash5054 (2001)
[583] K Thirulagasanthar ST Ali Regular subspaces of a quaternionic Hilbert space fromquaternionic Hermite polynomials and associated coherent states J Math Phys 54013506 (2013)
[584] K Thirulogasanthar G Honnouvo A Krzyzak Coherent states and Hermite polynomialson quaternionic Hilbert spaces J Phys A Math Theor 43 385205 (2010)
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Ann Inst H Poincareacute 56 215ndash234 (1992)[588] B Torreacutesani Position-frequency analysis for signals defined on spheres Signal Proc 43
341ndash346 (2005)[589] DA Trifonov Generalized intelligent states and squeezing J Math Phys 35 2297ndash2308
(1994)[590] AS Trushechkin IV Volovich Localization properties of squeezed quantum states in
nanoscale space domains preprint (2013) arXiv13046277v1 [quant-ph][591] M Unser N Chenouard A unifying parametric framework for 2D steerable wavelet
transforms SIAM J Imaging Sci 6 102ndash135 (2013)[592] P Vandergheynst J-F Gobbers Directional dyadic wavelet transforms Design and
algorithms IEEE Trans Image Proc 11 363ndash372 (2002)[593] P Vandergheynst J-P Antoine E Van Vyve A Goldberg I Doghri Modelling and
simulation of an impact test using wavelets analytical and finite element models Int JSolids Struct 38 5481ndash5508 (2001)
[594] L Vanhamme RD Fierro S Van Huffel R de Beer Fast removal of residual water inproton spectra J Magn Reson 132 197ndash203 (1998)
[595] J Ville Theacuteorie et applications de la notion de signal analytique Cacircbles et Trans 2 61ndash74(1948)
[596] J Voisin On some unitary representations of the Galilei group I Irreducible representa-tions J Math Phys 6 1519ndash1529 (1965)
[597] A Vourdas Analytic representations in quantum mechanics J Phys A Math Gen 39R65ndashR141 (2006)
[598] DF Walls Squeezed states of light Nature 306 141ndash146 (1983)[599] YK Wang FT Hioe Phase transition in the Dicke maser model Phys Rev A 7 831ndash836
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Recogn Artif Intell 26 1255011 (2012)[601] I Weinreich A construction of C1-wavelets on the two-dimensional sphere Appl Comput
Harmon Anal 10 1ndash26 (2001)[602] H Weyl Quantenmechanik und Gruppentheorie Z Phys 46 1ndash46 (1927)
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[603] Y Wiaux L Jacques P Vandergheynst Correspondence principle between spherical andEuclidean wavelets Astrophys J 632 15ndash28 (2005)
[604] Y Wiaux L Jacques P Vielva P Vandergheynst Fast directional correlation on the spherewith steerable filters Astrophys J 652 820ndash832 (2006)
[605] Y Wiaux JD McEwen P Vandergheynst O Blanc Exact reconstruction with directionalwavelets on the sphere Mon Not R Astron Soc 388 770ndash788 (2008)
[606] WM Wieland Complex Ashtekar variables and reality conditions for Holstrsquos action AnnHenri Poincareacute 13 425ndash448 (2012)
[607] EP Wigner On the quantum correction for thermodynamic equilibrium Phys Rev 40749ndash759 (1932)
[608] RM Willette RD Nowak Platelets A multiscale approach for recovering edges andsurfaces in photon-limited medical imaging IEEE Trans Med Imaging 22 332ndash350(2003)
[609] W Wisnoe P Gajan A Strzelecki C Lempereur J-M Matheacute The use of the two-dimensional wavelet transform in flow visualization processing in Progress in WaveletAnalysis and Applications (Proc Toulouse 1992) ed by Y Meyer S Roques (EdFrontiegraveres Gif-sur-Yvette 1993) pp 455ndash458
[610] K Woacutedkiewicz On the quantum mechanics of squeezed states J Modern Optics 34 941ndash948(1987)
[611] JA Yeazell M Mallalieu CR Stroud Jr Observation of the collapse and revival of aRydberg electronic wave packet Phys Rev Lett 64 2007ndash2010 (1990)
[612] JA Yeazell CR Stroud Jr Observation of fractional revivals in the evolution of aRydberg atomic wave packet Phys Rev A 43 5153ndash5156 (1991)
[613] HP Yuen Two-photon coherent states of the radiation field Phys Rev A 13 2226ndash2243(1976)
[614] J Zak Balian-Low theorem for Landau levels Phys Rev Lett 79 533ndash536 (1997)[615] J Zak Orthonormal sets of localized functions for a Landau level J Math Phys 39 4195ndash
4200 (1998) and references quoted there[616] AA Zakharova On the properties of generalized frames Math Notes 83 190ndash200 (2008)[617] W-M Zhang DH Feng R Gilmore Coherent states Theory and some applications Rev
Mod Phys 26 867ndash927 (1990)[618] I Zlatev W-M Zhang DH Feng Possibility that Schroumldingerrsquos conjecture for the
hydrogen atom coherent states is not attainable Phys Rev A 50 R1973ndashR1975 (1994)[619] WH Zurek Decoherence einselection and the quantum origins of the classical Rev Mod
Phys 75 715ndash775 (2003)[620] WH Zurek S Habib JP Paz Coherent states via decoherence Phys Rev Lett 70 1187ndash
1190 (1993)[621] K Zyczkowski Squeezed states in a quantum chaotic system J Phys A Math Theor 22
of SU(11) 81 296 297HilbertClowast-modules 164holomorphic 140nonholomorphic 151nonlinear 146of affine Galilei group 505of affine Poincareacute group 509of affine Weyl-Heisenberg group GaWH
497of compact semisimple Lie groups 174of Euclidean group E(n) 266of Galilei group G (11) 290of isochronous Galilei group 237of non-semisimple Lie groups 179of noncompact semisimple Lie groups 177of Poincareacute group Puarr
+(11) 283massless case 288
of Poincareacute group Puarr+(13) 279
of Schroumldinger group 508quasi-coherent states 186quaternionic 164
ST Ali et al Coherent States Wavelets and Their Generalizations Theoreticaland Mathematical Physics DOI 101007978-1-4614-8535-3copy Springer Science+Business Media New York 2014
573
574 Index
coherent states (CS) (cont)spin or SU(2) 175square integrable covariant 166 180 264vector (VCS) 73 108 112 170weighted 184 523
of affine Weyl-Heisenberg group GaWH497
of Poincareacute group Puarr+(11) 284
cohomology group 393 403coboundaries 403cochains 402cocycle 403
algebraic 387Cauchy 418Cauchy-Paul 354 419 425conical 418difference 417 462directional 416 440kinematical 499local 488metabolite-based 355 374minimal uncertainty 425multiselective 440on a graph 493on the sphere S
2 458on the sphere S
n 479on the torus T2 481steerable 439von Mises 440
wedgelet transform 455Wigner function 322Wigner-Ville transform 349Windowed Fourier or Gabor transform 349
ZZak transform 518
References
A Books and Theses
B Articles
Index
References 543
[Fol95] GB Folland A Course in Abstract Harmonic Analysis (CRC Press Boca Raton FL1995)
[Fre97] W Freeden M Schreiner T Gervens Constructive Approximation on the Spherewith Applications to Geomathematics (Clarendon Press Oxford 1997)
[Fue05] H Fuumlhr Abstract Harmonic Analysis of Continuous Wavelet Transforms LectureNotes in Mathematics vol 1863 (Springer Berlin Heidelberg 2005)
[Gaa73] SA Gaal Linear Analysis and Representation Theory (Springer Berlin 1973)[Gaz09] J-P Gazeau Coherent States in Quantum Physics (Wiley-VCH Berlin 2009)[Gel64] IM Gelfand NY Vilenkin Generalized Functions vol 4 (Academic New York
1964)[Gen13] G Gentili C Stoppato DC Struppa Regular Functions for a Quaternionic Variable
Springer Monographs in Mathematics (Springer Berlin 2013)[Gol81] H Goldstein C Poole J Safko Classical Mechanics 3rd edn (Addison-Wesley
Reading MA 1981)[Got66] K Gottfried Quantum Mechanics Fundamentals vol I (Benjamin New York and
Amsterdam 1966)[Grouml01] K Groumlchenig Foundations of Time-Frequency Analysis (Birkhaumluser Boston 2001)[Gun94] H Guumlnther NMR Spectroscopy 2nd edn (Wiley Chichester New York 1994)[Gui84] V Guillemin S Sternberg Symplectic Techniques in Physics (Cambridge University
Press Cambridge 1984)[Hei06] C Heil D Walnut (eds) Fundamental Papers in Wavelet Theory (Princeton Univer-
sity Press Princeton NJ 2006)[Hel78] S Helgason Differential Geometry Lie Groups and Symmetric Spaces (Academic
New York 1978)[Hel76] CW Helstrom Quantum Detection and Estimation Theory (Academic New York
1976)[Her89] G Herzberg Molecular Spectra and Molecular Structure Spectra of Diatomic
Molecules 2nd edn (Krieger Pub Malabar FL 1989)[Hil71] P Hilton U Stammbach A Course in Homological Algebra (Springer Berlin 1971)[H0l01] AS Holevo Statistical Structure of Quantum Theory (Springer Berlin 2001)[Hol95] M Holschneider Wavelets An Analysis Tool (Oxford University Press Oxford 1995)[Hon07] G Honnouvo Gabor analysis and wavelet transforms on some non-Euclidean 2-
dimensional manifolds PhD thesis Concordia University Montreal PQ Canada2007
[Hua63] LK Hua Harmonic Analysis of Functions of Several Complex Variables in the Clas-sical Domains Translations of Mathematical Monographs (American MathematicalSociety Providence RI 1963)
[Hum72] JE Humphreys Introduction to Lie Algebras and Representation Theory (SpringerBerlin 1972)
[Inouml54] E Inoumlnuuml A study of the unitary representations of the Galilei group in relation toquantum mechanics PhD thesis University of Ankara 1954
[Ino92] A Inomata H Kuratsuji CC Gerry Path Integrals and Coherent States of SU(2)and SU(11) (World Scientific Singapore 1992)
[Jac62] N Jacobson Lie Algebras (Interscience New York and London 1962)[Jac04] L Jacques Ondelettes repegraveres et couronne solaire Thegravese de Doctorat Univ Cath
Louvain Louvain-la-Neuve 2004[Jaf96] S Jaffard Y Meyer Wavelet Methods for Pointwise Regularity and Local Oscillations
of Functions Memoirs of the American Mathematical Society vol 143 (AmericanMathematical Society Providence RI 1996)
[Kah98] J-P Kahane PG Lemarieacute-Rieusset Fourier Series and Wavelets (Gordon and BreachLuxembourg 1995) French translation Seacuteries de Fourier et ondelettes (Cassini Paris1998)
[Kai94] G Kaiser A Friendly Guide to Wavelets (Birkhaumluser Boston 1994)[Kat76] T Kato Perturbation Theory for Linear Operators (Springer Berlin 1976)
544 References
[Kem37] EC Kemble Fundamental Principles of Quantum Mechanics (McGraw Hill NewYork 1937)
[Kir76] AA Kirillov Elements of the Theory of Representations (Springer Berlin 1976)[Kla68] JR Klauder ECG Sudarshan Fundamentals of Quantum Optics (Benjamin New
York 1968)[Kla85] JR Klauder BS Skagerstam Coherent States ndash Applications in Physics and
Mathematical Physics (World Scientific Singapore 1985)[Kla00] JR Klauder Beyond Conventional Quantization (Cambridge University Press Cam-
bridge 2000)[Kla11] JR Klauder A Modern Approach to Functional Integration (BirkhaumluserSpringer
New York 2011)[Kna96] AW Knapp Lie Groups Beyond an Introduction (Birkhaumluser Basel 1996 2nd edn
2002)[Kut12] G Kutyniok D Labate (eds) Shearlets Multiscale Analysis for Multivariate Data
(Birkhaumluser Boston 2012)[Lan81] L Landau E Lifchitz Mechanics 3rd edn (Pergamon Oxford1981)[Lan93] S Lang Algebra 3rd edn (Addison-Wesley Reading MA 1993)[Lie97] EH Lieb M Loss Analysis (American Mathematical Society Providence RI 1997)[Lip74] RL Lipsman Group Representations Lecture Notes in Mathematics vol 388
(Springer Berlin 1974)[Lyn82] PA Lynn An Introduction to the Analysis and Processing of Signals 2nd edn
(MacMillan London 1982)[Mac68] GW Mackey Induced Representations of Groups and Quantum Mechanics (Ben-
jamin New York 1968)[Mac76] GW Mackey Theory of Unitary Group Representations (University of Chicago
Press Chicago 1976)[Mad95] J Madore An Introduction to Noncommutative Differential Geometry and Its Physical
Applications (Cambridge University Press Cambridge 1995)[Mae94] S Maes The wavelet transform in signal processing with application to the extraction
of the speech modulation model features Thegravese de Doctorat Univ Cath LouvainLouvain-la-Neuve 1994
[Mag66] W Magnus F Oberhettinger RP Soni Formulas and Theorems for the SpecialFunctions of Mathematical Physics (Springer Berlin 1966)
[Mal99] SG Mallat A Wavelet Tour of Signal Processing 2nd edn (Academic San Diego1999)
[Mar82] D Marr Vision (Freeman San Francisco 1982)[Mes62] H Meschkowsky Hilbertsche Raumlume mit Kernfunktionen (Springer Berlin 1962)[Mey91] Y Meyer (ed) Wavelets and Applications (Proc Marseille 1989) (Masson and
Springer Paris and Berlin 1991)[Mey92] Y Meyer Les Ondelettes Algorithmes et Applications (Armand Colin Paris 1992)
English translation Wavelets Algorithms and Applications (SIAM Philadelphia1993)
[Mey00] CD Meyer Matrix Analysis and Applied Linear Algebra (SIAM Philadelphia 2000)[Mey93] Y Meyer S Roques (eds) Progress in Wavelet Analysis and Applications (Proc
Toulouse 1992) (Ed Frontiegraveres Gif-sur-Yvette 1993)[Mur90] R Murenzi Ondelettes multidimensionnelles et applications agrave lrsquoanalyse drsquoimages
Thegravese de Doctorat Univ Cath Louvain Louvain-la-Neuve 1990[vNe55] J von Neumann Mathematical Foundations of Quantum Mechanics (Princeton
University Press Princeton NJ 1955) (English translated by RT Byer)[Pap02] A Papoulis SU Pillai Probability Random Variables and Stochastic Processes 4th
edn (McGraw Hill New York 2002)[Par05] KR Parthasarathy Probability Measures on Metric Spaces (AMS Chelsea Publish-
ing Providence RI 2005)
References 545
[Pau85] T Paul Ondelettes et Meacutecanique Quantique Thegravese de doctorat Univ drsquoAix-MarseilleII 1985
[Per86] AM Perelomov Generalized Coherent States and Their Applications (SpringerBerlin 1986)
[Per05] G Peyreacute Geacuteomeacutetrie multi-eacutechelles pour les images et les textures Thegravese de doctoratEcole Polytechnique Palaiseau 2005
[Pru86] E Prugovecki Stochastic Quantum Mechanics and Quantum Spacetime (ReidelDordrecht 1986)
[Rau04] H Rauhut Time-frequency and wavelet analysis of functions with symmetry proper-ties PhD thesis TU Muumlnich 2004
[Ree80] M Reed B Simon Methods of Modern Mathematical Physics I Functional Analysis(Academic New York 1980)
[Rud62] W Rudin Fourier Analysis on Groups (Interscience New York 1962)[Sch96] FE Schroeck Jr Quantum Mechanics on Phase Space (Kluwer Dordrecht 1996)[Sch61] L Schwartz Meacutethodes matheacutematiques pour les sciences physiques (Hermann Paris
1961)[Scu97] MO Scully MS Zubairy Quantum Optics (Cambridge University Press Cam-
bridge 1997)[Sho50] JA Shohat JD Tamarkin The Problem of Moments (American Mathematical
Society Providence RI 1950)[Ste71] EM Stein G Weiss Introduction to Fourier Analysis on Euclidean Spaces (Prince-
ton University Press Princeton NJ 1971)[Str64] RF Streater AS Wightman PCT Spin and Statistics and All That (Benjamin New
York 1964)[Sug90] M Sugiura Unitary Representations and Harmonic Analysis An Introduction
(North-HollandKodansha Ltd Tokyo 1990)[Suv11] A Suvichakorn C Lemke A Schuck Jr J-P Antoine The continuous wavelet
transform in MRS Tutorial text Marie Curie Research Training Network FAST(2011) httpwwwfast-mariecurie-rtn-projecteuWavelet
[Tak79] M Takesaki Theory of Operator Algebras I (Springer New York 1979)[Ter88] A Terras Harmonic Analysis on Symmetric Spaces and Applications II (Springer
Berlin 1988)[Tho98] G Thonet New aspects of time-frequency analysis for biomedical signal processing
Thegravese de Doctorat EPFL Lausanne 1998[Tor95] B Torreacutesani Analyse continue par ondelettes (InterEacuteditionsCNRS Eacuteditions Paris
1995)[Unt87] A Unterberger Analyse harmonique et analyse pseudo-diffeacuterentielle du cocircne de
lumiegravere Asteacuterisque 156 1ndash201 (1987)[Unt91] A Unterberger Quantification relativiste Meacutem Soc Math France 44ndash45 1ndash215
(1991)[Van98] P Vandergheynst Ondelettes directionnelles et ondelettes sur la sphegravere Thegravese de
Doctorat Univ Cath Louvain Louvain-la-Neuve 1998[Var85] VS Varadarajan Geometry of Quantum Theory 2nd edn (Springer New York 1985)[Vet95] M Vetterli J Kovacevic Wavelets and Subband Coding (Prentice Hall Englewood
Cliffs NJ 1995)[Vil69] NJ Vilenkin Fonctions speacuteciales et theacuteorie de la repreacutesentation des groupes (Dunod
Paris 1969)[Wel03] GV Welland Beyond Wavelets (Academic New York 2003)[vWe86] C von Westenholz Differential Forms in Mathematical Physics (North-Holland
Amsterdam 1986)[Wey28] H Weyl Gruppentheorie und Quantenmechanik (Hirzel Leipzig 1928)[Wey31] H Weyl The Theory of Groups and Quantum Mechanics (Dover New York 1931)[Wic94] MV Wickerhauser Adapted Wavelet Analysis from Theory to Software (A K Peters
Wellesley MA 1994)
546 References
[Wis93] W Wisnoe Utilisation de la meacutethode de transformeacutee en ondelettes 2D pour lrsquoanalysede visualisation drsquoeacutecoulements Thegravese de Doctorat ENSAE Toulouse 1993
[Woj97] P Wojtaszczyk A Mathematical Introduction to Wavelets (Cambridge UniversityPress Cambridge 1997)
[Zac06] C Zachos D Fairlie T Curtright Quantum Mechanics in Phase Space An OverviewWith Selected Papers (World Scientific Publishing Singapore 2006)
B Articles
[1] P Abry R Baraniuk P Flandrin R Riedi D Veitch Multiscale nature of network trafficIEEE Signal Process Mag 19 28ndash46 (2002)
[2] MD Adams The JPEG-2000 still image compression standardhttpwwweceuvicca~frodopublicationsjpeg2000pdf
[3] SL Adler AC Millard Coherent states in quaternionic quantum mechanics J MathPhys 38 2117ndash2126 (1997)
[4] GS Agarwal K Tara Nonclassical properties of states generated by the excitation on acoherent state Phys Rev A 43 492ndash497 (1991)
[5] GS Agarwal E Wolf Calculus for functions of noncommuting operators and generalphase-space methods in quantum mechanics I Mapping theorems and ordering of func-tions of noncommuting operators Phys Rev D 2 2161ndash2186 (1970)
[6] GS Agarwal E Wolf Calculus for functions of noncommuting operators and generalphase-space methods in quantum mechanics II Quantum mechanics in phase space PhysRev D 2 2187ndash2205 (1970)
[7] GS Agarwal E Wolf Calculus for functions of noncommuting operators and generalphase-space methods in quantum mechanics III A generalized Wick theorem and multi-time mapping Phys Rev D 2 2206ndash2225 (1970)
[8] V Aldaya J Guerrero G Marmo Quantization on a Lie group Higher-order polariza-tions in Symmetry in Sciences X ed by B Gruber M Ramek (Plenum Press Nerw York1998) pp 1ndash36
[9] M Alexandrescu D Gibert G Hulot J-L Le Mouel G Saracco Worldwide waveletanalysis of geomagnetic jerks J Geophys Res B 101 21975ndash21994 (1996)
[10] G Alexanian A Pinzul A Stern Generalized coherent state approach to star productsand applications to the fuzzy sphere Nucl Phys B 600 531ndash547 (2001)
[11] ST Ali A geometrical property of POV-measures and systems of covariance in Differ-ential Geometric Methods in Mathematical Physics ed by HD Doebner SI AnderssonHR Petry Lecture Notes in Mathematics vol 905 (Springer Berlin 1982) pp 207ndash22
[12] ST Ali Commutative systems of covariance and a generalization of Mackeyrsquos imprimi-tivity theorem Canad Math Bull 27 390ndash397 (1984)
[13] ST Ali Stochastic localisation quantum mechanics on phase space and quantum space-time Riv Nuovo Cim 8(11) 1ndash128 (1985)
[14] ST Ali A general theorem on square-integrability Vector coherent states J Math Phys39 3954ndash3964 (1998)
[15] ST Ali J-P Antoine Coherent states of 1+1 dimensional Poincareacute group Squareintegrability and a relativistic Weyl transform Ann Inst H Poincareacute 51 23ndash44 (1989)
[16] ST Ali S De Biegravevre Coherent states and quantization on homogeneous spaces in GroupTheoretical Methods in Physics ed by H-D Doebner et al Lecture Notes in Mathematicsvol 313 (Springer Berlin 1988) pp 201ndash207
References 547
[17] ST Ali H-D Doebner Ordering problem in quantum mechanics Prime quantization anda physical interpretation Phys Rev A 41 1199ndash1210 (1990)
[18] ST Ali GG Emch Geometric quantization Modular reduction theory and coherentstates J Math Phys 27 2936ndash2943 (1986)
[19] ST Ali M Engliš J-P Gazeau Vector coherent states from Plancherelrsquos theorem andClifford algebras J Phys A 37 6067ndash6089 (2004)
[20] ST Ali MEH Ismail Some orthogonal polynomials arising from coherent states JPhys A 45 125203 (2012) (16pp)
[21] ST Ali UA Mueller Quantization of a classical system on a coadjoint orbit of thePoincareacute group in 1+1 dimensions J Math Phys 35 4405ndash4422 (1994)
[22] ST Ali E Prugovecki Systems of imprimitivity and representations of quantum mechan-ics on fuzzy phase spaces J Math Phys 18 219ndash228 (1977)
[23] ST Ali E Prugovecki Mathematical problems of stochastic quantum mechanics Har-monic analysis on phase space and quantum geometry Acta Appl Math 6 1ndash18 (1986)
[24] ST Ali E Prugovecki Extended harmonic analysis of phase space representation for theGalilei group Acta Appl Math 6 19ndash45 (1986)
[25] ST Ali E Prugovecki Harmonic analysis and systems of covariance for phase spacerepresentation of the Poincareacute group Acta Appl Math 6 47ndash62 (1986)
[26] ST Ali J-P Antoine J-P Gazeau De Sitter to Poincareacute contraction and relativisticcoherent states Ann Inst H Poincareacute 52 83ndash111 (1990)
[27] ST Ali J-P Antoine J-P Gazeau Square integrability of group representations onhomogeneous spaces I Reproducing triples and frames Ann Inst H Poincareacute 55 829ndash855 (1991)
[28] ST Ali J-P Antoine J-P Gazeau Square integrability of group representations onhomogeneous spaces II Coherent and quasi-coherent states The case of the Poincareacutegroup Ann Inst H Poincareacute 55 857ndash890 (1991)
[29] ST Ali J-P Antoine J-P Gazeau Continuous frames in Hilbert space Ann Phys(NY)222 1ndash37 (1993)
[30] ST Ali J-P Antoine J-P Gazeau Relativistic quantum frames Ann Phys(NY) 222 38ndash88 (1993)
[31] ST Ali J-P Antoine J-P Gazeau UA Mueller Coherent states and their generalizationsA mathematical overview Rev Math Phys 7 1013ndash1104 (1995)
[32] ST Ali J-P Gazeau MR Karim Frames the β -duality in Minkowski space and spincoherent states J Phys A Math Gen 29 5529ndash5549 (1996)
[33] ST Ali M Engliš Quantization methods A guide for physicists and analysts Rev MathPhys 17 391ndash490 (2005)
[34] ST Ali J-P Gazeau B Heller Coherent states and Bayesian duality J Phys A MathTheor 41 365302 (2008)
[35] ST Ali L Balkovaacute EMF Curado J-P Gazeau MA Rego-Monteiro LMCSRodrigues K Sekimoto Non-commutative reading of the complex plane through Delonesequences J Math Phys 50 043517 (2009)
[36] ST Ali C Carmeli T Heinosaari A Toigo Commutative POVMS and fuzzy observ-ables Found Phys 39 593ndash612 (2009)
[37] ST Ali T Bhattacharyya SS Roy Coherent states on Hilbert modules J Phys A MathTheor 44 275202 (2011)
[38] ST Ali J-P Antoine F Bagarello J-P Gazeau (Guest Editors) Coherent states Acontemporary panorama preface to a special issue on Coherent states Mathematical andphysical aspects J Phys A Math Gen 45(24) (2012)
[39] ST Ali F Bagarello J-P Gazeau Quantizations from reproducing kernel spaces AnnPhys (NY) 332 127ndash142 (2013)
[40] STAli K Goacuterska A Horzela F Szafraniec Squeezed states and Hermite polynomials ina complex variable Preprint (2013) arXiv13084730v1 [quant-phy]
[41] P Aniello G Cassinelli E De Vito A Levrero Square-integrability of induced represen-tations of semidirect products Rev Math Phys 10 301ndash313 (1998)
548 References
[42] P Aniello G Cassinelli E De Vito A Levrero Wavelet transforms and discrete framesassociated to semidirect products J Math Phys 39 3965ndash3973 (1998)
[43] J-P Antoine Remarques sur le vecteur de Runge-Lenz Ann Soc Scient Bruxelles 80160ndash168 (1966)
[44] J-P Antoine Etude de la deacutegeacuteneacuterescence orbitale du potentiel coulombien en theacuteorie desgroupes I II Ann Soc Scient Bruxelles 80 169ndash184 (1966)
[45] J-P Antoine Etude de la deacutegeacuteneacuterescence orbitale du potentiel coulombien en theacuteorie desgroupes I II Ann Soc Scient Bruxelles 81 49ndash68 (1967)
[46] J-P Antoine Dirac formalism and symmetry problems in quantum mechanics I Generaldirac formalism J Math Phys 10 53ndash69 (1969)
[47] J-P Antoine Dirac formalism and symmetry problems in quantum mechanics II Symme-try problems J Math Phys 10 2276ndash2290 (1969)
[48] J-P Antoine Quantum mechanics beyond Hilbert space in Irreversibility and Causality mdashSemigroups and Rigged Hilbert Spaces ed by A Boumlhm H-D Doebner P KielanowskiLecture Notes in Physics vol 504 (Springer Berlin 1998) pp 3ndash33
[49] J-P Antoine Discrete wavelets on abelian locally compact groups Rev Cien Math(Habana) 19 3ndash21 (2003)
[50] J-P Antoine Introduction to precursors in physics Affine coherent states in FundamentalPapers in Wavelet Theory ed by C Heil D Walnut (Princeton University Press PrincetonNJ 2006) pp 113ndash116
[51] J-P Antoine F Bagarello Wavelet-like orthonormal bases for the lowest Landau levelJ Phys A Math Gen 27 2471ndash2481 (1994)
[52] J-P Antoine P Balazs Frames and semi-frames J Phys A Math Theor 44 205201(2011) (25 pages) Corrigendum J-P Antoine P Balazs Frames and semi-frames J PhysA Math Theor 44 479501 (2011) (2 pages)
[53] J-P Antoine P Balazs Frames semi-frames and Hilbert scales Numer Funct AnalOptim 33 736ndash769 (2012)
[54] J-P Antoine A Coron Time-frequency and time-scale approach to magnetic resonancespectroscopy J Comput Methods Sci Eng (JCMSE) 1 327ndash352 (2001)
[55] J-P Antoine AL Hohoueacuteto Discrete frames of Poincareacute coherent states in 1+3 dimen-sions J Fourier Anal Appl 9 141ndash173 (2003)
[56] J-P Antoine I Mahara Galilean wavelets Coherent states for the affine Galilei groupJ Math Phys 40 5956ndash5971 (1999)
[57] J-P Antoine U Moschella Poincareacute coherent states The two-dimensional massless caseJ Phys A Math Gen 26 591ndash607 (1993)
[58] J-P Antoine R Murenzi Two-dimensional directional wavelets and the scale-anglerepresentation Signal Process 52 259ndash281 (1996)
[59] J-P Antoine R Murenzi Two-dimensional continuous wavelet transform as linear phasespace representation of two-dimensional signals in Wavelet Applications IV SPIE Pro-ceedings vol 3078 (SPIE Bellingham WA 1997) pp 206ndash217
[60] J-P Antoine D Rosca The wavelet transform on the two-sphere and related manifolds mdashA review in Optical and Digital Image Processing SPIE Proceedings vol 7000 (2008)pp 70000B-1ndash15
[61] J-P Antoine D Speiser Characters of irreducible representations of simple Lie groupsJ Math Phys 5 1226ndash1234 (1964)
[62] J-P Antoine P Vandergheynst Wavelets on the n-sphere and related manifolds J MathPhys 39 3987ndash4008 (1998)
[63] J-P Antoine P Vandergheynst Wavelets on the 2-sphere A group-theoretical approachAppl Comput Harmon Anal 7 262ndash291 (1999)
[64] J-P Antoine P Vandergheynst Wavelets on the two-sphere and other conic sections JFourier Anal Appl 13 369ndash386 (2007)
[65] J-P Antoine M Duval-Destin R Murenzi B Piette Image analysis with 2D wavelettransform Detection of position orientation and visual contrast of simple objects inWavelets and Applications (Proc Marseille 1989) ed by Y Meyer (Masson and SpringerParis and Berlin 1991) pp144ndash159
References 549
[66] J-P Antoine P Carrette R Murenzi B Piette Image analysis with 2D continuous wavelettransform Signal Process 31 241ndash272 (1993)
[67] J-P Antoine P Vandergheynst K Bouyoucef R Murenzi Alternative representations ofan image via the 2D wavelet transform Application to character recognition in VisualInformation Processing IV SPIE Proceedings vol 2488 (SPIE Bellingham WA 1995)pp 486ndash497
[68] J-P Antoine R Murenzi P Vandergheynst Two-dimensional directional wavelets inimage processing Int J Imaging Syst Tech 7 152ndash165 (1996)
[69] J-P Antoine D Barache RM Cesar Jr LF Costa Shape characterization with thewavelet transform Signal Process 62 265ndash290 (1997)
[70] J-P Antoine P Antoine B Piraux Wavelets in atomic physics in Spline Functions andthe Theory of Wavelets ed by S Dubuc G Deslauriers CRM Proceedings and LectureNotes vol 18 (AMS Providence RI 1999) pp261ndash276
[71] J-P Antoine P Antoine B Piraux Wavelets in atomic physics and in solid state physicsin Wavelets in Physics Chap 8 ed by JC van den Berg (Cambridge University PressCambridge 1999)
[72] J-P Antoine R Murenzi P Vandergheynst Directional wavelets revisited Cauchywavelets and symmetry detection in patterns Appl Comput Harmon Anal 6 314ndash345(1999)
[73] J-P Antoine L Jacques R Twarock Wavelet analysis of a quasiperiodic tiling withfivefold symmetry Phys Lett A 261 265ndash274 (1999)
[74] J-P Antoine L Jacques P Vandergheynst Penrose tilings quasicrystals and wavelets inWavelet Applications in Signal and Image Processing VII SPIE Proceedings vol 3813(SPIE Bellingham WA 1999) pp 28ndash39
[75] J-P Antoine YB Kouagou D Lambert B Torreacutesani An algebraic approach to discretedilations Application to discrete wavelet transforms J Fourier Anal Appl 6 113ndash141(2000)
[76] J-P Antoine A Coron J-M Dereppe Water peak suppression Time-frequency vs time-scale approach J Magn Reson 144 189ndash194 (2000)
[77] J-P Antoine J-P Gazeau P Monceau J R Klauder K Penson Temporally stablecoherent states for infinite well and Poumlschl-Teller potentials J Math Phys 42 2349ndash2387(2001)
[78] J-P Antoine A Coron C Chauvin Wavelets and related time-frequency techniques inmagnetic resonance spectroscopy NMR Biomed 14 265ndash270 (2001)
[79] J-P Antoine L Demanet J-F Hochedez L Jacques R Terrier E Verwichte Applicationof the 2-D wavelet transform to astrophysical images Phys Mag 24 93ndash116 (2002)
[80] J-P Antoine L Demanet L Jacques P Vandergheynst Wavelets on the sphere Imple-mentation and approximations Appl Comput Harmon Anal 13 177ndash200 (2002)
[81] J-P Antoine I Bogdanova P Vandergheynst The continuous wavelet transform on conicsections Int J Wavelets Multires Inform Proc 6 137ndash156 (2007)
[82] J-P Antoine D Rosca P Vandergheynst Wavelet transform on manifolds Old and newapproaches Appl Comput Harmon Anal 28 189ndash202 (2010)
[83] P Antoine B Piraux A Maquet Time profile of harmonics generated by a single atom ina strong electromagnetic field Phys Rev A 51 R1750ndashR1753 (1995)
[84] P Antoine B Piraux DB Miloševic M Gajda Generation of ultrashort pulses ofharmonics Phys Rev A 54 R1761ndashR1764 (1996)
[85] P Antoine B Piraux DB Miloševic M Gajda Temporal profile and time control ofharmonic generation Laser Phys 7 594ndash601 (1997)
[86] Apollonius see Wikipedia httpenwikipediaorgwikiApollonius_of_Perga[87] FT Arecchi E Courtens R Gilmore H Thomas Atomic coherent states in quantum
optics Phys Rev A 6 2211ndash2237 (1972)[88] I Aremua J-P Gazeau MN Hounkonnou Action-angle coherent states for quantum
systems with cylindric phase space J Phys A Math Theor 45 335302 (2012)
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[90] F Argoul A Arneacuteodo J Elezgaray G Grasseau R Murenzi Wavelet analysis of theself-similarity of diffusion-limited aggregates and electrodeposition clusters Phys Rev A41 5537ndash5560 (1990)
[91] TA Arias Multiresolution analysis of electronic structure Semicardinal and waveletbases Rev Mod Phys 71 267ndash312 (1999)
[92] A Arneacuteodo F Argoul E Bacry J Elezgaray E Freysz G Grasseau JF Muzy BPouligny Wavelet transform of fractals in Wavelets and Applications (Proc Marseille1989) ed by Y Meyer (Masson and Springer Paris and Berlin 1991) pp 286ndash352
[93] A Arneacuteodo E Bacry JF Muzy The thermodynamics of fractals revisited with waveletsPhysica A 213 232ndash275 (1995)
[94] A Arneacuteodo E Bacry JF Muzy Oscillating singularities in locally self-similar functionsPhys Rev Lett 74 4823ndash4826 (1995)
[95] A Arneacuteodo E Bacry PV Graves JF Muzy Characterizing long-range correlations inDNA sequences from wavelet analysis Phys Rev Lett 74 3293ndash3296 (1996)
[96] A Arneacuteodo Y drsquoAubenton E Bacry PV Graves JF Muzy C Thermes Wavelet basedfractal analysis of DNA sequences Physica D 96 291ndash320 (1996)
[97] A Arneacuteodo E Bacry S Jaffard JF Muzy Oscillating singularities on Cantor sets Agrand canonical multifractal formalism J Stat Phys 87 179ndash209 (1997)
[98] A Arneacuteodo E Bacry S Jaffard JF Muzy Singularity spectrum of multifractal functionsinvolving oscillating singularities J Fourier Anal Appl 4 159ndash174 (1998)
[99] N Aronszajn Theory of reproducing kernels Trans Amer Math Soc 66 337ndash404 (1950)[100] A Ashtekar J Lewandowski D Marolf J Mouratildeo T Thiemann Coherent state
transforms for spaces of connections J Funct Analysis 135 519ndash551 (1996)[101] A Askari-Hemmat MA Dehghan M Radjabalipour Generalized frames and their
redundancy Proc Amer Math Soc 129 1143ndash1147 (2001)[102] EW Aslaksen JR Klauder Unitary representations of the affine group J Math Phys 9
206ndash211 (1968)[103] EW Aslaksen JR Klauder Continuous representation theory using the affine group
J Math Phys 10 2267ndash2275 (1969)[104] D Astruc L Plantieacute R Murenzi Y Lebret D Vandromme On the use of the 3D
wavelet transform for the analysis of computational fluid dynamics results in Progressin Wavelet Analysis and Applications (Proc Toulouse 1992) ed by Y Meyer S Roques(Ed Frontiegraveres Gif-sur-Yvette 1993) pp 463ndash470
[105] PW Atkins JC Dobson Angular momentum coherent states Proc Roy Soc London A321 321ndash340 (1971)
[106] BW Atkinson DO Bruff JS Geronimo D P Hardin Wavelets centered on a knotsequence Piecewise polynomial wavelets on a quasi-crystal lattice preprint (2011)arXiv11024246v1 [mathNA]
[107] IS Averbuch NF Perelman Fractional revivals Universality in the long-term evolutionof quantum wave packets beyond the correspondence principle dynamics Phys Lett A139 449ndash453 (1989)
[108] H Bacry J-M Leacutevy-Leblond Possible kinematics J Math Phys 9 1605ndash1614 (1968)[109] H Bacry A Grossmann J Zak Proof of the completeness of lattice states in kq
representation Phys Rev B 12 1118ndash1120 (1975)[110] L Baggett KF Taylor Groups with completely reducible regular representation Proc
Amer Math Soc 72 593ndash600 (1978)[111] VG Bagrov J-P Gazeau D Gitman A Levine Coherent states and related quantizations
for unbounded motions J Phys A Math Theor 45 125306 (2012) arXiv12010955v2[quant-ph]
[112] P Balazs J-P Antoine A Grybos Weighted and controlled frames Mutual relationshipand first numerical properties Int J Wavelets Multires Inform Proc 8 109ndash132 (2010)
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[114] P Balazs D Bayer A Rahimi Multipliers for continuous frames in Hilbert spaces JPhys A Math Gen 45 244023 (2012)
[115] P Baldi G Kerkyacharian D Marinucci D Picard High frequency asymptotics forwavelet-based tests for Gaussianity and isotropy on the torus J Multivar Anal 99 606ndash636 (2008)
[116] P Baldi G Kerkyacharian D Marinucci D Picard Asymptotics for spherical needletsAnn of Stat 37 1150ndash1171 (2009)
[117] MC Baldiotti J-P Gazeau DM Gitman Coherent states of a particle in magnetic fieldand Stieltjes moment problem Phys Lett A 373 1916ndash1920 (2009) Erratum Phys LettA 373 2600 (2009)
[118] MC Baldiotti J-P Gazeau DM Gitman Semiclassical and quantum description ofmotion on the noncommutative plane Phys Lett A 373 3937ndash3943 (2009)
[119] R Balian Un principe drsquoincertitude fort en theacuteorie du signal ou en meacutecanique quantiqueCR Acad Sci(Paris) 292 1357ndash1362 (1981)
[120] M Bander C Itzykson Group theory and the hydrogen atom I II Rev Mod Phys 38330ndash345 346ndash358 (1966)
[121] D Barache S De Biegravevre J-P Gazeau Affine symmetry semigroups for quasicrystalsEurophys Lett 25 435ndash440 (1994)
[122] D Barache J-P Antoine J-M Dereppe The continuous wavelet transform a tool for NMRspectroscopy J Magn Reson 128 1ndash11 (1997)
[123] V Bargmann On a Hilbert space of analytic functions and an associated integral transformPart I Commun Pure Appl Math 14 187ndash214 (1961)
[124] V Bargmann On a Hilbert space of analytic functions and an associated integral transformPart II A family of related function spaces Application to distribution theory CommunPure Appl Math 20 1ndash101 (1967)
[125] V Bargmann P Butera L Girardello JR Klauder On the completeness of coherentstates Reports Math Phys 2 221ndash228 (1971)
[126] AO Barut L Girardello New ldquocoherentrdquo states associated with non compact groupsCommun Math Phys 21 41ndash55 (1971)
[127] AO Barut H Kleinert Transition probabilities of the hydrogen atom from noncompactdynamical groups Phys Rev 156 1541ndash1545 (1967)
[128] AO Barut BW Xu Non-spreading coherent states riding on Kepler orbits Helv PhysActa 66 711ndash720 (1993)
[129] G Battle Wavelets A renormalization group point of view in Wavelets and TheirApplications ed by MB Ruskai G Beylkin R Coifman I Daubechies S Mallat YMeyer L Raphael (Jones and Bartlett Boston 1992) pp 323ndash349
[130] P Bellomo CR Stroud Jr Dispersion of Klauderrsquos temporally stable coherent states forthe hydrogen atom J Phys A Math Gen 31 L445ndashL450 (1998)
[131] J Ben Geloun J R Klauder Ladder operators and coherent states for continuous spectraJ Phys A Math Theor 42 375209 (2009)
[132] J Ben Geloun J Hnybida JR Klauder Coherent states for continuous spectrum operatorswith non-normalizable fiducial states J Phys A Math Theor 45 085301 (2012)
[133] JJ Benedetto TD Andrews Intrinsic wavelet and frame applications in IndependentComponent Analyses Wavelets Neural Networks Biosystems and Nanoengineering IXed by H Szu L Dai SPIE Proceedings vol 8058 (SPIE Bellingham WA 2011) p805802
[134] JJ Benedetto A Teolis A wavelet auditory model and data compression Appl ComputHarmon Anal 1 3ndash28 (1993)
[135] FA Berezin Quantization Math USSR Izvestija 8 1109ndash1165 (1974)[136] FA Berezin General concept of quantization Commun Math Phys 40 153ndash174 (1975)[137] H Bergeron From classical to quantum mechanics How to translate physical ideas into
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[139] H Bergeron and J-P Gazeau Integral quantization with two basic examples Preprint(2013) arXiv13082348v1
[140] H Bergeron A Valance Overcomplete basis for one dimensional Hamiltonians J MathPhys 36 1572ndash1592 (1995)
[141] H Bergeron J-P Gazeau P Siegl A Youssef Semi-classical behavior of Poumlschl-Tellercoherent states Eur Phys Lett 92 60003 (2010)
[142] H Bergeron P Siegl A Youssef New SUSYQM coherent states for Poumlschl-Tellerpotentials A detailed mathematical analysis J Phys A Math Theor 45 244028 (2012)
[143] H Bergeron J-P Gazeau A Youssef Are the Weyl and coherent state descriptionsphysically equivalent Phys Lett A 377 598ndash605 (2013)
[144] H Bergeron A Dapor J-P Gazeau P Małkiewicz Wavelet quantum cosmology preprint(2013) arXiv13050653 [gr-qc]
[145] S Bergman Uumlber die Kernfunktion eines Bereiches und ihr Verhalten am Rande I ReineAngw Math 169 1ndash42 (1933)
[146] D Bernier KF Taylor Wavelets from square-integrable representations SIAM J MathAnal 27 594ndash608 (1996)
[147] G Bernuau Wavelet bases associated to a self-similar quasicrystal J Math Phys 394213ndash4225 (1998)
[148] A Bertrand Deacuteveloppements en base de Pisot et reacutepartition modulo 1 C R Acad SciParis 285 419ndash421 (1977)
[149] J Bertrand P Bertrand Classification of affine Wigner functions via an extendedcovariance principle in Group Theoretical Methods in Physics (Proc Sainte-Adegravele 1988)ed by Y Saint-Aubin L Vinet (World Scientific Singapore 1989) pp 1380ndash1383
[150] Z Białynicka-Birula I Białynicki-Birula Space-time description of squeezing J OptSoc Am B4 1621ndash1626 (1987)
[151] E Bianchi E Magliaro C Perini Coherent spin-networks Phys Rev D 82 024012(2010)
[152] S Biskri J-P Antoine B Inhester F Mekideche Extraction of Solar coronal magneticloops with the 2-D Morlet wavelet transform Solar Phys 262 373ndash385 (2010)
[153] R Bluhm VA Kostelecky JA Porter The evolution and revival structure of localizedquantum wave packets Am J Phys 64 944ndash953 (1996)
[154] I Bogdanova P Vandergheynst J-P Antoine L Jacques M Morvidone Stereographicwavelet frames on the sphere Appl Comput Harmon Anal 19 223ndash252 (2005)
[155] I Bogdanova X Bresson J-P Thiran P Vandergheynst Scale space analysis and activecontours for omnidirectional images IEEE Trans Image Process 16 1888ndash1901 (2007)
[156] I Bogdanova P Vandergheynst J-P Gazeau Continuous wavelet transform on thehyperboloid Appl Comput Harmon Anal 23 (2007) 286ndash306 (2007)
[157] P Boggiatto E Cordero Anti-Wick quantization of tempered distributions in Progress inAnalysis Berlin (2001) vol I II (World Sci Publ River Edge NJ 2003) pp 655ndash662
[158] P Boggiatto E Cordero K Groumlchenig Generalized Anti-Wick operators with symbols indistributional Sobolev spaces Int Equ Oper Theory 48 427ndash442 (2004)
[159] A Boumlhm The Rigged Hilbert Space in quantum mechanics in Lectures in TheoreticalPhysics vol IX A ed by WA Brittin et al (Gordon amp Breach New York 1967) pp255ndash315
[160] G Bohnkeacute Treillis drsquoondelettes associeacutes aux groupes de Lorentz Ann Inst H Poincareacute54 245ndash259 (1991)
[161] WR Bomstad JR Klauder Linearized quantum gravity using the projection operatorformalism Class Quantum Grav 23 5961ndash5981 (2006)
[162] VV Borzov Orthogonal polynomials and generalized oscillator algebras Int TransformSpec Funct 12 115ndash138 (2001)
[163] VV Borzov EV Damaskinsky Generalized coherent states for classical orthogonalpolynomials Day on Diffraction (2002) arXivmathQA0209181v1 (SPb 2002)
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[165] A Bouzouina S De Biegravevre Equipartition of the eigenfunctions of quantized ergodic mapson the torus Commun Math Phys 178 83ndash105 (1996)
[166] P Brault J-P Antoine A spatio-temporal Gaussian-Conical wavelet with high apertureselectivity for motion and speed analysis Appl Comput Harmon Anal 34 148ndash161(2012)
[167] A Briguet S Cavassila D Graveron-Demilly Suppression of huge signals using theCadzow enhancement procedure The NMR Newslett 440 26 (1995)
[168] CM Brislawn Fingerprints go digital Notices Amer Math Soc 42 1278ndash1283 (1995)[169] CM Brislawn On the group-theoretic structure of lifted filter banks in Excursions in
Harmonic Analysis vol 1 2 ed by TD Andrews R Balan JJ Benedetto W CzajaKA Okoudjou (Birkhaumluser Boston 2013) pp 113ndash135
[170] F Bruhat Sur les repreacutesentations induites des groupes de Lie Bull Soc Math France 8497ndash205 (1956)
[171] T Buumllow Multiscale image processing on the sphere in DAGM-Symposium (2002) pp609ndash617
[172] C Burdik C Frougny J-P Gazeau R Krejcar Beta-integers as natural counting systemsfor quasicrystals J Phys A Math Gen 31 6449ndash6472 (1998)
[173] KE Cahill Coherent-state representations for the photon density Phys Rev 138 B1566ndash1576 (1965)
[174] KE Cahill R Glauber Density operators and quasiprobability distributions Phys Rev177 1882ndash1902 (1969)
[175] KE Cahill R Glauber Ordered expansions in boson amplitude operators Phys Rev 1771857ndash1881 (1969)
[176] AR Calderbank I Daubechies W Sweldens BL Yeo Wavelets that map integers tointegers Appl Comput Harmon Anal 5 332ndash369 (1998)
[177] M Calixto J Guerrero Wavelet transform on the circle and the real line A unified group-theoretical treatment Appl Comput Harmon Anal 21 204ndash229 (2006)
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[180] EJ Candegraves Harmonic analysis of neural networks Appl Comput Harmon Anal 6 197ndash218 (1999)
[181] EJ Candegraves Ridgelets and the representation of mutilated Sobolev functions SIAM JMath Anal 33 347ndash368 (2001)
[182] EJ Candegraves L Demanet Curvelets and Fourier integral operators CR Acad Sci ParisSeacuter I Math 336 395ndash398 (2003)
[183] EJ Candegraves L Demanet The curvelet representation of wave propagators is optimallysparse Commun Pure Appl Math 58 1472ndash1528 (2004)
[184] EJ Candegraves L Demanet The curvelet representation of wave propagators is optimallysparse Commun Pure Appl Math 58 1472ndash1528 (2005)
[185] EJ Candegraves DL Donoho Curvelets ndash A surprisingly effective nonadaptive representationfor objects with edges in Curves and Surfaces ed by LL Schumaker et al (VanderbiltUniversity Press Nashville TN 1999)
[186] EJ Candegraves DL Donoho Ridgelets A key to higher-dimensional intermittency PhilTrans R Soc Lond A 357 2495ndash2509 (1999)
[187] EJ Candegraves DL Donoho Curvelets multiresolution representation and scaling laws inWavelet Applications in Signal and Image Processing VIII ed by A Aldroubi A LaineM Unser SPIE Proceedings vol 4119 (SPIE Bellingham WA 2000) pp 1ndash12
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[189] EJ Candegraves DL Donoho New tight frames of curvelets and optimal representations ofobjects with piecewise C2 singularities Commun Pure Appl Math 57 219ndash266 (2004)
[190] EJ Candegraves DL Donoho Continuous curvelet transform I Resolution of the wavefrontset II Discretization and frames Appl Comput Harmon Anal 19 162ndash197 198ndash222(2005)
[191] EJ Candegraves F Guo New multiscale transforms minimum total variationsynthesisApplications to edge-preserving image reconstruction Signal Proc 82 1519ndash1543 (2002)
[192] EJ Candegraves L Demanet D Donoho L Ying Fast discrete curvelet transforms MultiscaleModel Simul 5 861ndash899 (2006)
[193] AL Carey Square integrable representations of non-unimodular groups Bull AustrMath Soc 15 1ndash12 (1976)
[194] AL Carey Group representations in reproducing kernel Hilbert spaces Rep Math Phys14 247ndash259 (1978)
[195] P Carruthers MM Nieto Phase and angle variables in quantum mechanics Rev ModPhys 40 411ndash440 (1968)
[196] PG Casazza G Kutyniok Frames of subspaces in Wavelets Frames and Operator The-ory Contemporary Mathematics vol 345 (American Mathematical Society ProvidenceRI 2004) pp 87ndash113
[197] PG Casazza D Han DR Larson Frames for Banach spaces Contemp Math 247 149ndash182 (1999)
[198] P Casazza O Christensen S Li A Lindner Riesz-Fischer sequences and lower framebounds Z Anal Anwend 21 305ndash314 (2002)
[199] PG Casazza G Kutyniok S Li Fusion frames and distributed processing ApplComputHarmon Anal 25 114ndash132 (2008)
[200] DPL Castrigiano RW Henrichs Systems of covariance and subrepresentations ofinduced representations Lett Math Phys 4 169ndash175 (1980)
[201] U Cattaneo Densities of covariant observables J Math Phys 23 659ndash664 (1982)[202] A Cerioni L Genovese I Duchemin Th Deutsch Accurate complex scaling of three
dimensional numerical potentials Preprint (2013) arXiv13036439v2[203] S-J Chang K-J Shi Evolution and exact eigenstates of a resonant quantum system Phys
Rev A 34 7ndash22 (1986)[204] SHH Chowdhury ST Ali All the groups of signal analysis from the (1+1) affine Galilei
group J Math Phys 52 103504 (2011)[205] SL Chown Antarctic marine biodiversity and deep-sea hydrothermal vents PLoS Biol
10 1ndash4 (2012)[206] C Cishahayo S De Biegravevre On the contraction of the discrete series of SU(11) Ann Inst
Fourier (Grenoble) 43 551ndash567 (1993)[207] M Clerc and S Mallat Shape from texture and shading with wavelets in Dynamical
Systems Control Coding Computer Vision Progress in Systems and Control Theory 25393ndash417 (1999)
[208] L Cohen General phase-space distribution functions J Math Phys 7 781ndash786 (1966)[209] A Cohen I Daubechies J-C Feauveau Biorthogonal bases of compactly supported
wavelets Commun Pure Appl Math 45 485ndash560 (1992)[210] R Coifman Y Meyer MV Wickerhauser Wavelet analysis and signal processing
in Wavelets and Their Applications ed by MB Ruskai G Beylkin R CoifmanI Daubechies S Mallat Y Meyer L Raphael (Jones and Bartlett Boston 1992)pp 153ndash178
[211] R Coifman Y Meyer MV Wickerhauser Entropy-based algorithms for best basisselection IEEE Trans Inform Theory 38 713ndash718 (1992)
[212] R Coquereaux A Jadczyk Conformal theories curved spaces relativistic wavelets andthe geometry of complex domains Rev Math Phys 2 1ndash44 (1990)
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[213] A Coron L Vanhamme J-P Antoine P Van Hecke S Van Huffel The filtering approachto solvent peak suppression in MRS A critical review J Magn Reson 152 26ndash40 (2001)
[214] N Cotfas J-P Gazeau Finite tight frames and some applications (topical review) J PhysA Math Theor 43 193001 (2010)
[215] N Cotfas J-P Gazeau K Goacuterska Complex and real Hermite polynomials and relatedquantizations J Phys A Math Theor 43 305304 (2010)
[216] N Cotfas J-P Gazeau A Vourdas Finite-dimensional Hilbert space and frame quantiza-tion J Phys A Math Gen 44 175303 (2011)
[217] EMF Curado MA Rego-Monteiro LMCS Rodrigues Y Hassouni Coherent statesfor a degenerate system The hydrogen atom Physica A 371 16ndash19 (2006)
[218] S Dahlke P Maass The affine uncertainty principle in one and two dimensions CompMath Appl 30 293ndash305 (1995)
[219] S Dahlke W Dahmen E Schmidt I Weinreich Multiresolution analysis and wavelets onS
2 and S3 Numer Funct Anal Optim 16 19ndash41 (1995)
[220] S Dahlke V Lehmann G Teschke Applications of wavelet methods to the analysis ofmeteorological radar data - An overview Arabian J Sci Eng 28 3ndash44 (2003)
[221] S Dahlke G Kutyniok P Maass C Sagiv H-G Stark G Teschke The uncertaintyprinciple associated with the continuous shearlet transform Int J Wavelets MultiresolutInf Process 6 157ndash181 (2008)
[222] S Dahlke G Kutyniok G Steidl G Teschke Shearlet coorbit spaces and associatedBanach frames Appl Comput Harmon Anal 27 195ndash214 (2009)
[223] S Dahlke G Steidl G Teschke The continuous shearlet transform in arbitrary spacedimensions J Fourier Anal Appl 16 340ndash364 (2010)
[224] S Dahlke G Steidl G Teschke Shearlet coorbit spaces Compactly supported analyzingshearlets traces and embeddings J Fourier Anal Appl 17 1232ndash1355 (2011)
[225] T Dallard GR Spedding 2-D wavelet transforms Generalisation of the Hardy space andapplication to experimental studies Eur J Mech BFluids 12 107ndash134 (1993)
[226] C Daskaloyannis Generalized deformed oscillator and nonlinear algebras J Phys AMath Gen 24 L789ndashL794 (1991)
[227] C Daskaloyannis K Ypsilantis A deformed oscillator with Coulomb energy spectrumJ Phys A Math Gen 25 4157ndash4166 (1992)
[228] I Daubechies On the distributions corresponding to bounded operators in the Weylquantization Commun Math Phys 75 229ndash238 (1980)
[229] I Daubechies and A Grossmann An integral transform related to quantization I J MathPhys 21 2080ndash2090 (1980)
[230] I Daubechies A Grossmann J Reignier An integral transform related to quantization IIJ Math Phys 24 239ndash254 (1983)
[231] I Daubechies Orthonormal bases of compactly supported wavelets Commun Pure ApplMath 41 909ndash996 (1988)
[232] I Daubechies The wavelet transform time-frequency localisation and signal analysisIEEE Trans Inform Theory 36 961ndash1005 (1990)
[233] I Daubechies S Maes A nonlinear squeezing of the continuous wavelet transform basedon auditory nerve models in Wavelets in Medicine and Biology ed by A Aldroubi MUnser (CRC Press Boca Raton 1996) pp 527ndash546
[234] I Daubechies A Grossmann Y Meyer Painless nonorthogonal expansions J Math Phys27 1271ndash1283 (1986)
[235] ER Davies Introduction to texture analysis in Handbook of texture analysis ed by MMirmehdi X Xie J Suri (World Scientific Singapore 2008) pp 1ndash31
[236] R De Beer D van Ormondt FTAW Wajer S Cavassila D Graveron-Demilly S VanHuffel SVD-based modelling of medical NMR signals in SVD and Signal ProcessingIII Algorithms Architectures and Applications ed by M Moonen B De Moor (Elsevier(North-Holland) Amsterdam 1995) pp 467ndash474
[237] S De Biegravevre Coherent states over symplectic homogeneous spaces J Math Phys 301401ndash1407 (1989)
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[238] S De Biegravevre JA Gonzalez Semi-classical behaviour of the Weyl correspondence on thecircle in Group-Theoretical Methods in Physics (Proc Salamanca 1992) ed by M delOlmo M Santander J Mateos Guilarte (CIEMAT Madrid 1993) pp 343ndash346
[239] S De Biegravevre JA Gonzaacutelez Semiclassical behaviour of coherent states on the circle inQuantization and Coherent States Methods in Physics ed by A Odzijewicz et al (WorldScientific Singapore 1993)
[240] S De Biegravevre AE Gradechi Quantum mechanics and coherent states on the anti-de Sitterspace-time and their Poincareacute contraction Ann Inst H Poincareacute 57 403ndash428 (1992)
[241] J Deenen C Quesne Dynamical group of collective states I II III J Math Phys 23878ndash889 2004ndash2015 (1982)
[242] J Deenen C Quesne Dynamical group of collective states I II III J Math Phys 251638ndash1650 (1984)
[243] J Deenen C Quesne Partially coherent states of the real symplectic group J Math Phys25 2354ndash2366 (1984)
[244] J Deenen C Quesne Boson representations of the real symplectic group and theirapplication to the nuclear collective model J Math Phys 26 2705ndash2716 (1985)
[245] R Delbourgo Minimal uncertainty states for the rotation and allied groups J Phys AMath Gen 10 1837ndash1846 (1977)
[246] R Delbourgo J R Fox Maximum weight vectors possess minimal uncertainty J PhysA Math Gen 10 L233ndashL235 (1977)
[247] V Delouille J de Patoul J-F Hochedez L Jacques J-P Antoine Wavelet spectrumanalysis of EITSoHO images Solar Phys 228 301ndash321 (2005)
[248] N Delprat B Escudieacute P Guillemain R Kronland-Martinet P Tchamitchian B Tor-reacutesani Asymptotic wavelet and Gabor analysis Extraction of instantaneous frequenciesIEEE Trans Inform Theory 38 644ndash664 (1992)
[249] Th Deutsch L Genovese Wavelets for electronic structure calculations Collection SocFr Neut 12 33ndash76 (2011)
[250] B Dewitt Quantum theory of gravity I The canonical theory Phys Rev 160 1113ndash1148(1967)
[251] RH Dicke Coherence in spontaneous radiation processes Phys Rev 93 99ndash110 (1954)[252] AN Dinkelaker AL MacKinnon Wavelets intermittency and solar flare hard X-rays 1
Local intermittency measure in cascade and avalanche scenarios Solar Phys 282 471ndash481(2013)
[253] AN Dinkelaker AL MacKinnon Wavelets intermittency and solar flare hard X-rays 2LIM analysis of high time resolution BATSE data Solar Phys 282 483ndash501 (2013)
[254] MN Do M Vetterli Contourlets in Beyond Wavelets ed by GV Welland (AcademicSan Diego 2003) pp 83ndash105
[255] MN Do M Vetterli The contourlet transform An efficient directional multiresolutionimage representation IEEE Trans Image Process 14 2091ndash2106 (2005)
[256] VV Dodonov Nonclassical states in quantum optics A ldquosqueezedrdquo review of the first 75years J Opt B Quant Semiclass Opot 4 R1ndashR33 (2002)
[257] DL Donoho Nonlinear wavelet methods for recovery of signals densities and spectrafrom indirect and noisy data in Different Perspectives on Wavelets Proceedings ofSymposia in Applied Mathematics vol 38 ed by I Daubechies (American MathematicalSociety Providence RI 1993) pp 173ndash205
[258] DL Donoho Wedgelets Nearly minimax estimation of edges Ann Stat 27 859ndash897(1999)
[259] DL Donoho X Huo Beamlet pyramids A new form of multiresolution analysis suitedfor extracting lines curves and objects from very noisy image data in SPIE Proceedingsvol 5914 (SPIE Bellingham WA 2005) pp 1ndash12
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[261] AH Dooley JW Rice Contractions of rotation groups and their representations MathProc Camb Phil Soc 94 509ndash517 (1983)
[262] AH Dooley JW Rice On contractions of semisimple Lie groups Trans Amer MathSoc 289 185ndash202 (1985)
[263] JR Driscoll DM Healy Computing Fourier transforms and convolutions on the 2-sphereAdv Appl Math 15 202ndash250 (1994)
[264] H Drissi F Regragui J-P Antoine M Bennouna Wavelet transform analysis of visualevoked potentials Some preliminary results ITBM-RBM 21 84ndash91 (2000)
[265] RJ Duffin AC Schaeffer A class of nonharmonic Fourier series Trans Amer MathSoc 72 341ndash366 (1952)
[266] M Duflo CC Moore On the regular representation of a nonunimodular locally compactgroup J Funct Anal 21 209ndash243 (1976)
[267] M Duval-Destin R Murenzi Spatio-temporal wavelets Application to the analysis ofmoving patterns in Progress in Wavelet Analysis and Applications (Proc Toulouse 1992)ed by Y Meyer S Roques (Ed Frontiegraveres Gif-sur-Yvette 1993) pp 399ndash408
[268] M Duval-Destin M-A Muschietti B Torreacutesani Continuous wavelet decompositionsmultiresolution and contrast analysis SIAM J Math Anal 24 739ndash755 (1993)
[269] SJL van Eindhoven JLH Meyers New orthogonality relations for the Hermitepolynomials and related Hilbert spaces J Math Anal Appl 146 89ndash98 (1990)
[270] M ElBaz R Fresneda J-P Gazeau Y Hassouni Coherent state quantization of para-grassmann algebras J Phys A Math Theor 43 385202 (2010) Corrigendum J PhysA Math Theor 45 (2012)
[271] A Elkharrat J-P Gazeau F Deacutenoyer Multiresolution of quasicrystal diffraction spectraActa Cryst A65 466ndash489 (2009)
[272] Q Fan Phase space analysis of the identity decompositions J Math Phys 34 3471ndash3477(1993)
[273] M Fanuel S Zonetti Affine quantization and the initial cosmological singularity Euro-phys Lett 101 10001 (2013)
[274] M Farge Wavelet transforms and their applications to turbulence Annu Rev Fluid Mech24 395ndash457 (1992)
[275] M Farge N Kevlahan V Perrier E Goirand Wavelets and turbulence Proc IEEE 84639ndash669 (1996)
[276] M Farge NK-R Kevlahan V Perrier K Schneider Turbulence analysis modellingand computing using wavelets in Wavelets in Physics Chap 4 ed by JC van den Berg(Cambridge University Press Cambridge 1999)
[277] HG Feichtinger Coherent frames and irregular sampling in Recent Advances in FourierAnalysis and Its applications ed by JS Byrnes JL Byrnes (Kluwer Dordrecht 1990)pp 427ndash440
[278] HG Feichtinger KH Groumlchenig Banach spaces related to integrable group representa-tions and their atomic decompositions I J Funct Anal 86 307ndash340 (1989)
[279] HG Feichtinger KH Groumlchenig Banach spaces related to integrable group representa-tions and their atomic decompositions II Mh Math 108 129ndash148 (1989)
[280] M Flensted-Jensen Discrete series for semisimple symmetric spaces Ann of Math 111253ndash311 (1980)
[281] K Flornes A Grossmann M Holschneider B Torreacutesani Wavelets on discrete fieldsAppl Comput Harmon Anal 1 137ndash146 (1994)
[282] V Fock Zur Theorie der Wasserstoffatoms Zs f Physik 98 145ndash54 (1936)[283] M Fornasier H Rauhut Continuous frames function spaces and the discretization
problem J Fourier Anal Appl 11 245ndash287 (2005)
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[285] W Freeden U Windheuser Combined spherical harmonic and wavelet expansion mdash Afuture concept in Earthrsquos gravitational determination Appl Comput Harmon Anal 4 1ndash37 (1997)
[286] W Freeden T Maier S Zimmermann A survey on wavelet methods for (geo)applicationsRevista Mathematica Complutense 16 (2003) 277ndash310
[287] W Freeden M Schreiner Biorthogonal locally supported wavelets on the sphere based onzonal kernel functions J Fourier Anal Appl 13 693ndash709 (2007)
[288] WT Freeman EH Adelson The design and use of steerable filters IEEE Trans PatternAnal Machine Intell 13 891ndash906 (1991)
[289] L Freidel ER Livine U(N) coherent states for loop quantum gravity J Math Phys 52052502 (2011)
[290] J Froment S Mallat Arbitrary low bit rate image compression using wavelets in Progressin Wavelet Analysis and Applications (Proc Toulouse 1992) ed by Y Meyer S Roques(Ed Frontiegraveres Gif-sur-Yvette 1993) pp 413ndash418 and references therein
[291] L Freidel S Speziale Twisted geometries A geometric parameterisation of SU(2) phasespace Phys Rev D 82 084040 (2010)
[292] H Fuumlhr Wavelet frames and admissibility in higher dimensions J Math Phys 37 6353ndash6366 (1996)
[293] H Fuumlhr M Mayer Continuous wavelet transforms from semidirect products Cyclicrepresentations and Plancherel measure J Fourier Anal Appl 8 375ndash396 (2002)
[294] D Gabor Theory of communication J Inst Electr Engrg(London) 93 429ndash457 (1946)[295] J-P Gabardo D Han Frames associated with measurable spaces Adv Comput Math 18
127ndash147 (2003)[296] E Galapon Paulirsquos theorem and quantum canonical pairs The consistency of a bounded
self-adjoint time operator canonically conjugate to a Hamiltonian with non-empty pointspectrum Proc R Soc Lond A 458 451ndash472 (2002)
[297] PL Garciacutea de Leacuteon J-P Gazeau Coherent state quantization and phase operator PhysLett A 361 301ndash304 (2007)
[298] L Garciacutea de Leoacuten J-P Gazeau J Queacuteva The infinite well revisited Coherent states andquantization Phys Lett A 372 3597ndash3607 (2008)
[299] T Garidi J-P Gazeau E Huguet M Lachiegraveze Rey J Renaud Fuzzy spheres frominequivalent coherent states quantization J Phys A Math Theor 40 10225ndash10249 (2007)
[300] J-P Gazeau Four Euclidean conformal group in atomic calculations Exact analyticalexpressions for the bound-bound two-photon transition matrix elements in the H atomJ Math Phys 19 1041ndash1048 (1978)
[301] J-P Gazeau On the four Euclidean conformal group structure of the sturmian operatorLett Math Phys 3 285ndash292 (1979)
[302] J-P Gazeau Technique Sturmienne pour le spectre discret de lrsquoeacutequation de SchroumldingerJ Phys A Math Gen 13 3605ndash3617 (1980)
[303] J-P Gazeau Four Euclidean conformal group approach to the multiphoton processes in theH atom J Math Phys 23 156ndash164 (1982)
[304] J-P Gazeau A remarkable duality in one particle quantum mechanics between someconfining potentials and (R+Linfin
ε ) potentials Phys Lett 75A 159ndash163 (1980)[305] J-P Gazeau SL(2R)-coherent states and integrable systems in classical and quantum
physics in Quantization Coherent States and Complex Structures ed by J-P AntoineST Ali W Lisiecki IM Mladenov A Odzijewicz (Plenum Press New York and London1995) pp 147ndash158
[306] J-P Gazeau S Graffi Quantum harmonic oscillator A relativistic and statistical point ofview Boll Unione Mat Ital 11-A 815ndash839 (1997)
[307] J-P Gazeau V Hussin Poincareacute contraction of SU(11) Fock-Bargmann structure J PhysA Math Gen 25 1549ndash1573 (1992)
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[310] J-P Gazeau P Monceau Generalized coherent states for arbitrary quantum systems inColloquium M Flato (Dijon Sept 99) vol II (Kluumlwer Dordrecht 2000) pp 131ndash144
[311] J-P Gazeau M Novello The question of mass in (Anti-) de Sitter space-times J Phys AMath Theor 41 304008 (2008)
[312] J-P Gazeau M del Olmo q-coherent states quantization of the harmonic oscillator AnnPhys (NY) 330 220ndash245 (2013) arXiv12071200 [quant-ph]
[313] J-P Gazeau J Patera Tau-wavelets of Haar J Phys A Math Gen 29 4549ndash4559 (1996)[314] J-P Gazeau W Piechocki Coherent states quantization of a particle in de Sitter space
J Phys A Math Gen 37 6977ndash6986 (2004)[315] J-P Gazeau J Renaud Lie algorithm for an interacting SU(11) elementary system and its
contraction Ann Phys (NY) 222 89ndash121 (1993)[316] J-P Gazeau J Renaud Relativistic harmonic oscillator and space curvature Phys Lett A
179 67ndash71 (1993)[317] J-P Gazeau V Spiridonov Toward discrete wavelets with irrational scaling factor J Math
plane J Phys A Math Theor 44 495201 (2011)[319] J-P Gazeau J Patera E Pelantovaacute Tau-wavelets in the plane J Math Phys 39 4201ndash
4212 (1998)[320] J-P Gazeau M Andrle C Burdiacutek R Krejcar Wavelet multiresolutions for the Fibonacci
chain J Phys A Math Gen 33 L47ndashL51 (2000)[321] J-P Gazeau M Andrle C Burdiacutek Bernuau spline wavelets and sturmian sequences
J Fourier Anal Appl 10 269ndash300 (2004)[322] J-P Gazeau F-X Josse-Michaux P Monceau Finite dimensional quantizations of the
(q p) plane new space and momentum inequalities Int J Modern Phys B 20 1778ndash1791 (2006)
[323] J-P Gazeau J Mourad J Queacuteva Fuzzy de Sitter space-times via coherent statesquantization in Proceedings of the XXVIth Colloquium on Group Theoretical Methodsin Physics New York 2006 ed by J Birman S Catto B Nicolescu (Canopus PublishingLimited London 2009)
[324] D Geller A Mayeli Continuous wavelets on compact manifolds Math Z 262 895ndash927(2009)
[325] D Geller A Mayeli Nearly tight frames and space-frequency analysis on compactmanifolds Math Z 263 235ndash264 (2009)
[326] L Genovese B Videau M Ospici Th Deutsch S Goedecker J-F Mhaut Daubechieswavelets for high performance electronic structure calculations The BigDFT project CR Mecanique 339 149ndash164 (2011)
[327] G Gentili C Stoppato Power series and analyticity over the quaternions Math Ann 352113ndash131 (2012)
[328] G Gentili DC Struppa A new theory of regular functions of a quaternionic variable AdvMath 216 279ndash301 (2007)
[329] C Geyer K Daniilidis Catadioptric projective geometry Int J Comput Vision 45 223ndash243 (2001)
[330] R Gilmore Geometry of symmetrized states Ann Phys (NY) 74 391ndash463 (1972)[331] R Gilmore On properties of coherent states Rev Mex Fis 23 143ndash187 (1974)[332] J Ginibre Statistical ensembles of complex quaternion and real matrices J Math Phys
6 440ndash449 (1965)[333] RJ Glauber The quantum theory of optical coherence Phys Rev 130 2529ndash2539 (1963)
560 References
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[335] J Glimm Locally compact transformation groups Trans Amer Math Soc 101 124ndash138(1961)
[336] R Godement Sur les relations drsquoorthogonaliteacute de V Bargmann C R Acad Sci Paris 255521ndash523 657ndash659 (1947)
[337] C Gonnet B Torreacutesani Local frequency analysis with two-dimensional wavelet trans-form Signal Proc 37 389ndash404 (1994)
[338] JA Gonzalez MA del Olmo Coherent states on the circle J Phys A Math Gen 318841ndash8857 (1998)
[339] XGonze B Amadon et al ABINIT First-principles approach to material and nanosystemproperties Computer Physics Comm 180 2582ndash2615 (2009)
[340] KM Gograverski E Hivon AJ Banday BD Wandelt FK Hansen M Reinecke MBartelmann HEALPix A framework for high-resolution discretization and fast analysisof data distributed on the sphere Astrophys J 622 759ndash771 (2005)
[341] P Goupillaud A Grossmann J Morlet Cycle-octave and related transforms in seismicsignal analysis Geoexploration 23 85ndash102 (1984)
[342] KH Groumlchenig A new approach to irregular sampling of band-limited functions in RecentAdvances in Fourier Analysis and Its applications ed by JS Byrnes JL Byrnes (KluwerDordrecht 1990) pp 251ndash260
[343] KH Groumlchenig Gabor analysis over LCA groups in Gabor Analysis and Algorithms ndashTheory and Applications ed by HG Feichtinger T Strohmer (Birkhaumluser Boston-Basel-Berlin 1998) pp 211ndash231
[344] HJ Groenewold On the principles of elementary quantum mechanics Physica 12 405ndash460 (1946)
[345] P Grohs Continuous shearlet tight frames J Fourier Anal Appl 17 506ndash518 (2011)[346] P Grohs G Kutyniok Parabolic molecules preprint TU Berlin (2012)[347] M Grosser A note on distribution spaces on manifolds Novi Sad J Math 38 121ndash128
(2008)[348] A Grossmann Parity operator and quantization of δ -functions Commun Math Phys 48
191ndash194 (1976)[349] A Grossmann J Morlet Decomposition of Hardy functions into square integrable
wavelets of constant shape SIAM J Math Anal 15 723ndash736 (1984)[350] A Grossmann J Morlet Decomposition of functions into wavelets of constant shape and
related transforms in Mathematics + Physics Lectures on recent results I ed by L Streit(World Scientific Singapore 1985) pp 135ndash166
[351] A Grossmann J Morlet T Paul Integral transforms associated to square integrablerepresentations I General results J Math Phys 26 2473ndash2479 (1985)
[352] A Grossmann J Morlet T Paul Integral transforms associated to square integrablerepresentations II Examples Ann Inst H Poincareacute 45 293ndash309 (1986)
[353] A Grossmann R Kronland-Martinet J Morlet Reading and understanding the contin-uous wavelet transform in Wavelets Time-Frequency Methods and Phase Space (ProcMarseille 1987) ed by J-M Combes A Grossmann P Tchamitchian 2nd edn (SpringerBerlin 1990) pp 2ndash20
[354] P Guillemain R Kronland-Martinet B Martens Estimation of spectral lines with helpof the wavelet transform Application in NMR spectroscopy in Wavelets and Applications(Proc Marseille 1989) ed by Y Meyer (Masson and Springer Paris and Berlin 1991) pp38ndash60
[355] H de Guise M Bertola Coherent state realizations of su(n+ 1) on the n-torus J MathPhys 43 3425ndash3444 (2002)
[356] K Guo D Labate Representation of Fourier Integral Operators using shearlets J FourierAnal Appl 14 327ndash371 (2008)
References 561
[357] K Guo G Kutyniok D Labate Sparse multidimensional representations usinganisotropic dilation and shear operators in Wavelets and Spines (Athens GA 2005)(Nashboro Press Nashville TN 2006) pp 189ndash201
[358] K Guo D Labate W-Q Lim G Weiss E Wilson Wavelets with composite dilationsand their MRA properties Appl Comput Harmon Anal 20 202ndash236 (2006)
[359] EA Gutkin Overcomplete subspace systems and operator symbols Funct Anal Appl 9260ndash261 (1975)
[360] G Gyoumlrgyi Integration of the dynamical symmetry groups for the 1r potential Acta PhysAcad Sci Hung 27 435ndash439 (1969)
[361] BC Hall The Segal-Bargmann ldquoCoherent Staterdquo transform for compact Lie groups JFunct Analysis 122 103ndash151 (1994)
[362] B Hall JJ Mitchell Coherent states on spheres J Math Phys 43 1211ndash1236 (2002)[363] DK Hammond P Vandergheynst R Gribonval Wavelets on graphs via spectral theory
Appl Comput Harmon Anal 30 129ndash150 (2011)[364] Y Hassouni EMF Curado MA Rego-Monteiro Construction of coherent states for
physical algebraic system Phys Rev A 71 022104 (2005)[365] J He H Liu Admissible wavelets associated with the affine automorphism group of the
Siegel upper half-plane J Math Anal Appl 208 58ndash70 (1997)[366] J He H Liu Admissible wavelets associated with the classical domain of type one
Approx Appl 14 (1998) 89ndash105[367] J He L Peng Wavelet transform on the symmetric matrix space preprint Beijing (1997)
(unpublished)[368] J He L Peng Admissible wavelets on the unit disk Complex Variables 35 109ndash119
(1998)[369] DM Healy Jr FE Schroeck Jr On informational completeness of covariant localization
observables and Wigner coefficients J Math Phys 36 453ndash507 (1995)[370] C Heil D Walnut Continuous and discrete wavelet transforms SIAM Review 31 628ndash
666 (1989)[371] K Hepp EH Lieb On the superradiant phase transition for molecules in a quantized
radiation field The Dicke maser model Ann Phys (NY) 76 360ndash404 (1973)[372] K Hepp EH Lieb Equilibrium statistical mechanics of matter interacting with the
quantized radiation field Phys Rev A 8 2517ndash2525 (1973)[373] JA Hogan JD Lakey Extensions of the Heisenberg group by dilations and frames Appl
Comput Harmon Anal 2 174ndash199 (1995)[374] AL Hohoueacuteto K Thirulogasanthar ST Ali J-P Antoine Coherent states lattices and
square integrability of representations J Phys A Math Gen36 11817ndash11835 (2003)[375] M Holschneider On the wavelet transformation of fractal objects J Stat Phys 50 963ndash
993 (1988)[376] M Holschneider Wavelet analysis on the circle J Math Phys 31 39ndash44 (1990)[377] M Holschneider Inverse Radon transforms through inverse wavelet transforms Inv Probl
7 853ndash861 (1991)[378] M Holschneider Localization properties of wavelet transforms J Math Phys 34 3227ndash
3244 (1993)[379] M Holschneider General inversion formulas for wavelet transforms J Math Phys 34
4190ndash4198 (1993)[380] M Holschneider Wavelet analysis over abelian groups Applied Comput Harmon Anal
2 52ndash60 (1995)[381] M Holschneider Continuous wavelet transforms on the sphere J Math Phys 37 4156ndash
4165 (1996)[382] M Holschneider I Iglewska-Nowak Poisson wavelets on the sphere J Fourier Anal
Appl 13 405ndash419 (2007)
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[383] M Holschneider R Kronland-Martinet J Morlet P Tchamitchian A real-time algorithmfor signal analysis with the help of wavelet transform in Wavelets Time-FrequencyMethods and Phase Space (Proc Marseille 1987) ed by J-M Combes A Grossmann PTchamitchian 2nd edn (Springer Berlin 1990) pp 286ndash297
[384] M Holschneider P Tchamitchian Pointwise analysis of Riemannrsquos ldquonondifferentiablerdquofunction Invent Math 105 157ndash175 (1991)
[385] GR Honarasa MK Tavassoly M Hatami R Roknizadeh Nonclassical properties ofcoherent states and excited coherent states for continuous spectra J Phys A Math Theor44 085303 (2011)
[386] M Hongoh Coherent states associated with the continuous spectrum of noncompactgroups J Math Phys 18 2081ndash2085 (1977)
[387] A Horzela FH Szafraniec A measure free approach to coherent states J Phys A MathGen 45 244018 (2012)
[388] W-L Hwang S Mallat Characterization of self-similar multifractals with waveletmaxima Appl Comput Harmon Anal 1 316ndash328 (1994)
[389] W-L Hwang C-S Lu P-C Chung Shape from texture Estimation of planar surfaceorientation through the ridge surfaces of continuous wavelet transform IEEE Trans ImageProc 7 773ndash780 (1998)
[390] I Iglewska-Nowak M Holschneider Frames of Poisson wavelets on the sphere ApplComput Harmon Anal 28 227ndash248 (2010)
[391] E Inoumlnuuml EP Wigner On the contraction of groups and their representations Proc NatAcad Sci U S 39 510ndash524 (1953)
[392] S Iqbal F Saif Generalized coherent states and their statistical characteristics in power-law potentials J Math Phys 52 082105 (2011)
[393] CJ Isham JR Klauder Coherent states for n-dimensional Euclidean groups E(n) andtheir application J MathPhys 32 607ndash620 (1991)
[394] L Jacques J-P Antoine Multiselective pyramidal decomposition of images Wavelets withadaptive angular selectivity Int J Wavelets Multires Inform Proc 5 785ndash814 (2007)
[395] L Jacques L Duval C Chaux G Peyreacute A panorama on multiscale geometric rep-resentations intertwining spatial directional and frequency selectivity Signal Proc 912699ndash2730 (2011)
[396] HR Jalali M K Tavassoly On the ladder operators and nonclassicality of generalizedcoherent state associated with a particle in an infinite square well preprint (2013)arXiv13034100v1 [quant-ph]
[397] C Johnston On the pseudo-dilation representations of Flornes Grossmann Holschneiderand Torreacutesani Appl Comput Harmon Anal 3 377ndash385 (1997)
[398] G Kaiser Phase-space approach to relativistic quantum mechanics I Coherent staterepresentation for massive scalar particles J MathPhys 18 952ndash959 (1977)
[399] G Kaiser Phase-space approach to relativistic quantum mechanics II Geometrical aspectsJ MathPhys 19 502ndash507 (1978)
[400] C Kalisa B Torreacutesani N-dimensional affine Weyl-Heisenberg wavelets Ann Inst HPoincareacute 59 201ndash236 (1993)
[401] W Kaminski J Lewandowski T Pawłowski Quantum constraints Dirac observables andevolution group averaging versus the Schroumldinger picture in LQC Class Quant Grav 26245016 (2009)
[402] MR Karim ST Ali A relativistic windowed Fourier transform preprint ConcordiaUniversity Montreacuteal (1997) (unpublished)
[403] M R Karim ST Ali M Bodruzzaman A relativistic windowed Fourier transform inProceedings of IEEE SoutheastCon 2000 Nashville Tennessee pp 253ndash260 (2000)
[404] T Kawazoe Wavelet transforms associated to a principal series representation of semisim-ple Lie groups I II Proc Japan Acad Ser A ndash Math Sci 71 154ndash157 158ndash160 (1995)
[405] T Kawazoe Wavelet transform associated to an induced representation of SL(n+ 2R)Ann Inst H Poincareacute 65 1ndash13 (1996)
References 563
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[407] P Kittipoom G Kutyniok W-Q Lim Construction of compactly supported shearletframes Constr Approx 35 21ndash72 (2012)
[408] J Kiukas P Lahti K Ylinenc Phase space quantization and the operator moment problemJ Math Phys 47 072104 (2006)
[409] JR Klauder Continuous-representation theory I Postulates of continuous-representationtheory J Math Phys 4 1055ndash1058 (1963)
[410] JR Klauder Continuous-representation theory II Generalized relation between quantumand classical dynamics J Math Phys 4 1058ndash1073 (1963)
[411] JR Klauder Path integrals for affine variables in Functional Integration Theory andApplications ed by J-P Antoine E Tirapegui (Plenum Press New York and London1980) pp 101ndash119
[412] JR Klauder Are coherent states the natural language of quantum mechanics inFundamental Aspects of Quantum Theory ed by V Gorini A Frigerio NATO ASI Seriesvol B 144 (Plenum Press New York 1986) pp 1ndash12
[413] JR Klauder Quantization without quantization Ann Phys (NY) 237 147ndash160 (1995)[414] JR Klauder Coherent states for the hydrogen atom J Phys A Math Gen 29 L293ndash
L296 (1996)[415] JR Klauder An affinity for affine quantum gravity Proc Steklov Inst Math 272 169ndash176
(2011) and references therein[416] JR Klauder RF Streater A wavelet transform for the Poincareacute group J Math Phys 32
1609ndash1611 (1991)[417] JR Klauder RF Streater Wavelets and the Poincareacute half-plane J Math Phys 35 471ndash
478 (1994)[418] JR Klauder K Penson J-M Sixdeniers Constructing coherent states through solutions
of Stieltjes and Hausdorff moment problems Phys Rev A 64 013817 (2001)[419] A Kleppner RL Lipsman The Plancherel formula for group extensions Ann Ec Norm
Sup 5 459ndash516 (1972)[420] AB Klimov C Muntildeoz Coherent isotropic and squeezed states in a N-qubit system Phys
Scr 87 038110 (2013)[421] A Klyashko Dynamical symmetry approach to entanglement in Physics and Theoretical
Computer Science From Numbers and Languages to (Quantum) Cryptography - NATOSecurity through Science Series D - Information and Communication Security vol 7 edby J-P Gazeau J Nesetril B Rovan (IOS Press Washington DC 2007) pp 25ndash54
[422] S Kobayashi Irreducibility of certain unitary representations J Math Soc Japan 20 638ndash642 (1968)
[423] K Kowalski J Rembielinski LC Papaloucas Coherent states for a quantum particle ona circle J Phys A Math Gen 29 4149ndash4167 (1996)
[424] K Kowalski J Rembielinski Quantum mechanics on a sphere and coherent states J PhysA Math Gen 33 6035ndash6048 (2000)
[425] K Kowalski J Rembielinski The Bargmann representation for the quantum mechanicson a sphere J Math Phys 42 4138ndash4147 (2001)
[426] C Kristjansen J Plefka GW Semenoff M Staudacher A new double-scaling limit ofN = 4 super-Yang-Mills theory and pp-wave strings Nuclear Phys B 643 3ndash30 (2002)
[427] M Kulesh M Holschneider MS Diallo Geophysical wavelet library Applications ofthe continuous wavelet transform to the polarization and dispersion analysis of signalsComput Geosci 34 1732ndash1752 (2008)
[428] R Kunze On the Frobenius reciprocity theorem for square integrable representationsPacific J Math 53 465ndash471 (1974)
[429] Y Kuroda A Wada T Yamazaki K Nagayama Postacquisition data processing methodfor suppression of the solvent signal I J Magn Reson 84 604ndash610 (1989)
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[431] G Kutyniok D Labate Resolution of the wavefront set using continuous shearlets TransAmer Math Soc 361 2719ndash2754 (2009)
[432] G Kutyniok W-Q Lim Compactly supported shearlets are optimally sparse J ApproxTheory 163 1564ndash1589 (2011)
[433] D Labate W-Q Lim G Kutyniok G Weiss Sparse multidimensional representationusing shearlets in Wavelets XI (San Diego CA 2005) ed by M Papadakis A Laine MUnser SPIE Proceedings vol 5914 (SPIE Bellingham WA 2005) pp 254ndash262
[434] P Lahti J-P Pellonpaumlauml Continuous variable tomographic measurements Phys Lett A373 3435ndash3438 (2009)
[435] Lambertrsquos projection see WikipediahttpenwikipediaorgwikiLambert_azimuthal_equal-area_projection
[436] J-P Leduc F Mujica R Murenzi MJT Smith Missile-tracking algorithm using target-adapted spatio-temporal wavelets in Automatic Object Recognition VII SPIE Proceedingsvol 5914 (SPIE Bellingham WA 1997) pp 400ndash411
[437] J-P Leduc F Mujica R Murenzi MJT Smith Spatio-temporal wavelet transforms formotion tracking in IEEE ICASSP 1997 vol 4 (1997) pp 3013ndash3016
[438] J-P Leduc F Mujica R Murenzi MJT Smith Spatio-temporal continuous waveletsapplied to missile warhead detection and tracking in SPIE VCIP rsquo97 vol 3024 ed byJ Biemond EJ Delp (1997) pp 787ndash798
[439] B Leistedt JD McEwen Exact wavelets on the ball IEEE Trans Signal Proc 60 1564ndash1589 (2012)
[440] PG Lemarieacute Y Meyer Ondelettes et bases hilbertiennes Rev Math Iberoamer 2 1ndash18(1986)
[441] C Lemke A Schuck Jr J-P Antoine D Sima Metabolite-sensitive analysis of magneticresonance spectroscopic signals using the continuous wavelet transform Meas SciTechnol 22 (2011) Art 114013
[442] J-M Leacutevy-Leblond Galilei group and non-relativistic quantum mechanics J Math Phys4 776-788 (1963)
[443] J-M Leacutevy-Leblond Galilei group and Galilean invariance in Group Theory and ItsApplications vol II ed by EM Loebl (Academic New York 1971) pp 221ndash299
[444] J-M Leacutevy-Leblond On the conceptual nature of the physical constants Riv Nuovo Cim7 187ndash214 (1977)
[445] EH Lieb The classical limit of quantum spin systems Commun Math Phys 31 327ndash340(1973)
[446] G Lindblad B Nagel Continuous bases for unitary irreducible representations of SU(11)Ann Inst H Poincareacute 13 27ndash56 (1970)
[447] W Lisiecki Kaumlhler coherent states orbits for representations of semisimple Lie groupsAnn Inst H Poincareacute 53 857ndash890 (1990)
[448] A Lisowska Moment-based fast wedgelet transform J Math Imaging Vis 39 180ndash192(2011)
[449] H Liu L Peng Admissible wavelets associated with the Heisenberg group Pacific JMath 180 101ndash123 (1997)
[450] E Livine S Speziale Physical boundary state for the quantum tetrahedron Class QuantGrav 25 085003 (2008)
[451] F Low Complete sets of wave packets in A Passion for Physics ndash Essay in Honor ofGeoffrey Chew ed by C DeTar (World Scientific Singapore 1985) pp 17ndash22
[452] G Mack All unitary ray representations of the conformal group SU(22) with positiveenergy Commun Math Phys 55 1ndash28 (1977)
[453] GW Mackey Imprimitivity for representations of locally compact groups I Proc NatAcad Sci 35 537ndash545 (1949)
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[456] SG Mallat Multifrequency channel decompositions of images and wavelet models IEEETrans Acoust Speech Signal Proc 37 2091ndash2110 (1989)
[457] SG Mallat A theory for multiresolution signal decomposition The wavelet representa-tion IEEE Trans Pattern Anal Machine Intell 11 674ndash693 (1989)
[458] S Mallat W-L Hwang Singularity detection and processing with wavelets IEEE TransInform Theory 38 617ndash643 (1992)
[459] S Mallat Z Zhang Matching pursuits with time frequency dictionaries IEEE TransSignal Proc 41 3397ndash3415 (1993)
[460] S Mallat S Zhong Wavelet maxima representation in Wavelets and Applications (ProcMarseille 1989) ed by Y Meyer (Masson and Springer Paris and Berlin 1991) pp 207ndash284
[461] VI Manrsquoko G Marmo ECG Sudarshan F Zaccaria f -oscillators and non-linearcoherent states Phys Scr 55 528ndash541 (1997)
[462] D Marinucci D Pietrobon A Baldi P Baldi P Cabella G Kerkyacharian P Natoli DPicard N Vittorio Spherical needlets for CMB data analysis Mon Not R Astron Soc383 539ndash545 (2008)
[463] D Marion M Ikura A Bax Improved solvent suppression in one- and two-dimensionalNMR spectra by convolution of time-domain data J Magn Reson 84 425ndash430 (1989)
[464] Y Meyer Principe drsquoincertitude bases hilbertiennes et algegravebres drsquoopeacuterateurs SeacuteminaireBourbaki 662 (1985ndash1986)
[465] Y Meyer Principe drsquoincertitude bases hilbertiennes et algegravebres drsquoopeacuterateurs Asteacuterisque145ndash146 209ndash223 (1987)
[466] Y Meyer H Xu Wavelet analysis and chirps Appl Comput Harmon Anal 4 366ndash379(1997)
[467] L Michel Invariance in quantum mechanics and group extensions in Group TheoreticalConcepts and Methods in Elementary Particle Physics ed by F Guumlrsey (Gordon andBreach New York and London 1964) pp 135ndash200
[468] J Mickelsson J Niederle Contractions of representations of the de Sitter groupsCommun Math Phys 27 167ndash180 (1972)
[469] MM Miller Convergence of the Sudarshan expansion for the diagonal coherent-stateweight functional J Math Phys 9 1270ndash1274 (1968)
[470] V F Molchanov Harmonic analysis on homogeneous spaces in Representation Theoryand Noncommutative Harmonic Analysis II ed by AA Kirillov (Springer Berlin 1995)
[471] MI Monastyrsky AM Perelomov Coherent states and symmetric spaces II Ann InstH Poincareacute 23 23ndash48 (1975)
[472] B Moran S Howard D Cochran Positive-operator-valued measures A general settingfor frames in Excursions in Harmonic Analysis vol 1 2 ed by TD Andrews R BalanJJ Benedetto W Czaja KA Okoudjou (Birkhaumluser Boston 2013) pp 49ndash64
[473] H Moscovici Coherent states representations of nilpotent Lie groups Commun MathPhys 54 63ndash68 (1977)
[474] H Moscovici A Verona Coherent states and square integrable representations Ann InstH Poincareacute 29 139ndash156 (1978)
[475] F Mujica R Murenzi MJT Smith J-P Leduc Robust tracking in compressed imagesequences J Electr Imaging 7 746ndash754 (1998)
[476] R Murenzi Wavelet transforms associated to the n-dimensional Euclidean group withdilations Signals in more than one dimension in Wavelets Time-Frequency Methodsand Phase Space (Proc Marseille 1987) ed by J-M Combes A Grossmann PTchamitchian 2nd edn (Springer Berlin 1990) pp 239ndash246
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[479] MA Naımark Dokl Akad Nauk SSSR 41 359ndash361 (1943) see also B Sz-NagyExtensions of linear transformations in Hilbert space which extend beyond this spaceAppendix to F Riesz B Sz-Nagy Functional Analysis (Frederick Ungar New York 1960)
[480] FJ Narcowich P Petrushev JD Ward Localized tight frames on spheres SIAM J MathAnal 38 574ndash594 (2006)
[481] M Nauenberg Quantum wave packets on Kepler elliptic orbits Phys Rev A 40 1133ndash1136 (1989)
[482] M Nauenberg C Stroud J Yeazell The classical limit of an atom Scient Amer 27024ndash29 (1994)
[483] H Neumann Transformation properties of observables Helv Phys Acta 45 811ndash819(1972)
[484] U Niederer The maximal kinematical invariance group of the free Schroumldinger equationHelv Phys Acta 45 802ndash881 (1972)
[485] MM Nieto LM Simmons Jr Coherent states for general potentials I Formalism IIConfining one-dimensional examples III Nonconfining one-dimensional examples PhysRev D 20 1321ndash1331 1332ndash1341 1342ndash1350 (1979)
[486] MM Nieto LM Simmons Jr Coherent states for general potentials Phys Rev Lett 41207ndash210 (1987)
[487] A Odzijewicz On reproducing kernels and quantization of states Commun Math Phys114 577ndash597 (1988)
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[489] A Odzijewicz Quantum algebras and q-special functions related to coherent states mapsof the disc Commun Math Phys 192 183ndash215 (1998)
[490] A Odzijewicz M Horowski A Tereszkiewicz Integrable multi-boson systems andorthogonal polynomials J Phys A Math Gen 34 4353ndash4376 (2001)
[491] G Oacutelafsson B Oslashrsted The holomorphic discrete series for affine symmetric spaces JFunct Anal 81 126ndash159 (1988)
[492] G Oacutelafsson H Schlichtkrull Representation theory Radon transform and the heatequation on a Riemannian symmetric space Contemp Math 449 315ndash344 (2008)
[493] E Onofri A note on coherent state representations of Lie groups J Math Phys 16 1087ndash1089 (1975)
[494] E Onofri Dynamical quantization of the Kepler manifold J Math Phys 17 401ndash408(1976)
[495] D Oriti R Pereira L Sindoni Coherent states in quantum gravity A construction basedon the flux representation of loop quantum gravity J Phys A Math Theor 45 244004(2012)
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[499] T Paul Affine coherent states and the radial Schroumldinger equation I preprint CPT-84P1710 (1984) (unpublished)
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[501] AM Perelomov On the completeness of a system of coherent states Theor Math Phys6 156ndash164 (1971)
[502] AM Perelomov Coherent states for arbitrary Lie group Commun Math Phys 26 222ndash236 (1972)
[503] AM Perelomov Coherent states and symmetric spaces Commun Math Phys 44 197ndash210 (1975)
[504] M Perroud Projective representations of the Schroumldinger group Helv Phys Acta 50 233ndash252 (1977)
[505] J Phillips A note on square-integrable representations J Funct Anal 20 83ndash92 (1975)[506] D Pietrobon P Baldi D Marinucci Integrated Sachs-Wolfe effect from the cross
correlation of WMAP3 year and the NRAO VLA sky survey data New results andconstraints on dark energy Phys Rev D 74 043524 (2006)
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[508] V Pop D Rosca Generalized piecewise constant orthogonal wavelet bases on 2D-domains Appl Anal 90 715ndash723 (2011)
[509] G Poumlschl E Teller Bemerkungen zur Quantenmechanik des anharmonischen OszillatorsZ Physik 83 143ndash151 (1933)
[510] D Potts G Steidl M Tasche Kernels of spherical harmonics and spherical frames inAdvanced Topics in Multivariate Approximation ed by F Fontanella K Jetter PJ Laurent(World Scientific Singapore 1996) pp 287ndash301
[511] E Prugovecki Consistent formulation of relativistic dynamics for massive spin-zeroparticles in external fields Phys Rev D 18 3655ndash3673 (1978) (Appendix C)
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[513] C Quesne Coherent states of the real symplectic group in a complex analytic parametriza-tion I II J Math Phys 27 428ndash441 869ndash878 (1986)
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[515] JM Radcliffe Some properties of spin coherent states J Phys A Math Gen 4 313ndash323(1971)
[516] A Rahimi A Najati YN Dehghan Continuous frames in Hilbert spaces Methods FunctAnal Topol 12 170ndash182 (2006)
[517] H Rauhut M Roumlsler Radial multiresolution in dimension three Constr Approx 22 193ndash218 (2005)
[518] JH Rawnsley Coherent states and Kaumlhler manifolds Quart J Math Oxford 28(2) 403ndash415 (1977)
[519] J Renaud The contraction of the SU(11) discrete series of representations by means ofcoherent states J Math Phys 37 3168ndash3179 (1996)
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[521] D Robert La coheacuterence dans tous ses eacutetats SMF Gazette 132 (2012)[522] JE Roberts The Dirac bra and ket formalism J Math Phys 7 1097ndash1104 (1966)[523] JE Roberts Rigged Hilbert spaces in quantum mechanics Commun Math Phys 3 98ndash
119 (1966)[524] S Roques F Bourzeix K Bouyoucef Soft-thresholding technique and restoration of
3C273 jet Astrophys Space Sci Nr 239 297ndash304 (1996)[525] D Rosca Haar wavelets on spherical triangulations in Advances in Multiresolution for
Geometric Modelling ed by NA Dogson MS Floater MA Sabin (Springer Berlin2005) pp 407ndash419
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501ndash511 (2007)[529] D Rosca Wavelet bases on the sphere obtained by radial projection J Fourier Anal Appl
13 421ndash434 (2007)[530] D Rosca Piecewise constant wavelets on triangulations obtained by 1ndash3 splitting Int J
Wavelets Multiresolut Inf Process 6 209ndash222 (2008)[531] D Rosca On a norm equivalence on L2(S2) Results Math 53 399ndash405 (2009)[532] D Rosca New uniform grids on the sphere Astron Astrophys 520 (2010) Art A63[533] D Rosca Uniform and refinable grids on elliptic domains and on some surfaces of
revolution Appl Math Comput 217 7812ndash7817 (2011)[534] D Rosca Wavelet analysis on some surfaces of revolution via area preserving projection
Appl Comput Harmon Anal 30 262ndash272 (2011)[535] D Rosca J-P Antoine Locally supported orthogonal wavelet bases on the sphere via
stereographic projection Math Probl Eng 2009 124904 (2009)[536] D Rosca J-P Antoine Constructing wavelet frames and orthogonal wavelet bases on the
sphere in Recent Advances in Signal Processing ed by S Miron (IN-TECH ViennaAustria and Rijeka Croatia 2010) pp 59ndash76
[537] D Rosca G Plonka Uniform spherical grids via area preserving projection from the cubeto the sphere J Comput Appl Math 236 1033ndash1041 (2011)
[538] D Rosca G Plonka An area preserving projection from the regular octahedron to thesphere Results Math 63 429ndash444 (2012)
[539] H Rossi M Vergne Analytic continuation of the holomorphic discrete series for a semi-simple Lie group Acta Math 136 1ndash59 (1976)
[540] DJ Rotenberg Application of Sturmian functions to the Schroedinger three-body prob-lem Elastic e+ndashH scattering Ann Phys (NY) 19 262ndash278 (1962)
[541] C Rovelli Zakopane lectures on loop gravity in Proceedings of 3rd Quantum Gravityand Quantum Geometry School 28 Febndash13 March 2011 (Zakopane Poland 2011)arXiv11023660v5
[542] C Rovelli S Speziale A semiclassical tetrahedron Class Quant Grav 23 5861ndash5870(2006)
[543] DJ Rowe Coherent state theory of the noncompact symplectic group J Math Phys 252662ndash2271 (1984)
[544] DJ Rowe Microscopic theory of the nuclear collective model Rep Prog Phys 48 1419ndash1480 (1985)
[545] DJ Rowe Vector coherent state representations and their inner products J Phys A MathGen 45 244003 (2012) (This paper belongs to the special issue [38])
[546] DJ Rowe J Repka Vector-coherent-state theory as a theory of induced representationsJ Math Phys 32 2614ndash2634 (1991)
[547] DJ Rowe G Rosensteel R Gilmore Vector coherent state representation theory J MathPhys 26 2787ndash2791 (1985)
[548] A Royer Phase states and phase operators for the quantum harmonic oscillator Phys RevA 53 70ndash108 (1996)
[549] J Saletan Contraction of Lie groups J Math Phys 2 1ndash21 (1961)[550] G Saracco A Grossmann P Tchamitchian Use of wavelet transforms in the study of
propagation of transient acoustic signals across a plane interface between two homoge-neous media in Wavelets Time-Frequency Methods and Phase Space (Proc Marseille1987) ed by J-M Combes A Grossmann P Tchamitchian 2nd edn (Springer Berlin1990) pp 139ndash146
[551] P Schroumlder W Sweldens Spherical wavelets Efficiently representing functions on thesphere in Computer Graphics Proceedings (SIGGRAPH95) (ACM Siggraph Los Angeles1995) pp 161ndash175
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[554] H Scutaru Coherent states and induced representations Lett Math Phys 2 101ndash107(1977)
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Math 137 82ndash203 (1998)[557] R Simon ECG Sudarshan N Mukunda Gaussian pure states in quantum mechanics
and the symplectic group Phys Rev A37 3028ndash3038 (1988)[558] S Sivakumar Studies on nonlinear coherent states J Opt B Quant Semiclass Opt 2
R61ndashR75 (2000)[559] E Slezak A Bijaoui G Mars Identification of structures from galaxy counts Use of the
wavelet transform Astron Astroph 227 301ndash316 (1990)[560] A Solomon A characteristic functional for deformed photon phenomenology Phys Lett
A 196 29ndash34 (1994)[561] SB Sontz Paragrassmann algebras as quantum spaces Part I Reproducing kernels in
Geometric Methods in Physics XXXI Workshop 2012 (Trends in Mathematics ed byP Kielanowski et al Birkhaumluser Verlag Basel 2013) pp 47ndash63
[562] SB Sontz Paragrassmann algebras as quantum spaces Part II Toeplitz operators J OperTh (2013 to appear) arXiv12055493
[563] SB Sontz A reproducing kernel and Toeplitz operators in the quantum plane Preprint(2013) arXiv13056986 [math-ph]
[564] SB Sontz Toeplitz quantization of an algebra with conjugation Preprint (2013)arXiv13085454 [math-ph]
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[567] J-L Starck DL Donoho E J Candegraves Astronomical image representation by the curvelettransform Astron Astroph 398 785ndash800 (2003)
[568] J-L Starck Y Moudden P Abrial M Nguyen Wavelets ridgelets and curvelets on thesphere Astron Astroph 446 1191ndash1204 (2006)
[569] MB Stenzel The Segal-Bargmann transform on a symmetric space of compact type JFunct Analysis 165 44ndash58 (1994)
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[572] W Sweldens The lifting scheme A custom-design construction of biorthogonal waveletsApplied Comput Harmon Anal 3 1186ndash1200 (1996)
[573] W Sweldens The lifting scheme A construction of second generation wavelets SIAM JMath Anal 29 511ndash546 (1998)
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[575] FH Szafraniec Multipliers in the reproducing kernel Hilbert space subnormality andnoncommutative complex analysis in Reproducing Kernel Spaces and Applications edby D Alpay Operator Theory Advances and Applications vol 143 (Birkhaumluser Basel2003) pp 313ndash331
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Proceedings of the 27th International Cosmic Ray Conference (ICRC 2001) (CopernicusGesellschaft DE 2001) pp 2923ndash2926
[579] T Thiemann Gauge field theory coherent states (GCS) 1 General properties Class QuantGrav 18 2025ndash2064 (2001)
[580] T Thiemann O Winkler Gauge field theory coherent states (GCS) 2 Peakednessproperties Class Quant Grav 18 2561ndash2636 (2001)
[581] T Thiemann O Winkler Gauge field theory coherent states (GCS) 3 Ehrenfest theoremsClass Quant Grav 18 4629ndash4682 (2001)
[582] T Thiemann O Winkler Gauge field theory coherent states (GCS) 4 Infinite tensorproduct and thermodynamical limit Class Quant Grav 18 4997ndash5054 (2001)
[583] K Thirulagasanthar ST Ali Regular subspaces of a quaternionic Hilbert space fromquaternionic Hermite polynomials and associated coherent states J Math Phys 54013506 (2013)
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Ann Inst H Poincareacute 56 215ndash234 (1992)[588] B Torreacutesani Position-frequency analysis for signals defined on spheres Signal Proc 43
341ndash346 (2005)[589] DA Trifonov Generalized intelligent states and squeezing J Math Phys 35 2297ndash2308
(1994)[590] AS Trushechkin IV Volovich Localization properties of squeezed quantum states in
nanoscale space domains preprint (2013) arXiv13046277v1 [quant-ph][591] M Unser N Chenouard A unifying parametric framework for 2D steerable wavelet
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simulation of an impact test using wavelets analytical and finite element models Int JSolids Struct 38 5481ndash5508 (2001)
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[596] J Voisin On some unitary representations of the Galilei group I Irreducible representa-tions J Math Phys 6 1519ndash1529 (1965)
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[598] DF Walls Squeezed states of light Nature 306 141ndash146 (1983)[599] YK Wang FT Hioe Phase transition in the Dicke maser model Phys Rev A 7 831ndash836
(1973)[600] PSP Wang J Yang A review of wavelet-based edge detection methods Int J Patt
Recogn Artif Intell 26 1255011 (2012)[601] I Weinreich A construction of C1-wavelets on the two-dimensional sphere Appl Comput
Harmon Anal 10 1ndash26 (2001)[602] H Weyl Quantenmechanik und Gruppentheorie Z Phys 46 1ndash46 (1927)
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[603] Y Wiaux L Jacques P Vandergheynst Correspondence principle between spherical andEuclidean wavelets Astrophys J 632 15ndash28 (2005)
[604] Y Wiaux L Jacques P Vielva P Vandergheynst Fast directional correlation on the spherewith steerable filters Astrophys J 652 820ndash832 (2006)
[605] Y Wiaux JD McEwen P Vandergheynst O Blanc Exact reconstruction with directionalwavelets on the sphere Mon Not R Astron Soc 388 770ndash788 (2008)
[606] WM Wieland Complex Ashtekar variables and reality conditions for Holstrsquos action AnnHenri Poincareacute 13 425ndash448 (2012)
[607] EP Wigner On the quantum correction for thermodynamic equilibrium Phys Rev 40749ndash759 (1932)
[608] RM Willette RD Nowak Platelets A multiscale approach for recovering edges andsurfaces in photon-limited medical imaging IEEE Trans Med Imaging 22 332ndash350(2003)
[609] W Wisnoe P Gajan A Strzelecki C Lempereur J-M Matheacute The use of the two-dimensional wavelet transform in flow visualization processing in Progress in WaveletAnalysis and Applications (Proc Toulouse 1992) ed by Y Meyer S Roques (EdFrontiegraveres Gif-sur-Yvette 1993) pp 455ndash458
[610] K Woacutedkiewicz On the quantum mechanics of squeezed states J Modern Optics 34 941ndash948(1987)
[611] JA Yeazell M Mallalieu CR Stroud Jr Observation of the collapse and revival of aRydberg electronic wave packet Phys Rev Lett 64 2007ndash2010 (1990)
[612] JA Yeazell CR Stroud Jr Observation of fractional revivals in the evolution of aRydberg atomic wave packet Phys Rev A 43 5153ndash5156 (1991)
[613] HP Yuen Two-photon coherent states of the radiation field Phys Rev A 13 2226ndash2243(1976)
[614] J Zak Balian-Low theorem for Landau levels Phys Rev Lett 79 533ndash536 (1997)[615] J Zak Orthonormal sets of localized functions for a Landau level J Math Phys 39 4195ndash
4200 (1998) and references quoted there[616] AA Zakharova On the properties of generalized frames Math Notes 83 190ndash200 (2008)[617] W-M Zhang DH Feng R Gilmore Coherent states Theory and some applications Rev
Mod Phys 26 867ndash927 (1990)[618] I Zlatev W-M Zhang DH Feng Possibility that Schroumldingerrsquos conjecture for the
hydrogen atom coherent states is not attainable Phys Rev A 50 R1973ndashR1975 (1994)[619] WH Zurek Decoherence einselection and the quantum origins of the classical Rev Mod
Phys 75 715ndash775 (2003)[620] WH Zurek S Habib JP Paz Coherent states via decoherence Phys Rev Lett 70 1187ndash
1190 (1993)[621] K Zyczkowski Squeezed states in a quantum chaotic system J Phys A Math Theor 22
of SU(11) 81 296 297HilbertClowast-modules 164holomorphic 140nonholomorphic 151nonlinear 146of affine Galilei group 505of affine Poincareacute group 509of affine Weyl-Heisenberg group GaWH
497of compact semisimple Lie groups 174of Euclidean group E(n) 266of Galilei group G (11) 290of isochronous Galilei group 237of non-semisimple Lie groups 179of noncompact semisimple Lie groups 177of Poincareacute group Puarr
+(11) 283massless case 288
of Poincareacute group Puarr+(13) 279
of Schroumldinger group 508quasi-coherent states 186quaternionic 164
ST Ali et al Coherent States Wavelets and Their Generalizations Theoreticaland Mathematical Physics DOI 101007978-1-4614-8535-3copy Springer Science+Business Media New York 2014
573
574 Index
coherent states (CS) (cont)spin or SU(2) 175square integrable covariant 166 180 264vector (VCS) 73 108 112 170weighted 184 523
of affine Weyl-Heisenberg group GaWH497
of Poincareacute group Puarr+(11) 284
cohomology group 393 403coboundaries 403cochains 402cocycle 403
algebraic 387Cauchy 418Cauchy-Paul 354 419 425conical 418difference 417 462directional 416 440kinematical 499local 488metabolite-based 355 374minimal uncertainty 425multiselective 440on a graph 493on the sphere S
2 458on the sphere S
n 479on the torus T2 481steerable 439von Mises 440
wedgelet transform 455Wigner function 322Wigner-Ville transform 349Windowed Fourier or Gabor transform 349
ZZak transform 518
References
A Books and Theses
B Articles
Index
544 References
[Kem37] EC Kemble Fundamental Principles of Quantum Mechanics (McGraw Hill NewYork 1937)
[Kir76] AA Kirillov Elements of the Theory of Representations (Springer Berlin 1976)[Kla68] JR Klauder ECG Sudarshan Fundamentals of Quantum Optics (Benjamin New
York 1968)[Kla85] JR Klauder BS Skagerstam Coherent States ndash Applications in Physics and
Mathematical Physics (World Scientific Singapore 1985)[Kla00] JR Klauder Beyond Conventional Quantization (Cambridge University Press Cam-
bridge 2000)[Kla11] JR Klauder A Modern Approach to Functional Integration (BirkhaumluserSpringer
New York 2011)[Kna96] AW Knapp Lie Groups Beyond an Introduction (Birkhaumluser Basel 1996 2nd edn
2002)[Kut12] G Kutyniok D Labate (eds) Shearlets Multiscale Analysis for Multivariate Data
(Birkhaumluser Boston 2012)[Lan81] L Landau E Lifchitz Mechanics 3rd edn (Pergamon Oxford1981)[Lan93] S Lang Algebra 3rd edn (Addison-Wesley Reading MA 1993)[Lie97] EH Lieb M Loss Analysis (American Mathematical Society Providence RI 1997)[Lip74] RL Lipsman Group Representations Lecture Notes in Mathematics vol 388
(Springer Berlin 1974)[Lyn82] PA Lynn An Introduction to the Analysis and Processing of Signals 2nd edn
(MacMillan London 1982)[Mac68] GW Mackey Induced Representations of Groups and Quantum Mechanics (Ben-
jamin New York 1968)[Mac76] GW Mackey Theory of Unitary Group Representations (University of Chicago
Press Chicago 1976)[Mad95] J Madore An Introduction to Noncommutative Differential Geometry and Its Physical
Applications (Cambridge University Press Cambridge 1995)[Mae94] S Maes The wavelet transform in signal processing with application to the extraction
of the speech modulation model features Thegravese de Doctorat Univ Cath LouvainLouvain-la-Neuve 1994
[Mag66] W Magnus F Oberhettinger RP Soni Formulas and Theorems for the SpecialFunctions of Mathematical Physics (Springer Berlin 1966)
[Mal99] SG Mallat A Wavelet Tour of Signal Processing 2nd edn (Academic San Diego1999)
[Mar82] D Marr Vision (Freeman San Francisco 1982)[Mes62] H Meschkowsky Hilbertsche Raumlume mit Kernfunktionen (Springer Berlin 1962)[Mey91] Y Meyer (ed) Wavelets and Applications (Proc Marseille 1989) (Masson and
Springer Paris and Berlin 1991)[Mey92] Y Meyer Les Ondelettes Algorithmes et Applications (Armand Colin Paris 1992)
English translation Wavelets Algorithms and Applications (SIAM Philadelphia1993)
[Mey00] CD Meyer Matrix Analysis and Applied Linear Algebra (SIAM Philadelphia 2000)[Mey93] Y Meyer S Roques (eds) Progress in Wavelet Analysis and Applications (Proc
Toulouse 1992) (Ed Frontiegraveres Gif-sur-Yvette 1993)[Mur90] R Murenzi Ondelettes multidimensionnelles et applications agrave lrsquoanalyse drsquoimages
Thegravese de Doctorat Univ Cath Louvain Louvain-la-Neuve 1990[vNe55] J von Neumann Mathematical Foundations of Quantum Mechanics (Princeton
University Press Princeton NJ 1955) (English translated by RT Byer)[Pap02] A Papoulis SU Pillai Probability Random Variables and Stochastic Processes 4th
edn (McGraw Hill New York 2002)[Par05] KR Parthasarathy Probability Measures on Metric Spaces (AMS Chelsea Publish-
ing Providence RI 2005)
References 545
[Pau85] T Paul Ondelettes et Meacutecanique Quantique Thegravese de doctorat Univ drsquoAix-MarseilleII 1985
[Per86] AM Perelomov Generalized Coherent States and Their Applications (SpringerBerlin 1986)
[Per05] G Peyreacute Geacuteomeacutetrie multi-eacutechelles pour les images et les textures Thegravese de doctoratEcole Polytechnique Palaiseau 2005
[Pru86] E Prugovecki Stochastic Quantum Mechanics and Quantum Spacetime (ReidelDordrecht 1986)
[Rau04] H Rauhut Time-frequency and wavelet analysis of functions with symmetry proper-ties PhD thesis TU Muumlnich 2004
[Ree80] M Reed B Simon Methods of Modern Mathematical Physics I Functional Analysis(Academic New York 1980)
[Rud62] W Rudin Fourier Analysis on Groups (Interscience New York 1962)[Sch96] FE Schroeck Jr Quantum Mechanics on Phase Space (Kluwer Dordrecht 1996)[Sch61] L Schwartz Meacutethodes matheacutematiques pour les sciences physiques (Hermann Paris
1961)[Scu97] MO Scully MS Zubairy Quantum Optics (Cambridge University Press Cam-
bridge 1997)[Sho50] JA Shohat JD Tamarkin The Problem of Moments (American Mathematical
Society Providence RI 1950)[Ste71] EM Stein G Weiss Introduction to Fourier Analysis on Euclidean Spaces (Prince-
ton University Press Princeton NJ 1971)[Str64] RF Streater AS Wightman PCT Spin and Statistics and All That (Benjamin New
York 1964)[Sug90] M Sugiura Unitary Representations and Harmonic Analysis An Introduction
(North-HollandKodansha Ltd Tokyo 1990)[Suv11] A Suvichakorn C Lemke A Schuck Jr J-P Antoine The continuous wavelet
transform in MRS Tutorial text Marie Curie Research Training Network FAST(2011) httpwwwfast-mariecurie-rtn-projecteuWavelet
[Tak79] M Takesaki Theory of Operator Algebras I (Springer New York 1979)[Ter88] A Terras Harmonic Analysis on Symmetric Spaces and Applications II (Springer
Berlin 1988)[Tho98] G Thonet New aspects of time-frequency analysis for biomedical signal processing
Thegravese de Doctorat EPFL Lausanne 1998[Tor95] B Torreacutesani Analyse continue par ondelettes (InterEacuteditionsCNRS Eacuteditions Paris
1995)[Unt87] A Unterberger Analyse harmonique et analyse pseudo-diffeacuterentielle du cocircne de
lumiegravere Asteacuterisque 156 1ndash201 (1987)[Unt91] A Unterberger Quantification relativiste Meacutem Soc Math France 44ndash45 1ndash215
(1991)[Van98] P Vandergheynst Ondelettes directionnelles et ondelettes sur la sphegravere Thegravese de
Doctorat Univ Cath Louvain Louvain-la-Neuve 1998[Var85] VS Varadarajan Geometry of Quantum Theory 2nd edn (Springer New York 1985)[Vet95] M Vetterli J Kovacevic Wavelets and Subband Coding (Prentice Hall Englewood
Cliffs NJ 1995)[Vil69] NJ Vilenkin Fonctions speacuteciales et theacuteorie de la repreacutesentation des groupes (Dunod
Paris 1969)[Wel03] GV Welland Beyond Wavelets (Academic New York 2003)[vWe86] C von Westenholz Differential Forms in Mathematical Physics (North-Holland
Amsterdam 1986)[Wey28] H Weyl Gruppentheorie und Quantenmechanik (Hirzel Leipzig 1928)[Wey31] H Weyl The Theory of Groups and Quantum Mechanics (Dover New York 1931)[Wic94] MV Wickerhauser Adapted Wavelet Analysis from Theory to Software (A K Peters
Wellesley MA 1994)
546 References
[Wis93] W Wisnoe Utilisation de la meacutethode de transformeacutee en ondelettes 2D pour lrsquoanalysede visualisation drsquoeacutecoulements Thegravese de Doctorat ENSAE Toulouse 1993
[Woj97] P Wojtaszczyk A Mathematical Introduction to Wavelets (Cambridge UniversityPress Cambridge 1997)
[Zac06] C Zachos D Fairlie T Curtright Quantum Mechanics in Phase Space An OverviewWith Selected Papers (World Scientific Publishing Singapore 2006)
B Articles
[1] P Abry R Baraniuk P Flandrin R Riedi D Veitch Multiscale nature of network trafficIEEE Signal Process Mag 19 28ndash46 (2002)
[2] MD Adams The JPEG-2000 still image compression standardhttpwwweceuvicca~frodopublicationsjpeg2000pdf
[3] SL Adler AC Millard Coherent states in quaternionic quantum mechanics J MathPhys 38 2117ndash2126 (1997)
[4] GS Agarwal K Tara Nonclassical properties of states generated by the excitation on acoherent state Phys Rev A 43 492ndash497 (1991)
[5] GS Agarwal E Wolf Calculus for functions of noncommuting operators and generalphase-space methods in quantum mechanics I Mapping theorems and ordering of func-tions of noncommuting operators Phys Rev D 2 2161ndash2186 (1970)
[6] GS Agarwal E Wolf Calculus for functions of noncommuting operators and generalphase-space methods in quantum mechanics II Quantum mechanics in phase space PhysRev D 2 2187ndash2205 (1970)
[7] GS Agarwal E Wolf Calculus for functions of noncommuting operators and generalphase-space methods in quantum mechanics III A generalized Wick theorem and multi-time mapping Phys Rev D 2 2206ndash2225 (1970)
[8] V Aldaya J Guerrero G Marmo Quantization on a Lie group Higher-order polariza-tions in Symmetry in Sciences X ed by B Gruber M Ramek (Plenum Press Nerw York1998) pp 1ndash36
[9] M Alexandrescu D Gibert G Hulot J-L Le Mouel G Saracco Worldwide waveletanalysis of geomagnetic jerks J Geophys Res B 101 21975ndash21994 (1996)
[10] G Alexanian A Pinzul A Stern Generalized coherent state approach to star productsand applications to the fuzzy sphere Nucl Phys B 600 531ndash547 (2001)
[11] ST Ali A geometrical property of POV-measures and systems of covariance in Differ-ential Geometric Methods in Mathematical Physics ed by HD Doebner SI AnderssonHR Petry Lecture Notes in Mathematics vol 905 (Springer Berlin 1982) pp 207ndash22
[12] ST Ali Commutative systems of covariance and a generalization of Mackeyrsquos imprimi-tivity theorem Canad Math Bull 27 390ndash397 (1984)
[13] ST Ali Stochastic localisation quantum mechanics on phase space and quantum space-time Riv Nuovo Cim 8(11) 1ndash128 (1985)
[14] ST Ali A general theorem on square-integrability Vector coherent states J Math Phys39 3954ndash3964 (1998)
[15] ST Ali J-P Antoine Coherent states of 1+1 dimensional Poincareacute group Squareintegrability and a relativistic Weyl transform Ann Inst H Poincareacute 51 23ndash44 (1989)
[16] ST Ali S De Biegravevre Coherent states and quantization on homogeneous spaces in GroupTheoretical Methods in Physics ed by H-D Doebner et al Lecture Notes in Mathematicsvol 313 (Springer Berlin 1988) pp 201ndash207
References 547
[17] ST Ali H-D Doebner Ordering problem in quantum mechanics Prime quantization anda physical interpretation Phys Rev A 41 1199ndash1210 (1990)
[18] ST Ali GG Emch Geometric quantization Modular reduction theory and coherentstates J Math Phys 27 2936ndash2943 (1986)
[19] ST Ali M Engliš J-P Gazeau Vector coherent states from Plancherelrsquos theorem andClifford algebras J Phys A 37 6067ndash6089 (2004)
[20] ST Ali MEH Ismail Some orthogonal polynomials arising from coherent states JPhys A 45 125203 (2012) (16pp)
[21] ST Ali UA Mueller Quantization of a classical system on a coadjoint orbit of thePoincareacute group in 1+1 dimensions J Math Phys 35 4405ndash4422 (1994)
[22] ST Ali E Prugovecki Systems of imprimitivity and representations of quantum mechan-ics on fuzzy phase spaces J Math Phys 18 219ndash228 (1977)
[23] ST Ali E Prugovecki Mathematical problems of stochastic quantum mechanics Har-monic analysis on phase space and quantum geometry Acta Appl Math 6 1ndash18 (1986)
[24] ST Ali E Prugovecki Extended harmonic analysis of phase space representation for theGalilei group Acta Appl Math 6 19ndash45 (1986)
[25] ST Ali E Prugovecki Harmonic analysis and systems of covariance for phase spacerepresentation of the Poincareacute group Acta Appl Math 6 47ndash62 (1986)
[26] ST Ali J-P Antoine J-P Gazeau De Sitter to Poincareacute contraction and relativisticcoherent states Ann Inst H Poincareacute 52 83ndash111 (1990)
[27] ST Ali J-P Antoine J-P Gazeau Square integrability of group representations onhomogeneous spaces I Reproducing triples and frames Ann Inst H Poincareacute 55 829ndash855 (1991)
[28] ST Ali J-P Antoine J-P Gazeau Square integrability of group representations onhomogeneous spaces II Coherent and quasi-coherent states The case of the Poincareacutegroup Ann Inst H Poincareacute 55 857ndash890 (1991)
[29] ST Ali J-P Antoine J-P Gazeau Continuous frames in Hilbert space Ann Phys(NY)222 1ndash37 (1993)
[30] ST Ali J-P Antoine J-P Gazeau Relativistic quantum frames Ann Phys(NY) 222 38ndash88 (1993)
[31] ST Ali J-P Antoine J-P Gazeau UA Mueller Coherent states and their generalizationsA mathematical overview Rev Math Phys 7 1013ndash1104 (1995)
[32] ST Ali J-P Gazeau MR Karim Frames the β -duality in Minkowski space and spincoherent states J Phys A Math Gen 29 5529ndash5549 (1996)
[33] ST Ali M Engliš Quantization methods A guide for physicists and analysts Rev MathPhys 17 391ndash490 (2005)
[34] ST Ali J-P Gazeau B Heller Coherent states and Bayesian duality J Phys A MathTheor 41 365302 (2008)
[35] ST Ali L Balkovaacute EMF Curado J-P Gazeau MA Rego-Monteiro LMCSRodrigues K Sekimoto Non-commutative reading of the complex plane through Delonesequences J Math Phys 50 043517 (2009)
[36] ST Ali C Carmeli T Heinosaari A Toigo Commutative POVMS and fuzzy observ-ables Found Phys 39 593ndash612 (2009)
[37] ST Ali T Bhattacharyya SS Roy Coherent states on Hilbert modules J Phys A MathTheor 44 275202 (2011)
[38] ST Ali J-P Antoine F Bagarello J-P Gazeau (Guest Editors) Coherent states Acontemporary panorama preface to a special issue on Coherent states Mathematical andphysical aspects J Phys A Math Gen 45(24) (2012)
[39] ST Ali F Bagarello J-P Gazeau Quantizations from reproducing kernel spaces AnnPhys (NY) 332 127ndash142 (2013)
[40] STAli K Goacuterska A Horzela F Szafraniec Squeezed states and Hermite polynomials ina complex variable Preprint (2013) arXiv13084730v1 [quant-phy]
[41] P Aniello G Cassinelli E De Vito A Levrero Square-integrability of induced represen-tations of semidirect products Rev Math Phys 10 301ndash313 (1998)
548 References
[42] P Aniello G Cassinelli E De Vito A Levrero Wavelet transforms and discrete framesassociated to semidirect products J Math Phys 39 3965ndash3973 (1998)
[43] J-P Antoine Remarques sur le vecteur de Runge-Lenz Ann Soc Scient Bruxelles 80160ndash168 (1966)
[44] J-P Antoine Etude de la deacutegeacuteneacuterescence orbitale du potentiel coulombien en theacuteorie desgroupes I II Ann Soc Scient Bruxelles 80 169ndash184 (1966)
[45] J-P Antoine Etude de la deacutegeacuteneacuterescence orbitale du potentiel coulombien en theacuteorie desgroupes I II Ann Soc Scient Bruxelles 81 49ndash68 (1967)
[46] J-P Antoine Dirac formalism and symmetry problems in quantum mechanics I Generaldirac formalism J Math Phys 10 53ndash69 (1969)
[47] J-P Antoine Dirac formalism and symmetry problems in quantum mechanics II Symme-try problems J Math Phys 10 2276ndash2290 (1969)
[48] J-P Antoine Quantum mechanics beyond Hilbert space in Irreversibility and Causality mdashSemigroups and Rigged Hilbert Spaces ed by A Boumlhm H-D Doebner P KielanowskiLecture Notes in Physics vol 504 (Springer Berlin 1998) pp 3ndash33
[49] J-P Antoine Discrete wavelets on abelian locally compact groups Rev Cien Math(Habana) 19 3ndash21 (2003)
[50] J-P Antoine Introduction to precursors in physics Affine coherent states in FundamentalPapers in Wavelet Theory ed by C Heil D Walnut (Princeton University Press PrincetonNJ 2006) pp 113ndash116
[51] J-P Antoine F Bagarello Wavelet-like orthonormal bases for the lowest Landau levelJ Phys A Math Gen 27 2471ndash2481 (1994)
[52] J-P Antoine P Balazs Frames and semi-frames J Phys A Math Theor 44 205201(2011) (25 pages) Corrigendum J-P Antoine P Balazs Frames and semi-frames J PhysA Math Theor 44 479501 (2011) (2 pages)
[53] J-P Antoine P Balazs Frames semi-frames and Hilbert scales Numer Funct AnalOptim 33 736ndash769 (2012)
[54] J-P Antoine A Coron Time-frequency and time-scale approach to magnetic resonancespectroscopy J Comput Methods Sci Eng (JCMSE) 1 327ndash352 (2001)
[55] J-P Antoine AL Hohoueacuteto Discrete frames of Poincareacute coherent states in 1+3 dimen-sions J Fourier Anal Appl 9 141ndash173 (2003)
[56] J-P Antoine I Mahara Galilean wavelets Coherent states for the affine Galilei groupJ Math Phys 40 5956ndash5971 (1999)
[57] J-P Antoine U Moschella Poincareacute coherent states The two-dimensional massless caseJ Phys A Math Gen 26 591ndash607 (1993)
[58] J-P Antoine R Murenzi Two-dimensional directional wavelets and the scale-anglerepresentation Signal Process 52 259ndash281 (1996)
[59] J-P Antoine R Murenzi Two-dimensional continuous wavelet transform as linear phasespace representation of two-dimensional signals in Wavelet Applications IV SPIE Pro-ceedings vol 3078 (SPIE Bellingham WA 1997) pp 206ndash217
[60] J-P Antoine D Rosca The wavelet transform on the two-sphere and related manifolds mdashA review in Optical and Digital Image Processing SPIE Proceedings vol 7000 (2008)pp 70000B-1ndash15
[61] J-P Antoine D Speiser Characters of irreducible representations of simple Lie groupsJ Math Phys 5 1226ndash1234 (1964)
[62] J-P Antoine P Vandergheynst Wavelets on the n-sphere and related manifolds J MathPhys 39 3987ndash4008 (1998)
[63] J-P Antoine P Vandergheynst Wavelets on the 2-sphere A group-theoretical approachAppl Comput Harmon Anal 7 262ndash291 (1999)
[64] J-P Antoine P Vandergheynst Wavelets on the two-sphere and other conic sections JFourier Anal Appl 13 369ndash386 (2007)
[65] J-P Antoine M Duval-Destin R Murenzi B Piette Image analysis with 2D wavelettransform Detection of position orientation and visual contrast of simple objects inWavelets and Applications (Proc Marseille 1989) ed by Y Meyer (Masson and SpringerParis and Berlin 1991) pp144ndash159
References 549
[66] J-P Antoine P Carrette R Murenzi B Piette Image analysis with 2D continuous wavelettransform Signal Process 31 241ndash272 (1993)
[67] J-P Antoine P Vandergheynst K Bouyoucef R Murenzi Alternative representations ofan image via the 2D wavelet transform Application to character recognition in VisualInformation Processing IV SPIE Proceedings vol 2488 (SPIE Bellingham WA 1995)pp 486ndash497
[68] J-P Antoine R Murenzi P Vandergheynst Two-dimensional directional wavelets inimage processing Int J Imaging Syst Tech 7 152ndash165 (1996)
[69] J-P Antoine D Barache RM Cesar Jr LF Costa Shape characterization with thewavelet transform Signal Process 62 265ndash290 (1997)
[70] J-P Antoine P Antoine B Piraux Wavelets in atomic physics in Spline Functions andthe Theory of Wavelets ed by S Dubuc G Deslauriers CRM Proceedings and LectureNotes vol 18 (AMS Providence RI 1999) pp261ndash276
[71] J-P Antoine P Antoine B Piraux Wavelets in atomic physics and in solid state physicsin Wavelets in Physics Chap 8 ed by JC van den Berg (Cambridge University PressCambridge 1999)
[72] J-P Antoine R Murenzi P Vandergheynst Directional wavelets revisited Cauchywavelets and symmetry detection in patterns Appl Comput Harmon Anal 6 314ndash345(1999)
[73] J-P Antoine L Jacques R Twarock Wavelet analysis of a quasiperiodic tiling withfivefold symmetry Phys Lett A 261 265ndash274 (1999)
[74] J-P Antoine L Jacques P Vandergheynst Penrose tilings quasicrystals and wavelets inWavelet Applications in Signal and Image Processing VII SPIE Proceedings vol 3813(SPIE Bellingham WA 1999) pp 28ndash39
[75] J-P Antoine YB Kouagou D Lambert B Torreacutesani An algebraic approach to discretedilations Application to discrete wavelet transforms J Fourier Anal Appl 6 113ndash141(2000)
[76] J-P Antoine A Coron J-M Dereppe Water peak suppression Time-frequency vs time-scale approach J Magn Reson 144 189ndash194 (2000)
[77] J-P Antoine J-P Gazeau P Monceau J R Klauder K Penson Temporally stablecoherent states for infinite well and Poumlschl-Teller potentials J Math Phys 42 2349ndash2387(2001)
[78] J-P Antoine A Coron C Chauvin Wavelets and related time-frequency techniques inmagnetic resonance spectroscopy NMR Biomed 14 265ndash270 (2001)
[79] J-P Antoine L Demanet J-F Hochedez L Jacques R Terrier E Verwichte Applicationof the 2-D wavelet transform to astrophysical images Phys Mag 24 93ndash116 (2002)
[80] J-P Antoine L Demanet L Jacques P Vandergheynst Wavelets on the sphere Imple-mentation and approximations Appl Comput Harmon Anal 13 177ndash200 (2002)
[81] J-P Antoine I Bogdanova P Vandergheynst The continuous wavelet transform on conicsections Int J Wavelets Multires Inform Proc 6 137ndash156 (2007)
[82] J-P Antoine D Rosca P Vandergheynst Wavelet transform on manifolds Old and newapproaches Appl Comput Harmon Anal 28 189ndash202 (2010)
[83] P Antoine B Piraux A Maquet Time profile of harmonics generated by a single atom ina strong electromagnetic field Phys Rev A 51 R1750ndashR1753 (1995)
[84] P Antoine B Piraux DB Miloševic M Gajda Generation of ultrashort pulses ofharmonics Phys Rev A 54 R1761ndashR1764 (1996)
[85] P Antoine B Piraux DB Miloševic M Gajda Temporal profile and time control ofharmonic generation Laser Phys 7 594ndash601 (1997)
[86] Apollonius see Wikipedia httpenwikipediaorgwikiApollonius_of_Perga[87] FT Arecchi E Courtens R Gilmore H Thomas Atomic coherent states in quantum
optics Phys Rev A 6 2211ndash2237 (1972)[88] I Aremua J-P Gazeau MN Hounkonnou Action-angle coherent states for quantum
systems with cylindric phase space J Phys A Math Theor 45 335302 (2012)
550 References
[89] F Argoul A Arneacuteodo G Grasseau Y Gagne EJ Hopfinger Wavelet analysis ofturbulence reveals the multifractal nature of the Richardson cascade Nature 338 51ndash53(1989)
[90] F Argoul A Arneacuteodo J Elezgaray G Grasseau R Murenzi Wavelet analysis of theself-similarity of diffusion-limited aggregates and electrodeposition clusters Phys Rev A41 5537ndash5560 (1990)
[91] TA Arias Multiresolution analysis of electronic structure Semicardinal and waveletbases Rev Mod Phys 71 267ndash312 (1999)
[92] A Arneacuteodo F Argoul E Bacry J Elezgaray E Freysz G Grasseau JF Muzy BPouligny Wavelet transform of fractals in Wavelets and Applications (Proc Marseille1989) ed by Y Meyer (Masson and Springer Paris and Berlin 1991) pp 286ndash352
[93] A Arneacuteodo E Bacry JF Muzy The thermodynamics of fractals revisited with waveletsPhysica A 213 232ndash275 (1995)
[94] A Arneacuteodo E Bacry JF Muzy Oscillating singularities in locally self-similar functionsPhys Rev Lett 74 4823ndash4826 (1995)
[95] A Arneacuteodo E Bacry PV Graves JF Muzy Characterizing long-range correlations inDNA sequences from wavelet analysis Phys Rev Lett 74 3293ndash3296 (1996)
[96] A Arneacuteodo Y drsquoAubenton E Bacry PV Graves JF Muzy C Thermes Wavelet basedfractal analysis of DNA sequences Physica D 96 291ndash320 (1996)
[97] A Arneacuteodo E Bacry S Jaffard JF Muzy Oscillating singularities on Cantor sets Agrand canonical multifractal formalism J Stat Phys 87 179ndash209 (1997)
[98] A Arneacuteodo E Bacry S Jaffard JF Muzy Singularity spectrum of multifractal functionsinvolving oscillating singularities J Fourier Anal Appl 4 159ndash174 (1998)
[99] N Aronszajn Theory of reproducing kernels Trans Amer Math Soc 66 337ndash404 (1950)[100] A Ashtekar J Lewandowski D Marolf J Mouratildeo T Thiemann Coherent state
transforms for spaces of connections J Funct Analysis 135 519ndash551 (1996)[101] A Askari-Hemmat MA Dehghan M Radjabalipour Generalized frames and their
redundancy Proc Amer Math Soc 129 1143ndash1147 (2001)[102] EW Aslaksen JR Klauder Unitary representations of the affine group J Math Phys 9
206ndash211 (1968)[103] EW Aslaksen JR Klauder Continuous representation theory using the affine group
J Math Phys 10 2267ndash2275 (1969)[104] D Astruc L Plantieacute R Murenzi Y Lebret D Vandromme On the use of the 3D
wavelet transform for the analysis of computational fluid dynamics results in Progressin Wavelet Analysis and Applications (Proc Toulouse 1992) ed by Y Meyer S Roques(Ed Frontiegraveres Gif-sur-Yvette 1993) pp 463ndash470
[105] PW Atkins JC Dobson Angular momentum coherent states Proc Roy Soc London A321 321ndash340 (1971)
[106] BW Atkinson DO Bruff JS Geronimo D P Hardin Wavelets centered on a knotsequence Piecewise polynomial wavelets on a quasi-crystal lattice preprint (2011)arXiv11024246v1 [mathNA]
[107] IS Averbuch NF Perelman Fractional revivals Universality in the long-term evolutionof quantum wave packets beyond the correspondence principle dynamics Phys Lett A139 449ndash453 (1989)
[108] H Bacry J-M Leacutevy-Leblond Possible kinematics J Math Phys 9 1605ndash1614 (1968)[109] H Bacry A Grossmann J Zak Proof of the completeness of lattice states in kq
representation Phys Rev B 12 1118ndash1120 (1975)[110] L Baggett KF Taylor Groups with completely reducible regular representation Proc
Amer Math Soc 72 593ndash600 (1978)[111] VG Bagrov J-P Gazeau D Gitman A Levine Coherent states and related quantizations
for unbounded motions J Phys A Math Theor 45 125306 (2012) arXiv12010955v2[quant-ph]
[112] P Balazs J-P Antoine A Grybos Weighted and controlled frames Mutual relationshipand first numerical properties Int J Wavelets Multires Inform Proc 8 109ndash132 (2010)
References 551
[113] P Balazs DT Stoeva J-P Antoine Classification of general sequences by frame-relatedoperators Sampling Theory Signal Image Proc (STSIP) 10 151ndash170 (2011)
[114] P Balazs D Bayer A Rahimi Multipliers for continuous frames in Hilbert spaces JPhys A Math Gen 45 244023 (2012)
[115] P Baldi G Kerkyacharian D Marinucci D Picard High frequency asymptotics forwavelet-based tests for Gaussianity and isotropy on the torus J Multivar Anal 99 606ndash636 (2008)
[116] P Baldi G Kerkyacharian D Marinucci D Picard Asymptotics for spherical needletsAnn of Stat 37 1150ndash1171 (2009)
[117] MC Baldiotti J-P Gazeau DM Gitman Coherent states of a particle in magnetic fieldand Stieltjes moment problem Phys Lett A 373 1916ndash1920 (2009) Erratum Phys LettA 373 2600 (2009)
[118] MC Baldiotti J-P Gazeau DM Gitman Semiclassical and quantum description ofmotion on the noncommutative plane Phys Lett A 373 3937ndash3943 (2009)
[119] R Balian Un principe drsquoincertitude fort en theacuteorie du signal ou en meacutecanique quantiqueCR Acad Sci(Paris) 292 1357ndash1362 (1981)
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[121] D Barache S De Biegravevre J-P Gazeau Affine symmetry semigroups for quasicrystalsEurophys Lett 25 435ndash440 (1994)
[122] D Barache J-P Antoine J-M Dereppe The continuous wavelet transform a tool for NMRspectroscopy J Magn Reson 128 1ndash11 (1997)
[123] V Bargmann On a Hilbert space of analytic functions and an associated integral transformPart I Commun Pure Appl Math 14 187ndash214 (1961)
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[125] V Bargmann P Butera L Girardello JR Klauder On the completeness of coherentstates Reports Math Phys 2 221ndash228 (1971)
[126] AO Barut L Girardello New ldquocoherentrdquo states associated with non compact groupsCommun Math Phys 21 41ndash55 (1971)
[127] AO Barut H Kleinert Transition probabilities of the hydrogen atom from noncompactdynamical groups Phys Rev 156 1541ndash1545 (1967)
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[131] J Ben Geloun J R Klauder Ladder operators and coherent states for continuous spectraJ Phys A Math Theor 42 375209 (2009)
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[133] JJ Benedetto TD Andrews Intrinsic wavelet and frame applications in IndependentComponent Analyses Wavelets Neural Networks Biosystems and Nanoengineering IXed by H Szu L Dai SPIE Proceedings vol 8058 (SPIE Bellingham WA 2011) p805802
[134] JJ Benedetto A Teolis A wavelet auditory model and data compression Appl ComputHarmon Anal 1 3ndash28 (1993)
[135] FA Berezin Quantization Math USSR Izvestija 8 1109ndash1165 (1974)[136] FA Berezin General concept of quantization Commun Math Phys 40 153ndash174 (1975)[137] H Bergeron From classical to quantum mechanics How to translate physical ideas into
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[141] H Bergeron J-P Gazeau P Siegl A Youssef Semi-classical behavior of Poumlschl-Tellercoherent states Eur Phys Lett 92 60003 (2010)
[142] H Bergeron P Siegl A Youssef New SUSYQM coherent states for Poumlschl-Tellerpotentials A detailed mathematical analysis J Phys A Math Theor 45 244028 (2012)
[143] H Bergeron J-P Gazeau A Youssef Are the Weyl and coherent state descriptionsphysically equivalent Phys Lett A 377 598ndash605 (2013)
[144] H Bergeron A Dapor J-P Gazeau P Małkiewicz Wavelet quantum cosmology preprint(2013) arXiv13050653 [gr-qc]
[145] S Bergman Uumlber die Kernfunktion eines Bereiches und ihr Verhalten am Rande I ReineAngw Math 169 1ndash42 (1933)
[146] D Bernier KF Taylor Wavelets from square-integrable representations SIAM J MathAnal 27 594ndash608 (1996)
[147] G Bernuau Wavelet bases associated to a self-similar quasicrystal J Math Phys 394213ndash4225 (1998)
[148] A Bertrand Deacuteveloppements en base de Pisot et reacutepartition modulo 1 C R Acad SciParis 285 419ndash421 (1977)
[149] J Bertrand P Bertrand Classification of affine Wigner functions via an extendedcovariance principle in Group Theoretical Methods in Physics (Proc Sainte-Adegravele 1988)ed by Y Saint-Aubin L Vinet (World Scientific Singapore 1989) pp 1380ndash1383
[150] Z Białynicka-Birula I Białynicki-Birula Space-time description of squeezing J OptSoc Am B4 1621ndash1626 (1987)
[151] E Bianchi E Magliaro C Perini Coherent spin-networks Phys Rev D 82 024012(2010)
[152] S Biskri J-P Antoine B Inhester F Mekideche Extraction of Solar coronal magneticloops with the 2-D Morlet wavelet transform Solar Phys 262 373ndash385 (2010)
[153] R Bluhm VA Kostelecky JA Porter The evolution and revival structure of localizedquantum wave packets Am J Phys 64 944ndash953 (1996)
[154] I Bogdanova P Vandergheynst J-P Antoine L Jacques M Morvidone Stereographicwavelet frames on the sphere Appl Comput Harmon Anal 19 223ndash252 (2005)
[155] I Bogdanova X Bresson J-P Thiran P Vandergheynst Scale space analysis and activecontours for omnidirectional images IEEE Trans Image Process 16 1888ndash1901 (2007)
[156] I Bogdanova P Vandergheynst J-P Gazeau Continuous wavelet transform on thehyperboloid Appl Comput Harmon Anal 23 (2007) 286ndash306 (2007)
[157] P Boggiatto E Cordero Anti-Wick quantization of tempered distributions in Progress inAnalysis Berlin (2001) vol I II (World Sci Publ River Edge NJ 2003) pp 655ndash662
[158] P Boggiatto E Cordero K Groumlchenig Generalized Anti-Wick operators with symbols indistributional Sobolev spaces Int Equ Oper Theory 48 427ndash442 (2004)
[159] A Boumlhm The Rigged Hilbert Space in quantum mechanics in Lectures in TheoreticalPhysics vol IX A ed by WA Brittin et al (Gordon amp Breach New York 1967) pp255ndash315
[160] G Bohnkeacute Treillis drsquoondelettes associeacutes aux groupes de Lorentz Ann Inst H Poincareacute54 245ndash259 (1991)
[161] WR Bomstad JR Klauder Linearized quantum gravity using the projection operatorformalism Class Quantum Grav 23 5961ndash5981 (2006)
[162] VV Borzov Orthogonal polynomials and generalized oscillator algebras Int TransformSpec Funct 12 115ndash138 (2001)
[163] VV Borzov EV Damaskinsky Generalized coherent states for classical orthogonalpolynomials Day on Diffraction (2002) arXivmathQA0209181v1 (SPb 2002)
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[165] A Bouzouina S De Biegravevre Equipartition of the eigenfunctions of quantized ergodic mapson the torus Commun Math Phys 178 83ndash105 (1996)
[166] P Brault J-P Antoine A spatio-temporal Gaussian-Conical wavelet with high apertureselectivity for motion and speed analysis Appl Comput Harmon Anal 34 148ndash161(2012)
[167] A Briguet S Cavassila D Graveron-Demilly Suppression of huge signals using theCadzow enhancement procedure The NMR Newslett 440 26 (1995)
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[170] F Bruhat Sur les repreacutesentations induites des groupes de Lie Bull Soc Math France 8497ndash205 (1956)
[171] T Buumllow Multiscale image processing on the sphere in DAGM-Symposium (2002) pp609ndash617
[172] C Burdik C Frougny J-P Gazeau R Krejcar Beta-integers as natural counting systemsfor quasicrystals J Phys A Math Gen 31 6449ndash6472 (1998)
[173] KE Cahill Coherent-state representations for the photon density Phys Rev 138 B1566ndash1576 (1965)
[174] KE Cahill R Glauber Density operators and quasiprobability distributions Phys Rev177 1882ndash1902 (1969)
[175] KE Cahill R Glauber Ordered expansions in boson amplitude operators Phys Rev 1771857ndash1881 (1969)
[176] AR Calderbank I Daubechies W Sweldens BL Yeo Wavelets that map integers tointegers Appl Comput Harmon Anal 5 332ndash369 (1998)
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[180] EJ Candegraves Harmonic analysis of neural networks Appl Comput Harmon Anal 6 197ndash218 (1999)
[181] EJ Candegraves Ridgelets and the representation of mutilated Sobolev functions SIAM JMath Anal 33 347ndash368 (2001)
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[184] EJ Candegraves L Demanet The curvelet representation of wave propagators is optimallysparse Commun Pure Appl Math 58 1472ndash1528 (2005)
[185] EJ Candegraves DL Donoho Curvelets ndash A surprisingly effective nonadaptive representationfor objects with edges in Curves and Surfaces ed by LL Schumaker et al (VanderbiltUniversity Press Nashville TN 1999)
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[191] EJ Candegraves F Guo New multiscale transforms minimum total variationsynthesisApplications to edge-preserving image reconstruction Signal Proc 82 1519ndash1543 (2002)
[192] EJ Candegraves L Demanet D Donoho L Ying Fast discrete curvelet transforms MultiscaleModel Simul 5 861ndash899 (2006)
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[195] P Carruthers MM Nieto Phase and angle variables in quantum mechanics Rev ModPhys 40 411ndash440 (1968)
[196] PG Casazza G Kutyniok Frames of subspaces in Wavelets Frames and Operator The-ory Contemporary Mathematics vol 345 (American Mathematical Society ProvidenceRI 2004) pp 87ndash113
[197] PG Casazza D Han DR Larson Frames for Banach spaces Contemp Math 247 149ndash182 (1999)
[198] P Casazza O Christensen S Li A Lindner Riesz-Fischer sequences and lower framebounds Z Anal Anwend 21 305ndash314 (2002)
[199] PG Casazza G Kutyniok S Li Fusion frames and distributed processing ApplComputHarmon Anal 25 114ndash132 (2008)
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Fourier (Grenoble) 43 551ndash567 (1993)[207] M Clerc and S Mallat Shape from texture and shading with wavelets in Dynamical
Systems Control Coding Computer Vision Progress in Systems and Control Theory 25393ndash417 (1999)
[208] L Cohen General phase-space distribution functions J Math Phys 7 781ndash786 (1966)[209] A Cohen I Daubechies J-C Feauveau Biorthogonal bases of compactly supported
wavelets Commun Pure Appl Math 45 485ndash560 (1992)[210] R Coifman Y Meyer MV Wickerhauser Wavelet analysis and signal processing
in Wavelets and Their Applications ed by MB Ruskai G Beylkin R CoifmanI Daubechies S Mallat Y Meyer L Raphael (Jones and Bartlett Boston 1992)pp 153ndash178
[211] R Coifman Y Meyer MV Wickerhauser Entropy-based algorithms for best basisselection IEEE Trans Inform Theory 38 713ndash718 (1992)
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[215] N Cotfas J-P Gazeau K Goacuterska Complex and real Hermite polynomials and relatedquantizations J Phys A Math Theor 43 305304 (2010)
[216] N Cotfas J-P Gazeau A Vourdas Finite-dimensional Hilbert space and frame quantiza-tion J Phys A Math Gen 44 175303 (2011)
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[219] S Dahlke W Dahmen E Schmidt I Weinreich Multiresolution analysis and wavelets onS
2 and S3 Numer Funct Anal Optim 16 19ndash41 (1995)
[220] S Dahlke V Lehmann G Teschke Applications of wavelet methods to the analysis ofmeteorological radar data - An overview Arabian J Sci Eng 28 3ndash44 (2003)
[221] S Dahlke G Kutyniok P Maass C Sagiv H-G Stark G Teschke The uncertaintyprinciple associated with the continuous shearlet transform Int J Wavelets MultiresolutInf Process 6 157ndash181 (2008)
[222] S Dahlke G Kutyniok G Steidl G Teschke Shearlet coorbit spaces and associatedBanach frames Appl Comput Harmon Anal 27 195ndash214 (2009)
[223] S Dahlke G Steidl G Teschke The continuous shearlet transform in arbitrary spacedimensions J Fourier Anal Appl 16 340ndash364 (2010)
[224] S Dahlke G Steidl G Teschke Shearlet coorbit spaces Compactly supported analyzingshearlets traces and embeddings J Fourier Anal Appl 17 1232ndash1355 (2011)
[225] T Dallard GR Spedding 2-D wavelet transforms Generalisation of the Hardy space andapplication to experimental studies Eur J Mech BFluids 12 107ndash134 (1993)
[226] C Daskaloyannis Generalized deformed oscillator and nonlinear algebras J Phys AMath Gen 24 L789ndashL794 (1991)
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[228] I Daubechies On the distributions corresponding to bounded operators in the Weylquantization Commun Math Phys 75 229ndash238 (1980)
[229] I Daubechies and A Grossmann An integral transform related to quantization I J MathPhys 21 2080ndash2090 (1980)
[230] I Daubechies A Grossmann J Reignier An integral transform related to quantization IIJ Math Phys 24 239ndash254 (1983)
[231] I Daubechies Orthonormal bases of compactly supported wavelets Commun Pure ApplMath 41 909ndash996 (1988)
[232] I Daubechies The wavelet transform time-frequency localisation and signal analysisIEEE Trans Inform Theory 36 961ndash1005 (1990)
[233] I Daubechies S Maes A nonlinear squeezing of the continuous wavelet transform basedon auditory nerve models in Wavelets in Medicine and Biology ed by A Aldroubi MUnser (CRC Press Boca Raton 1996) pp 527ndash546
[234] I Daubechies A Grossmann Y Meyer Painless nonorthogonal expansions J Math Phys27 1271ndash1283 (1986)
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[236] R De Beer D van Ormondt FTAW Wajer S Cavassila D Graveron-Demilly S VanHuffel SVD-based modelling of medical NMR signals in SVD and Signal ProcessingIII Algorithms Architectures and Applications ed by M Moonen B De Moor (Elsevier(North-Holland) Amsterdam 1995) pp 467ndash474
[237] S De Biegravevre Coherent states over symplectic homogeneous spaces J Math Phys 301401ndash1407 (1989)
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[239] S De Biegravevre JA Gonzaacutelez Semiclassical behaviour of coherent states on the circle inQuantization and Coherent States Methods in Physics ed by A Odzijewicz et al (WorldScientific Singapore 1993)
[240] S De Biegravevre AE Gradechi Quantum mechanics and coherent states on the anti-de Sitterspace-time and their Poincareacute contraction Ann Inst H Poincareacute 57 403ndash428 (1992)
[241] J Deenen C Quesne Dynamical group of collective states I II III J Math Phys 23878ndash889 2004ndash2015 (1982)
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[246] R Delbourgo J R Fox Maximum weight vectors possess minimal uncertainty J PhysA Math Gen 10 L233ndashL235 (1977)
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[249] Th Deutsch L Genovese Wavelets for electronic structure calculations Collection SocFr Neut 12 33ndash76 (2011)
[250] B Dewitt Quantum theory of gravity I The canonical theory Phys Rev 160 1113ndash1148(1967)
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Local intermittency measure in cascade and avalanche scenarios Solar Phys 282 471ndash481(2013)
[253] AN Dinkelaker AL MacKinnon Wavelets intermittency and solar flare hard X-rays 2LIM analysis of high time resolution BATSE data Solar Phys 282 483ndash501 (2013)
[254] MN Do M Vetterli Contourlets in Beyond Wavelets ed by GV Welland (AcademicSan Diego 2003) pp 83ndash105
[255] MN Do M Vetterli The contourlet transform An efficient directional multiresolutionimage representation IEEE Trans Image Process 14 2091ndash2106 (2005)
[256] VV Dodonov Nonclassical states in quantum optics A ldquosqueezedrdquo review of the first 75years J Opt B Quant Semiclass Opot 4 R1ndashR33 (2002)
[257] DL Donoho Nonlinear wavelet methods for recovery of signals densities and spectrafrom indirect and noisy data in Different Perspectives on Wavelets Proceedings ofSymposia in Applied Mathematics vol 38 ed by I Daubechies (American MathematicalSociety Providence RI 1993) pp 173ndash205
[258] DL Donoho Wedgelets Nearly minimax estimation of edges Ann Stat 27 859ndash897(1999)
[259] DL Donoho X Huo Beamlet pyramids A new form of multiresolution analysis suitedfor extracting lines curves and objects from very noisy image data in SPIE Proceedingsvol 5914 (SPIE Bellingham WA 2005) pp 1ndash12
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[268] M Duval-Destin M-A Muschietti B Torreacutesani Continuous wavelet decompositionsmultiresolution and contrast analysis SIAM J Math Anal 24 739ndash755 (1993)
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[274] M Farge Wavelet transforms and their applications to turbulence Annu Rev Fluid Mech24 395ndash457 (1992)
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[280] M Flensted-Jensen Discrete series for semisimple symmetric spaces Ann of Math 111253ndash311 (1980)
[281] K Flornes A Grossmann M Holschneider B Torreacutesani Wavelets on discrete fieldsAppl Comput Harmon Anal 1 137ndash146 (1994)
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[286] W Freeden T Maier S Zimmermann A survey on wavelet methods for (geo)applicationsRevista Mathematica Complutense 16 (2003) 277ndash310
[287] W Freeden M Schreiner Biorthogonal locally supported wavelets on the sphere based onzonal kernel functions J Fourier Anal Appl 13 693ndash709 (2007)
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[289] L Freidel ER Livine U(N) coherent states for loop quantum gravity J Math Phys 52052502 (2011)
[290] J Froment S Mallat Arbitrary low bit rate image compression using wavelets in Progressin Wavelet Analysis and Applications (Proc Toulouse 1992) ed by Y Meyer S Roques(Ed Frontiegraveres Gif-sur-Yvette 1993) pp 413ndash418 and references therein
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[292] H Fuumlhr Wavelet frames and admissibility in higher dimensions J Math Phys 37 6353ndash6366 (1996)
[293] H Fuumlhr M Mayer Continuous wavelet transforms from semidirect products Cyclicrepresentations and Plancherel measure J Fourier Anal Appl 8 375ndash396 (2002)
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127ndash147 (2003)[296] E Galapon Paulirsquos theorem and quantum canonical pairs The consistency of a bounded
self-adjoint time operator canonically conjugate to a Hamiltonian with non-empty pointspectrum Proc R Soc Lond A 458 451ndash472 (2002)
[297] PL Garciacutea de Leacuteon J-P Gazeau Coherent state quantization and phase operator PhysLett A 361 301ndash304 (2007)
[298] L Garciacutea de Leoacuten J-P Gazeau J Queacuteva The infinite well revisited Coherent states andquantization Phys Lett A 372 3597ndash3607 (2008)
[299] T Garidi J-P Gazeau E Huguet M Lachiegraveze Rey J Renaud Fuzzy spheres frominequivalent coherent states quantization J Phys A Math Theor 40 10225ndash10249 (2007)
[300] J-P Gazeau Four Euclidean conformal group in atomic calculations Exact analyticalexpressions for the bound-bound two-photon transition matrix elements in the H atomJ Math Phys 19 1041ndash1048 (1978)
[301] J-P Gazeau On the four Euclidean conformal group structure of the sturmian operatorLett Math Phys 3 285ndash292 (1979)
[302] J-P Gazeau Technique Sturmienne pour le spectre discret de lrsquoeacutequation de SchroumldingerJ Phys A Math Gen 13 3605ndash3617 (1980)
[303] J-P Gazeau Four Euclidean conformal group approach to the multiphoton processes in theH atom J Math Phys 23 156ndash164 (1982)
[304] J-P Gazeau A remarkable duality in one particle quantum mechanics between someconfining potentials and (R+Linfin
ε ) potentials Phys Lett 75A 159ndash163 (1980)[305] J-P Gazeau SL(2R)-coherent states and integrable systems in classical and quantum
physics in Quantization Coherent States and Complex Structures ed by J-P AntoineST Ali W Lisiecki IM Mladenov A Odzijewicz (Plenum Press New York and London1995) pp 147ndash158
[306] J-P Gazeau S Graffi Quantum harmonic oscillator A relativistic and statistical point ofview Boll Unione Mat Ital 11-A 815ndash839 (1997)
[307] J-P Gazeau V Hussin Poincareacute contraction of SU(11) Fock-Bargmann structure J PhysA Math Gen 25 1549ndash1573 (1992)
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[309] J-P Gazeau JR Klauder Coherent states for systems with discrete and continuousspectrum J Phys A Math Gen 32 123ndash132 (1999)
[310] J-P Gazeau P Monceau Generalized coherent states for arbitrary quantum systems inColloquium M Flato (Dijon Sept 99) vol II (Kluumlwer Dordrecht 2000) pp 131ndash144
[311] J-P Gazeau M Novello The question of mass in (Anti-) de Sitter space-times J Phys AMath Theor 41 304008 (2008)
[312] J-P Gazeau M del Olmo q-coherent states quantization of the harmonic oscillator AnnPhys (NY) 330 220ndash245 (2013) arXiv12071200 [quant-ph]
[313] J-P Gazeau J Patera Tau-wavelets of Haar J Phys A Math Gen 29 4549ndash4559 (1996)[314] J-P Gazeau W Piechocki Coherent states quantization of a particle in de Sitter space
J Phys A Math Gen 37 6977ndash6986 (2004)[315] J-P Gazeau J Renaud Lie algorithm for an interacting SU(11) elementary system and its
contraction Ann Phys (NY) 222 89ndash121 (1993)[316] J-P Gazeau J Renaud Relativistic harmonic oscillator and space curvature Phys Lett A
179 67ndash71 (1993)[317] J-P Gazeau V Spiridonov Toward discrete wavelets with irrational scaling factor J Math
plane J Phys A Math Theor 44 495201 (2011)[319] J-P Gazeau J Patera E Pelantovaacute Tau-wavelets in the plane J Math Phys 39 4201ndash
4212 (1998)[320] J-P Gazeau M Andrle C Burdiacutek R Krejcar Wavelet multiresolutions for the Fibonacci
chain J Phys A Math Gen 33 L47ndashL51 (2000)[321] J-P Gazeau M Andrle C Burdiacutek Bernuau spline wavelets and sturmian sequences
J Fourier Anal Appl 10 269ndash300 (2004)[322] J-P Gazeau F-X Josse-Michaux P Monceau Finite dimensional quantizations of the
(q p) plane new space and momentum inequalities Int J Modern Phys B 20 1778ndash1791 (2006)
[323] J-P Gazeau J Mourad J Queacuteva Fuzzy de Sitter space-times via coherent statesquantization in Proceedings of the XXVIth Colloquium on Group Theoretical Methodsin Physics New York 2006 ed by J Birman S Catto B Nicolescu (Canopus PublishingLimited London 2009)
[324] D Geller A Mayeli Continuous wavelets on compact manifolds Math Z 262 895ndash927(2009)
[325] D Geller A Mayeli Nearly tight frames and space-frequency analysis on compactmanifolds Math Z 263 235ndash264 (2009)
[326] L Genovese B Videau M Ospici Th Deutsch S Goedecker J-F Mhaut Daubechieswavelets for high performance electronic structure calculations The BigDFT project CR Mecanique 339 149ndash164 (2011)
[327] G Gentili C Stoppato Power series and analyticity over the quaternions Math Ann 352113ndash131 (2012)
[328] G Gentili DC Struppa A new theory of regular functions of a quaternionic variable AdvMath 216 279ndash301 (2007)
[329] C Geyer K Daniilidis Catadioptric projective geometry Int J Comput Vision 45 223ndash243 (2001)
[330] R Gilmore Geometry of symmetrized states Ann Phys (NY) 74 391ndash463 (1972)[331] R Gilmore On properties of coherent states Rev Mex Fis 23 143ndash187 (1974)[332] J Ginibre Statistical ensembles of complex quaternion and real matrices J Math Phys
6 440ndash449 (1965)[333] RJ Glauber The quantum theory of optical coherence Phys Rev 130 2529ndash2539 (1963)
560 References
[334] RJ Glauber Coherent and incoherent states of radiation field Phys Rev 131 2766ndash2788(1963)
[335] J Glimm Locally compact transformation groups Trans Amer Math Soc 101 124ndash138(1961)
[336] R Godement Sur les relations drsquoorthogonaliteacute de V Bargmann C R Acad Sci Paris 255521ndash523 657ndash659 (1947)
[337] C Gonnet B Torreacutesani Local frequency analysis with two-dimensional wavelet trans-form Signal Proc 37 389ndash404 (1994)
[338] JA Gonzalez MA del Olmo Coherent states on the circle J Phys A Math Gen 318841ndash8857 (1998)
[339] XGonze B Amadon et al ABINIT First-principles approach to material and nanosystemproperties Computer Physics Comm 180 2582ndash2615 (2009)
[340] KM Gograverski E Hivon AJ Banday BD Wandelt FK Hansen M Reinecke MBartelmann HEALPix A framework for high-resolution discretization and fast analysisof data distributed on the sphere Astrophys J 622 759ndash771 (2005)
[341] P Goupillaud A Grossmann J Morlet Cycle-octave and related transforms in seismicsignal analysis Geoexploration 23 85ndash102 (1984)
[342] KH Groumlchenig A new approach to irregular sampling of band-limited functions in RecentAdvances in Fourier Analysis and Its applications ed by JS Byrnes JL Byrnes (KluwerDordrecht 1990) pp 251ndash260
[343] KH Groumlchenig Gabor analysis over LCA groups in Gabor Analysis and Algorithms ndashTheory and Applications ed by HG Feichtinger T Strohmer (Birkhaumluser Boston-Basel-Berlin 1998) pp 211ndash231
[344] HJ Groenewold On the principles of elementary quantum mechanics Physica 12 405ndash460 (1946)
[345] P Grohs Continuous shearlet tight frames J Fourier Anal Appl 17 506ndash518 (2011)[346] P Grohs G Kutyniok Parabolic molecules preprint TU Berlin (2012)[347] M Grosser A note on distribution spaces on manifolds Novi Sad J Math 38 121ndash128
(2008)[348] A Grossmann Parity operator and quantization of δ -functions Commun Math Phys 48
191ndash194 (1976)[349] A Grossmann J Morlet Decomposition of Hardy functions into square integrable
wavelets of constant shape SIAM J Math Anal 15 723ndash736 (1984)[350] A Grossmann J Morlet Decomposition of functions into wavelets of constant shape and
related transforms in Mathematics + Physics Lectures on recent results I ed by L Streit(World Scientific Singapore 1985) pp 135ndash166
[351] A Grossmann J Morlet T Paul Integral transforms associated to square integrablerepresentations I General results J Math Phys 26 2473ndash2479 (1985)
[352] A Grossmann J Morlet T Paul Integral transforms associated to square integrablerepresentations II Examples Ann Inst H Poincareacute 45 293ndash309 (1986)
[353] A Grossmann R Kronland-Martinet J Morlet Reading and understanding the contin-uous wavelet transform in Wavelets Time-Frequency Methods and Phase Space (ProcMarseille 1987) ed by J-M Combes A Grossmann P Tchamitchian 2nd edn (SpringerBerlin 1990) pp 2ndash20
[354] P Guillemain R Kronland-Martinet B Martens Estimation of spectral lines with helpof the wavelet transform Application in NMR spectroscopy in Wavelets and Applications(Proc Marseille 1989) ed by Y Meyer (Masson and Springer Paris and Berlin 1991) pp38ndash60
[355] H de Guise M Bertola Coherent state realizations of su(n+ 1) on the n-torus J MathPhys 43 3425ndash3444 (2002)
[356] K Guo D Labate Representation of Fourier Integral Operators using shearlets J FourierAnal Appl 14 327ndash371 (2008)
References 561
[357] K Guo G Kutyniok D Labate Sparse multidimensional representations usinganisotropic dilation and shear operators in Wavelets and Spines (Athens GA 2005)(Nashboro Press Nashville TN 2006) pp 189ndash201
[358] K Guo D Labate W-Q Lim G Weiss E Wilson Wavelets with composite dilationsand their MRA properties Appl Comput Harmon Anal 20 202ndash236 (2006)
[359] EA Gutkin Overcomplete subspace systems and operator symbols Funct Anal Appl 9260ndash261 (1975)
[360] G Gyoumlrgyi Integration of the dynamical symmetry groups for the 1r potential Acta PhysAcad Sci Hung 27 435ndash439 (1969)
[361] BC Hall The Segal-Bargmann ldquoCoherent Staterdquo transform for compact Lie groups JFunct Analysis 122 103ndash151 (1994)
[362] B Hall JJ Mitchell Coherent states on spheres J Math Phys 43 1211ndash1236 (2002)[363] DK Hammond P Vandergheynst R Gribonval Wavelets on graphs via spectral theory
Appl Comput Harmon Anal 30 129ndash150 (2011)[364] Y Hassouni EMF Curado MA Rego-Monteiro Construction of coherent states for
physical algebraic system Phys Rev A 71 022104 (2005)[365] J He H Liu Admissible wavelets associated with the affine automorphism group of the
Siegel upper half-plane J Math Anal Appl 208 58ndash70 (1997)[366] J He H Liu Admissible wavelets associated with the classical domain of type one
Approx Appl 14 (1998) 89ndash105[367] J He L Peng Wavelet transform on the symmetric matrix space preprint Beijing (1997)
(unpublished)[368] J He L Peng Admissible wavelets on the unit disk Complex Variables 35 109ndash119
(1998)[369] DM Healy Jr FE Schroeck Jr On informational completeness of covariant localization
observables and Wigner coefficients J Math Phys 36 453ndash507 (1995)[370] C Heil D Walnut Continuous and discrete wavelet transforms SIAM Review 31 628ndash
666 (1989)[371] K Hepp EH Lieb On the superradiant phase transition for molecules in a quantized
radiation field The Dicke maser model Ann Phys (NY) 76 360ndash404 (1973)[372] K Hepp EH Lieb Equilibrium statistical mechanics of matter interacting with the
quantized radiation field Phys Rev A 8 2517ndash2525 (1973)[373] JA Hogan JD Lakey Extensions of the Heisenberg group by dilations and frames Appl
Comput Harmon Anal 2 174ndash199 (1995)[374] AL Hohoueacuteto K Thirulogasanthar ST Ali J-P Antoine Coherent states lattices and
square integrability of representations J Phys A Math Gen36 11817ndash11835 (2003)[375] M Holschneider On the wavelet transformation of fractal objects J Stat Phys 50 963ndash
993 (1988)[376] M Holschneider Wavelet analysis on the circle J Math Phys 31 39ndash44 (1990)[377] M Holschneider Inverse Radon transforms through inverse wavelet transforms Inv Probl
7 853ndash861 (1991)[378] M Holschneider Localization properties of wavelet transforms J Math Phys 34 3227ndash
3244 (1993)[379] M Holschneider General inversion formulas for wavelet transforms J Math Phys 34
4190ndash4198 (1993)[380] M Holschneider Wavelet analysis over abelian groups Applied Comput Harmon Anal
2 52ndash60 (1995)[381] M Holschneider Continuous wavelet transforms on the sphere J Math Phys 37 4156ndash
4165 (1996)[382] M Holschneider I Iglewska-Nowak Poisson wavelets on the sphere J Fourier Anal
Appl 13 405ndash419 (2007)
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[383] M Holschneider R Kronland-Martinet J Morlet P Tchamitchian A real-time algorithmfor signal analysis with the help of wavelet transform in Wavelets Time-FrequencyMethods and Phase Space (Proc Marseille 1987) ed by J-M Combes A Grossmann PTchamitchian 2nd edn (Springer Berlin 1990) pp 286ndash297
[384] M Holschneider P Tchamitchian Pointwise analysis of Riemannrsquos ldquonondifferentiablerdquofunction Invent Math 105 157ndash175 (1991)
[385] GR Honarasa MK Tavassoly M Hatami R Roknizadeh Nonclassical properties ofcoherent states and excited coherent states for continuous spectra J Phys A Math Theor44 085303 (2011)
[386] M Hongoh Coherent states associated with the continuous spectrum of noncompactgroups J Math Phys 18 2081ndash2085 (1977)
[387] A Horzela FH Szafraniec A measure free approach to coherent states J Phys A MathGen 45 244018 (2012)
[388] W-L Hwang S Mallat Characterization of self-similar multifractals with waveletmaxima Appl Comput Harmon Anal 1 316ndash328 (1994)
[389] W-L Hwang C-S Lu P-C Chung Shape from texture Estimation of planar surfaceorientation through the ridge surfaces of continuous wavelet transform IEEE Trans ImageProc 7 773ndash780 (1998)
[390] I Iglewska-Nowak M Holschneider Frames of Poisson wavelets on the sphere ApplComput Harmon Anal 28 227ndash248 (2010)
[391] E Inoumlnuuml EP Wigner On the contraction of groups and their representations Proc NatAcad Sci U S 39 510ndash524 (1953)
[392] S Iqbal F Saif Generalized coherent states and their statistical characteristics in power-law potentials J Math Phys 52 082105 (2011)
[393] CJ Isham JR Klauder Coherent states for n-dimensional Euclidean groups E(n) andtheir application J MathPhys 32 607ndash620 (1991)
[394] L Jacques J-P Antoine Multiselective pyramidal decomposition of images Wavelets withadaptive angular selectivity Int J Wavelets Multires Inform Proc 5 785ndash814 (2007)
[395] L Jacques L Duval C Chaux G Peyreacute A panorama on multiscale geometric rep-resentations intertwining spatial directional and frequency selectivity Signal Proc 912699ndash2730 (2011)
[396] HR Jalali M K Tavassoly On the ladder operators and nonclassicality of generalizedcoherent state associated with a particle in an infinite square well preprint (2013)arXiv13034100v1 [quant-ph]
[397] C Johnston On the pseudo-dilation representations of Flornes Grossmann Holschneiderand Torreacutesani Appl Comput Harmon Anal 3 377ndash385 (1997)
[398] G Kaiser Phase-space approach to relativistic quantum mechanics I Coherent staterepresentation for massive scalar particles J MathPhys 18 952ndash959 (1977)
[399] G Kaiser Phase-space approach to relativistic quantum mechanics II Geometrical aspectsJ MathPhys 19 502ndash507 (1978)
[400] C Kalisa B Torreacutesani N-dimensional affine Weyl-Heisenberg wavelets Ann Inst HPoincareacute 59 201ndash236 (1993)
[401] W Kaminski J Lewandowski T Pawłowski Quantum constraints Dirac observables andevolution group averaging versus the Schroumldinger picture in LQC Class Quant Grav 26245016 (2009)
[402] MR Karim ST Ali A relativistic windowed Fourier transform preprint ConcordiaUniversity Montreacuteal (1997) (unpublished)
[403] M R Karim ST Ali M Bodruzzaman A relativistic windowed Fourier transform inProceedings of IEEE SoutheastCon 2000 Nashville Tennessee pp 253ndash260 (2000)
[404] T Kawazoe Wavelet transforms associated to a principal series representation of semisim-ple Lie groups I II Proc Japan Acad Ser A ndash Math Sci 71 154ndash157 158ndash160 (1995)
[405] T Kawazoe Wavelet transform associated to an induced representation of SL(n+ 2R)Ann Inst H Poincareacute 65 1ndash13 (1996)
References 563
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[407] P Kittipoom G Kutyniok W-Q Lim Construction of compactly supported shearletframes Constr Approx 35 21ndash72 (2012)
[408] J Kiukas P Lahti K Ylinenc Phase space quantization and the operator moment problemJ Math Phys 47 072104 (2006)
[409] JR Klauder Continuous-representation theory I Postulates of continuous-representationtheory J Math Phys 4 1055ndash1058 (1963)
[410] JR Klauder Continuous-representation theory II Generalized relation between quantumand classical dynamics J Math Phys 4 1058ndash1073 (1963)
[411] JR Klauder Path integrals for affine variables in Functional Integration Theory andApplications ed by J-P Antoine E Tirapegui (Plenum Press New York and London1980) pp 101ndash119
[412] JR Klauder Are coherent states the natural language of quantum mechanics inFundamental Aspects of Quantum Theory ed by V Gorini A Frigerio NATO ASI Seriesvol B 144 (Plenum Press New York 1986) pp 1ndash12
[413] JR Klauder Quantization without quantization Ann Phys (NY) 237 147ndash160 (1995)[414] JR Klauder Coherent states for the hydrogen atom J Phys A Math Gen 29 L293ndash
L296 (1996)[415] JR Klauder An affinity for affine quantum gravity Proc Steklov Inst Math 272 169ndash176
(2011) and references therein[416] JR Klauder RF Streater A wavelet transform for the Poincareacute group J Math Phys 32
1609ndash1611 (1991)[417] JR Klauder RF Streater Wavelets and the Poincareacute half-plane J Math Phys 35 471ndash
478 (1994)[418] JR Klauder K Penson J-M Sixdeniers Constructing coherent states through solutions
of Stieltjes and Hausdorff moment problems Phys Rev A 64 013817 (2001)[419] A Kleppner RL Lipsman The Plancherel formula for group extensions Ann Ec Norm
Sup 5 459ndash516 (1972)[420] AB Klimov C Muntildeoz Coherent isotropic and squeezed states in a N-qubit system Phys
Scr 87 038110 (2013)[421] A Klyashko Dynamical symmetry approach to entanglement in Physics and Theoretical
Computer Science From Numbers and Languages to (Quantum) Cryptography - NATOSecurity through Science Series D - Information and Communication Security vol 7 edby J-P Gazeau J Nesetril B Rovan (IOS Press Washington DC 2007) pp 25ndash54
[422] S Kobayashi Irreducibility of certain unitary representations J Math Soc Japan 20 638ndash642 (1968)
[423] K Kowalski J Rembielinski LC Papaloucas Coherent states for a quantum particle ona circle J Phys A Math Gen 29 4149ndash4167 (1996)
[424] K Kowalski J Rembielinski Quantum mechanics on a sphere and coherent states J PhysA Math Gen 33 6035ndash6048 (2000)
[425] K Kowalski J Rembielinski The Bargmann representation for the quantum mechanicson a sphere J Math Phys 42 4138ndash4147 (2001)
[426] C Kristjansen J Plefka GW Semenoff M Staudacher A new double-scaling limit ofN = 4 super-Yang-Mills theory and pp-wave strings Nuclear Phys B 643 3ndash30 (2002)
[427] M Kulesh M Holschneider MS Diallo Geophysical wavelet library Applications ofthe continuous wavelet transform to the polarization and dispersion analysis of signalsComput Geosci 34 1732ndash1752 (2008)
[428] R Kunze On the Frobenius reciprocity theorem for square integrable representationsPacific J Math 53 465ndash471 (1974)
[429] Y Kuroda A Wada T Yamazaki K Nagayama Postacquisition data processing methodfor suppression of the solvent signal I J Magn Reson 84 604ndash610 (1989)
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[431] G Kutyniok D Labate Resolution of the wavefront set using continuous shearlets TransAmer Math Soc 361 2719ndash2754 (2009)
[432] G Kutyniok W-Q Lim Compactly supported shearlets are optimally sparse J ApproxTheory 163 1564ndash1589 (2011)
[433] D Labate W-Q Lim G Kutyniok G Weiss Sparse multidimensional representationusing shearlets in Wavelets XI (San Diego CA 2005) ed by M Papadakis A Laine MUnser SPIE Proceedings vol 5914 (SPIE Bellingham WA 2005) pp 254ndash262
[434] P Lahti J-P Pellonpaumlauml Continuous variable tomographic measurements Phys Lett A373 3435ndash3438 (2009)
[435] Lambertrsquos projection see WikipediahttpenwikipediaorgwikiLambert_azimuthal_equal-area_projection
[436] J-P Leduc F Mujica R Murenzi MJT Smith Missile-tracking algorithm using target-adapted spatio-temporal wavelets in Automatic Object Recognition VII SPIE Proceedingsvol 5914 (SPIE Bellingham WA 1997) pp 400ndash411
[437] J-P Leduc F Mujica R Murenzi MJT Smith Spatio-temporal wavelet transforms formotion tracking in IEEE ICASSP 1997 vol 4 (1997) pp 3013ndash3016
[438] J-P Leduc F Mujica R Murenzi MJT Smith Spatio-temporal continuous waveletsapplied to missile warhead detection and tracking in SPIE VCIP rsquo97 vol 3024 ed byJ Biemond EJ Delp (1997) pp 787ndash798
[439] B Leistedt JD McEwen Exact wavelets on the ball IEEE Trans Signal Proc 60 1564ndash1589 (2012)
[440] PG Lemarieacute Y Meyer Ondelettes et bases hilbertiennes Rev Math Iberoamer 2 1ndash18(1986)
[441] C Lemke A Schuck Jr J-P Antoine D Sima Metabolite-sensitive analysis of magneticresonance spectroscopic signals using the continuous wavelet transform Meas SciTechnol 22 (2011) Art 114013
[442] J-M Leacutevy-Leblond Galilei group and non-relativistic quantum mechanics J Math Phys4 776-788 (1963)
[443] J-M Leacutevy-Leblond Galilei group and Galilean invariance in Group Theory and ItsApplications vol II ed by EM Loebl (Academic New York 1971) pp 221ndash299
[444] J-M Leacutevy-Leblond On the conceptual nature of the physical constants Riv Nuovo Cim7 187ndash214 (1977)
[445] EH Lieb The classical limit of quantum spin systems Commun Math Phys 31 327ndash340(1973)
[446] G Lindblad B Nagel Continuous bases for unitary irreducible representations of SU(11)Ann Inst H Poincareacute 13 27ndash56 (1970)
[447] W Lisiecki Kaumlhler coherent states orbits for representations of semisimple Lie groupsAnn Inst H Poincareacute 53 857ndash890 (1990)
[448] A Lisowska Moment-based fast wedgelet transform J Math Imaging Vis 39 180ndash192(2011)
[449] H Liu L Peng Admissible wavelets associated with the Heisenberg group Pacific JMath 180 101ndash123 (1997)
[450] E Livine S Speziale Physical boundary state for the quantum tetrahedron Class QuantGrav 25 085003 (2008)
[451] F Low Complete sets of wave packets in A Passion for Physics ndash Essay in Honor ofGeoffrey Chew ed by C DeTar (World Scientific Singapore 1985) pp 17ndash22
[452] G Mack All unitary ray representations of the conformal group SU(22) with positiveenergy Commun Math Phys 55 1ndash28 (1977)
[453] GW Mackey Imprimitivity for representations of locally compact groups I Proc NatAcad Sci 35 537ndash545 (1949)
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[455] M Mallalieu CR Stroud Jr Rydberg wave packets fractional revivals and classicalorbits in Coherent States Past Present and Future (Proc Oak Ridge 1993) ed by DHFeng JR Klauder M Strayer (World Scientific Singapore 1994) pp 301ndash314
[456] SG Mallat Multifrequency channel decompositions of images and wavelet models IEEETrans Acoust Speech Signal Proc 37 2091ndash2110 (1989)
[457] SG Mallat A theory for multiresolution signal decomposition The wavelet representa-tion IEEE Trans Pattern Anal Machine Intell 11 674ndash693 (1989)
[458] S Mallat W-L Hwang Singularity detection and processing with wavelets IEEE TransInform Theory 38 617ndash643 (1992)
[459] S Mallat Z Zhang Matching pursuits with time frequency dictionaries IEEE TransSignal Proc 41 3397ndash3415 (1993)
[460] S Mallat S Zhong Wavelet maxima representation in Wavelets and Applications (ProcMarseille 1989) ed by Y Meyer (Masson and Springer Paris and Berlin 1991) pp 207ndash284
[461] VI Manrsquoko G Marmo ECG Sudarshan F Zaccaria f -oscillators and non-linearcoherent states Phys Scr 55 528ndash541 (1997)
[462] D Marinucci D Pietrobon A Baldi P Baldi P Cabella G Kerkyacharian P Natoli DPicard N Vittorio Spherical needlets for CMB data analysis Mon Not R Astron Soc383 539ndash545 (2008)
[463] D Marion M Ikura A Bax Improved solvent suppression in one- and two-dimensionalNMR spectra by convolution of time-domain data J Magn Reson 84 425ndash430 (1989)
[464] Y Meyer Principe drsquoincertitude bases hilbertiennes et algegravebres drsquoopeacuterateurs SeacuteminaireBourbaki 662 (1985ndash1986)
[465] Y Meyer Principe drsquoincertitude bases hilbertiennes et algegravebres drsquoopeacuterateurs Asteacuterisque145ndash146 209ndash223 (1987)
[466] Y Meyer H Xu Wavelet analysis and chirps Appl Comput Harmon Anal 4 366ndash379(1997)
[467] L Michel Invariance in quantum mechanics and group extensions in Group TheoreticalConcepts and Methods in Elementary Particle Physics ed by F Guumlrsey (Gordon andBreach New York and London 1964) pp 135ndash200
[468] J Mickelsson J Niederle Contractions of representations of the de Sitter groupsCommun Math Phys 27 167ndash180 (1972)
[469] MM Miller Convergence of the Sudarshan expansion for the diagonal coherent-stateweight functional J Math Phys 9 1270ndash1274 (1968)
[470] V F Molchanov Harmonic analysis on homogeneous spaces in Representation Theoryand Noncommutative Harmonic Analysis II ed by AA Kirillov (Springer Berlin 1995)
[471] MI Monastyrsky AM Perelomov Coherent states and symmetric spaces II Ann InstH Poincareacute 23 23ndash48 (1975)
[472] B Moran S Howard D Cochran Positive-operator-valued measures A general settingfor frames in Excursions in Harmonic Analysis vol 1 2 ed by TD Andrews R BalanJJ Benedetto W Czaja KA Okoudjou (Birkhaumluser Boston 2013) pp 49ndash64
[473] H Moscovici Coherent states representations of nilpotent Lie groups Commun MathPhys 54 63ndash68 (1977)
[474] H Moscovici A Verona Coherent states and square integrable representations Ann InstH Poincareacute 29 139ndash156 (1978)
[475] F Mujica R Murenzi MJT Smith J-P Leduc Robust tracking in compressed imagesequences J Electr Imaging 7 746ndash754 (1998)
[476] R Murenzi Wavelet transforms associated to the n-dimensional Euclidean group withdilations Signals in more than one dimension in Wavelets Time-Frequency Methodsand Phase Space (Proc Marseille 1987) ed by J-M Combes A Grossmann PTchamitchian 2nd edn (Springer Berlin 1990) pp 239ndash246
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[478] B Nagel Generalized eigenvectors in group representations in Studies in MathematicalPhysics (Proc Istanbul 1970) ed by AO Barut (Reidel Dordrecht and Boston 1970)pp 135ndash154
[479] MA Naımark Dokl Akad Nauk SSSR 41 359ndash361 (1943) see also B Sz-NagyExtensions of linear transformations in Hilbert space which extend beyond this spaceAppendix to F Riesz B Sz-Nagy Functional Analysis (Frederick Ungar New York 1960)
[480] FJ Narcowich P Petrushev JD Ward Localized tight frames on spheres SIAM J MathAnal 38 574ndash594 (2006)
[481] M Nauenberg Quantum wave packets on Kepler elliptic orbits Phys Rev A 40 1133ndash1136 (1989)
[482] M Nauenberg C Stroud J Yeazell The classical limit of an atom Scient Amer 27024ndash29 (1994)
[483] H Neumann Transformation properties of observables Helv Phys Acta 45 811ndash819(1972)
[484] U Niederer The maximal kinematical invariance group of the free Schroumldinger equationHelv Phys Acta 45 802ndash881 (1972)
[485] MM Nieto LM Simmons Jr Coherent states for general potentials I Formalism IIConfining one-dimensional examples III Nonconfining one-dimensional examples PhysRev D 20 1321ndash1331 1332ndash1341 1342ndash1350 (1979)
[486] MM Nieto LM Simmons Jr Coherent states for general potentials Phys Rev Lett 41207ndash210 (1987)
[487] A Odzijewicz On reproducing kernels and quantization of states Commun Math Phys114 577ndash597 (1988)
[488] A Odzijewicz Coherent states and geometric quantization Commun Math Phys 150385ndash413 (1992)
[489] A Odzijewicz Quantum algebras and q-special functions related to coherent states mapsof the disc Commun Math Phys 192 183ndash215 (1998)
[490] A Odzijewicz M Horowski A Tereszkiewicz Integrable multi-boson systems andorthogonal polynomials J Phys A Math Gen 34 4353ndash4376 (2001)
[491] G Oacutelafsson B Oslashrsted The holomorphic discrete series for affine symmetric spaces JFunct Anal 81 126ndash159 (1988)
[492] G Oacutelafsson H Schlichtkrull Representation theory Radon transform and the heatequation on a Riemannian symmetric space Contemp Math 449 315ndash344 (2008)
[493] E Onofri A note on coherent state representations of Lie groups J Math Phys 16 1087ndash1089 (1975)
[494] E Onofri Dynamical quantization of the Kepler manifold J Math Phys 17 401ndash408(1976)
[495] D Oriti R Pereira L Sindoni Coherent states in quantum gravity A construction basedon the flux representation of loop quantum gravity J Phys A Math Theor 45 244004(2012)
[496] LC Papaloucas J Rembielinski W Tybor Vectorlike coherent states with noncompactstability group J Math Phys 30 2406ndash2410 (1989)
[497] Z Pasternak-Winiarski On the dependence of the reproducing kernel on the weight ofintegration J Funct Anal 94 110ndash134 (1990)
[498] Z Pasternak-Winiarski On reproducing kernels for holomorphic vector bundles inQuantization and Infinite Dimensional Systems (Proc Białowieza Poland 1993) ed by J-P Antoine ST Ali W Lisiecki IM Mladenov A Odzijewicz (Plenum Press New Yorkand London 1994) pp 109ndash112
[499] T Paul Affine coherent states and the radial Schroumldinger equation I preprint CPT-84P1710 (1984) (unpublished)
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[500] T Paul K Seip Wavelets in quantum mechanics in Wavelets and Their Applications edby MB Ruskai G Beylkin R Coifman I Daubechies S Mallat Y Meyer L Raphael(Jones and Bartlett Boston 1992) pp 303ndash322
[501] AM Perelomov On the completeness of a system of coherent states Theor Math Phys6 156ndash164 (1971)
[502] AM Perelomov Coherent states for arbitrary Lie group Commun Math Phys 26 222ndash236 (1972)
[503] AM Perelomov Coherent states and symmetric spaces Commun Math Phys 44 197ndash210 (1975)
[504] M Perroud Projective representations of the Schroumldinger group Helv Phys Acta 50 233ndash252 (1977)
[505] J Phillips A note on square-integrable representations J Funct Anal 20 83ndash92 (1975)[506] D Pietrobon P Baldi D Marinucci Integrated Sachs-Wolfe effect from the cross
correlation of WMAP3 year and the NRAO VLA sky survey data New results andconstraints on dark energy Phys Rev D 74 043524 (2006)
[507] WWF Pijnappel A van den Boogaart R de Beer D van Ormondt SVD-basedquantification of magnetic resonance signals J Magn Reson 97 122ndash134 (1992)
[508] V Pop D Rosca Generalized piecewise constant orthogonal wavelet bases on 2D-domains Appl Anal 90 715ndash723 (2011)
[509] G Poumlschl E Teller Bemerkungen zur Quantenmechanik des anharmonischen OszillatorsZ Physik 83 143ndash151 (1933)
[510] D Potts G Steidl M Tasche Kernels of spherical harmonics and spherical frames inAdvanced Topics in Multivariate Approximation ed by F Fontanella K Jetter PJ Laurent(World Scientific Singapore 1996) pp 287ndash301
[511] E Prugovecki Consistent formulation of relativistic dynamics for massive spin-zeroparticles in external fields Phys Rev D 18 3655ndash3673 (1978) (Appendix C)
[512] E Prugovecki Relativistic quantum kinematics on stochastic phase space for massiveparticles J MathPhys 19 2261ndash2270 (1978)
[513] C Quesne Coherent states of the real symplectic group in a complex analytic parametriza-tion I II J Math Phys 27 428ndash441 869ndash878 (1986)
[514] C Quesne Generalized vector coherent states of sp(2NR) vector operators and ofsp(2NR) sup u(N) reduced Wigner coefficients J Phys A Math Gen 24 2697ndash2714(1991)
[515] JM Radcliffe Some properties of spin coherent states J Phys A Math Gen 4 313ndash323(1971)
[516] A Rahimi A Najati YN Dehghan Continuous frames in Hilbert spaces Methods FunctAnal Topol 12 170ndash182 (2006)
[517] H Rauhut M Roumlsler Radial multiresolution in dimension three Constr Approx 22 193ndash218 (2005)
[518] JH Rawnsley Coherent states and Kaumlhler manifolds Quart J Math Oxford 28(2) 403ndash415 (1977)
[519] J Renaud The contraction of the SU(11) discrete series of representations by means ofcoherent states J Math Phys 37 3168ndash3179 (1996)
[520] A Reacutenyi Representations for real numbers and their ergodic properties Acta Math AcadSci Hungary 8(3ndash4) 477ndash493 (1957)
[521] D Robert La coheacuterence dans tous ses eacutetats SMF Gazette 132 (2012)[522] JE Roberts The Dirac bra and ket formalism J Math Phys 7 1097ndash1104 (1966)[523] JE Roberts Rigged Hilbert spaces in quantum mechanics Commun Math Phys 3 98ndash
119 (1966)[524] S Roques F Bourzeix K Bouyoucef Soft-thresholding technique and restoration of
3C273 jet Astrophys Space Sci Nr 239 297ndash304 (1996)[525] D Rosca Haar wavelets on spherical triangulations in Advances in Multiresolution for
Geometric Modelling ed by NA Dogson MS Floater MA Sabin (Springer Berlin2005) pp 407ndash419
568 References
[526] D Rosca Locally supported rational spline wavelets on the sphere Math Comput 741803ndash1829 (2005)
[527] D Rosca Wavelets defined on closed surfaces J Comput Anal Appl 8 121ndash132 (2006)[528] D Rosca Weighted Haar wavelets on the sphere Int J Wavelets Multiresol Inf Proc 5
501ndash511 (2007)[529] D Rosca Wavelet bases on the sphere obtained by radial projection J Fourier Anal Appl
13 421ndash434 (2007)[530] D Rosca Piecewise constant wavelets on triangulations obtained by 1ndash3 splitting Int J
Wavelets Multiresolut Inf Process 6 209ndash222 (2008)[531] D Rosca On a norm equivalence on L2(S2) Results Math 53 399ndash405 (2009)[532] D Rosca New uniform grids on the sphere Astron Astrophys 520 (2010) Art A63[533] D Rosca Uniform and refinable grids on elliptic domains and on some surfaces of
revolution Appl Math Comput 217 7812ndash7817 (2011)[534] D Rosca Wavelet analysis on some surfaces of revolution via area preserving projection
Appl Comput Harmon Anal 30 262ndash272 (2011)[535] D Rosca J-P Antoine Locally supported orthogonal wavelet bases on the sphere via
stereographic projection Math Probl Eng 2009 124904 (2009)[536] D Rosca J-P Antoine Constructing wavelet frames and orthogonal wavelet bases on the
sphere in Recent Advances in Signal Processing ed by S Miron (IN-TECH ViennaAustria and Rijeka Croatia 2010) pp 59ndash76
[537] D Rosca G Plonka Uniform spherical grids via area preserving projection from the cubeto the sphere J Comput Appl Math 236 1033ndash1041 (2011)
[538] D Rosca G Plonka An area preserving projection from the regular octahedron to thesphere Results Math 63 429ndash444 (2012)
[539] H Rossi M Vergne Analytic continuation of the holomorphic discrete series for a semi-simple Lie group Acta Math 136 1ndash59 (1976)
[540] DJ Rotenberg Application of Sturmian functions to the Schroedinger three-body prob-lem Elastic e+ndashH scattering Ann Phys (NY) 19 262ndash278 (1962)
[541] C Rovelli Zakopane lectures on loop gravity in Proceedings of 3rd Quantum Gravityand Quantum Geometry School 28 Febndash13 March 2011 (Zakopane Poland 2011)arXiv11023660v5
[542] C Rovelli S Speziale A semiclassical tetrahedron Class Quant Grav 23 5861ndash5870(2006)
[543] DJ Rowe Coherent state theory of the noncompact symplectic group J Math Phys 252662ndash2271 (1984)
[544] DJ Rowe Microscopic theory of the nuclear collective model Rep Prog Phys 48 1419ndash1480 (1985)
[545] DJ Rowe Vector coherent state representations and their inner products J Phys A MathGen 45 244003 (2012) (This paper belongs to the special issue [38])
[546] DJ Rowe J Repka Vector-coherent-state theory as a theory of induced representationsJ Math Phys 32 2614ndash2634 (1991)
[547] DJ Rowe G Rosensteel R Gilmore Vector coherent state representation theory J MathPhys 26 2787ndash2791 (1985)
[548] A Royer Phase states and phase operators for the quantum harmonic oscillator Phys RevA 53 70ndash108 (1996)
[549] J Saletan Contraction of Lie groups J Math Phys 2 1ndash21 (1961)[550] G Saracco A Grossmann P Tchamitchian Use of wavelet transforms in the study of
propagation of transient acoustic signals across a plane interface between two homoge-neous media in Wavelets Time-Frequency Methods and Phase Space (Proc Marseille1987) ed by J-M Combes A Grossmann P Tchamitchian 2nd edn (Springer Berlin1990) pp 139ndash146
[551] P Schroumlder W Sweldens Spherical wavelets Efficiently representing functions on thesphere in Computer Graphics Proceedings (SIGGRAPH95) (ACM Siggraph Los Angeles1995) pp 161ndash175
References 569
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[553] S Scodeller Oslash Rudjord FK Hansen D Marinucci D Geller A Mayeli IntroducingMexican needlets for CMB analysis Issues for practical applications and comparison withstandard needlets Astrophys J 733 (2011) Art 121
[554] H Scutaru Coherent states and induced representations Lett Math Phys 2 101ndash107(1977)
[555] B Simon Distributions and their Hermite expansions J Math Phys 12 140ndash148 (1971)[556] B Simon The classical moment problem as a self-adjoint finite difference operator Adv
Math 137 82ndash203 (1998)[557] R Simon ECG Sudarshan N Mukunda Gaussian pure states in quantum mechanics
and the symplectic group Phys Rev A37 3028ndash3038 (1988)[558] S Sivakumar Studies on nonlinear coherent states J Opt B Quant Semiclass Opt 2
R61ndashR75 (2000)[559] E Slezak A Bijaoui G Mars Identification of structures from galaxy counts Use of the
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A 196 29ndash34 (1994)[561] SB Sontz Paragrassmann algebras as quantum spaces Part I Reproducing kernels in
Geometric Methods in Physics XXXI Workshop 2012 (Trends in Mathematics ed byP Kielanowski et al Birkhaumluser Verlag Basel 2013) pp 47ndash63
[562] SB Sontz Paragrassmann algebras as quantum spaces Part II Toeplitz operators J OperTh (2013 to appear) arXiv12055493
[563] SB Sontz A reproducing kernel and Toeplitz operators in the quantum plane Preprint(2013) arXiv13056986 [math-ph]
[564] SB Sontz Toeplitz quantization of an algebra with conjugation Preprint (2013)arXiv13085454 [math-ph]
[565] M Spera On a generalized Uncertainty Principle coherent states and the moment mapJ Geom Phys 12 165ndash182 (1993)
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[567] J-L Starck DL Donoho E J Candegraves Astronomical image representation by the curvelettransform Astron Astroph 398 785ndash800 (2003)
[568] J-L Starck Y Moudden P Abrial M Nguyen Wavelets ridgelets and curvelets on thesphere Astron Astroph 446 1191ndash1204 (2006)
[569] MB Stenzel The Segal-Bargmann transform on a symmetric space of compact type JFunct Analysis 165 44ndash58 (1994)
[570] ECG Sudarshan Equivalence of semiclassical and quantum mechanical descriptions ofstatistical light beams Phys Rev Lett 10 277ndash279 (1963)
[571] A Suvichakorn H Ratiney A Bucur S Cavassila J-P Antoine Toward a quantitativeanalysis of in vivo magnetic resonance proton spectroscopic signals using the continuousMorlet wavelet transform Meas Sci Technol 20 (2009) Art 104029
[572] W Sweldens The lifting scheme A custom-design construction of biorthogonal waveletsApplied Comput Harmon Anal 3 1186ndash1200 (1996)
[573] W Sweldens The lifting scheme A construction of second generation wavelets SIAM JMath Anal 29 511ndash546 (1998)
[574] FH Szafraniec The reproducing kernel Hilbert space and its multiplication operatorsin Complex Analysis and Related Topics ed by E Ramirez de Arellano et al OperatorTheory Advances and Applications vol 114 (Birkhaumluser Basel 2000) pp 254ndash263
[575] FH Szafraniec Multipliers in the reproducing kernel Hilbert space subnormality andnoncommutative complex analysis in Reproducing Kernel Spaces and Applications edby D Alpay Operator Theory Advances and Applications vol 143 (Birkhaumluser Basel2003) pp 313ndash331
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[577] MC Teich BEA Saleh Squeezed states of light Quantum Opt 1 152ndash191 (1989)[578] R Terrier L Demanet IA Grenier J-P Antoine Wavelet analysis of EGRET data in
Proceedings of the 27th International Cosmic Ray Conference (ICRC 2001) (CopernicusGesellschaft DE 2001) pp 2923ndash2926
[579] T Thiemann Gauge field theory coherent states (GCS) 1 General properties Class QuantGrav 18 2025ndash2064 (2001)
[580] T Thiemann O Winkler Gauge field theory coherent states (GCS) 2 Peakednessproperties Class Quant Grav 18 2561ndash2636 (2001)
[581] T Thiemann O Winkler Gauge field theory coherent states (GCS) 3 Ehrenfest theoremsClass Quant Grav 18 4629ndash4682 (2001)
[582] T Thiemann O Winkler Gauge field theory coherent states (GCS) 4 Infinite tensorproduct and thermodynamical limit Class Quant Grav 18 4997ndash5054 (2001)
[583] K Thirulagasanthar ST Ali Regular subspaces of a quaternionic Hilbert space fromquaternionic Hermite polynomials and associated coherent states J Math Phys 54013506 (2013)
[584] K Thirulogasanthar G Honnouvo A Krzyzak Coherent states and Hermite polynomialson quaternionic Hilbert spaces J Phys A Math Theor 43 385205 (2010)
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Ann Inst H Poincareacute 56 215ndash234 (1992)[588] B Torreacutesani Position-frequency analysis for signals defined on spheres Signal Proc 43
341ndash346 (2005)[589] DA Trifonov Generalized intelligent states and squeezing J Math Phys 35 2297ndash2308
(1994)[590] AS Trushechkin IV Volovich Localization properties of squeezed quantum states in
nanoscale space domains preprint (2013) arXiv13046277v1 [quant-ph][591] M Unser N Chenouard A unifying parametric framework for 2D steerable wavelet
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algorithms IEEE Trans Image Proc 11 363ndash372 (2002)[593] P Vandergheynst J-P Antoine E Van Vyve A Goldberg I Doghri Modelling and
simulation of an impact test using wavelets analytical and finite element models Int JSolids Struct 38 5481ndash5508 (2001)
[594] L Vanhamme RD Fierro S Van Huffel R de Beer Fast removal of residual water inproton spectra J Magn Reson 132 197ndash203 (1998)
[595] J Ville Theacuteorie et applications de la notion de signal analytique Cacircbles et Trans 2 61ndash74(1948)
[596] J Voisin On some unitary representations of the Galilei group I Irreducible representa-tions J Math Phys 6 1519ndash1529 (1965)
[597] A Vourdas Analytic representations in quantum mechanics J Phys A Math Gen 39R65ndashR141 (2006)
[598] DF Walls Squeezed states of light Nature 306 141ndash146 (1983)[599] YK Wang FT Hioe Phase transition in the Dicke maser model Phys Rev A 7 831ndash836
(1973)[600] PSP Wang J Yang A review of wavelet-based edge detection methods Int J Patt
Recogn Artif Intell 26 1255011 (2012)[601] I Weinreich A construction of C1-wavelets on the two-dimensional sphere Appl Comput
Harmon Anal 10 1ndash26 (2001)[602] H Weyl Quantenmechanik und Gruppentheorie Z Phys 46 1ndash46 (1927)
References 571
[603] Y Wiaux L Jacques P Vandergheynst Correspondence principle between spherical andEuclidean wavelets Astrophys J 632 15ndash28 (2005)
[604] Y Wiaux L Jacques P Vielva P Vandergheynst Fast directional correlation on the spherewith steerable filters Astrophys J 652 820ndash832 (2006)
[605] Y Wiaux JD McEwen P Vandergheynst O Blanc Exact reconstruction with directionalwavelets on the sphere Mon Not R Astron Soc 388 770ndash788 (2008)
[606] WM Wieland Complex Ashtekar variables and reality conditions for Holstrsquos action AnnHenri Poincareacute 13 425ndash448 (2012)
[607] EP Wigner On the quantum correction for thermodynamic equilibrium Phys Rev 40749ndash759 (1932)
[608] RM Willette RD Nowak Platelets A multiscale approach for recovering edges andsurfaces in photon-limited medical imaging IEEE Trans Med Imaging 22 332ndash350(2003)
[609] W Wisnoe P Gajan A Strzelecki C Lempereur J-M Matheacute The use of the two-dimensional wavelet transform in flow visualization processing in Progress in WaveletAnalysis and Applications (Proc Toulouse 1992) ed by Y Meyer S Roques (EdFrontiegraveres Gif-sur-Yvette 1993) pp 455ndash458
[610] K Woacutedkiewicz On the quantum mechanics of squeezed states J Modern Optics 34 941ndash948(1987)
[611] JA Yeazell M Mallalieu CR Stroud Jr Observation of the collapse and revival of aRydberg electronic wave packet Phys Rev Lett 64 2007ndash2010 (1990)
[612] JA Yeazell CR Stroud Jr Observation of fractional revivals in the evolution of aRydberg atomic wave packet Phys Rev A 43 5153ndash5156 (1991)
[613] HP Yuen Two-photon coherent states of the radiation field Phys Rev A 13 2226ndash2243(1976)
[614] J Zak Balian-Low theorem for Landau levels Phys Rev Lett 79 533ndash536 (1997)[615] J Zak Orthonormal sets of localized functions for a Landau level J Math Phys 39 4195ndash
4200 (1998) and references quoted there[616] AA Zakharova On the properties of generalized frames Math Notes 83 190ndash200 (2008)[617] W-M Zhang DH Feng R Gilmore Coherent states Theory and some applications Rev
Mod Phys 26 867ndash927 (1990)[618] I Zlatev W-M Zhang DH Feng Possibility that Schroumldingerrsquos conjecture for the
hydrogen atom coherent states is not attainable Phys Rev A 50 R1973ndashR1975 (1994)[619] WH Zurek Decoherence einselection and the quantum origins of the classical Rev Mod
Phys 75 715ndash775 (2003)[620] WH Zurek S Habib JP Paz Coherent states via decoherence Phys Rev Lett 70 1187ndash
1190 (1993)[621] K Zyczkowski Squeezed states in a quantum chaotic system J Phys A Math Theor 22
of SU(11) 81 296 297HilbertClowast-modules 164holomorphic 140nonholomorphic 151nonlinear 146of affine Galilei group 505of affine Poincareacute group 509of affine Weyl-Heisenberg group GaWH
497of compact semisimple Lie groups 174of Euclidean group E(n) 266of Galilei group G (11) 290of isochronous Galilei group 237of non-semisimple Lie groups 179of noncompact semisimple Lie groups 177of Poincareacute group Puarr
+(11) 283massless case 288
of Poincareacute group Puarr+(13) 279
of Schroumldinger group 508quasi-coherent states 186quaternionic 164
ST Ali et al Coherent States Wavelets and Their Generalizations Theoreticaland Mathematical Physics DOI 101007978-1-4614-8535-3copy Springer Science+Business Media New York 2014
573
574 Index
coherent states (CS) (cont)spin or SU(2) 175square integrable covariant 166 180 264vector (VCS) 73 108 112 170weighted 184 523
of affine Weyl-Heisenberg group GaWH497
of Poincareacute group Puarr+(11) 284
cohomology group 393 403coboundaries 403cochains 402cocycle 403
algebraic 387Cauchy 418Cauchy-Paul 354 419 425conical 418difference 417 462directional 416 440kinematical 499local 488metabolite-based 355 374minimal uncertainty 425multiselective 440on a graph 493on the sphere S
2 458on the sphere S
n 479on the torus T2 481steerable 439von Mises 440
wedgelet transform 455Wigner function 322Wigner-Ville transform 349Windowed Fourier or Gabor transform 349
ZZak transform 518
References
A Books and Theses
B Articles
Index
References 545
[Pau85] T Paul Ondelettes et Meacutecanique Quantique Thegravese de doctorat Univ drsquoAix-MarseilleII 1985
[Per86] AM Perelomov Generalized Coherent States and Their Applications (SpringerBerlin 1986)
[Per05] G Peyreacute Geacuteomeacutetrie multi-eacutechelles pour les images et les textures Thegravese de doctoratEcole Polytechnique Palaiseau 2005
[Pru86] E Prugovecki Stochastic Quantum Mechanics and Quantum Spacetime (ReidelDordrecht 1986)
[Rau04] H Rauhut Time-frequency and wavelet analysis of functions with symmetry proper-ties PhD thesis TU Muumlnich 2004
[Ree80] M Reed B Simon Methods of Modern Mathematical Physics I Functional Analysis(Academic New York 1980)
[Rud62] W Rudin Fourier Analysis on Groups (Interscience New York 1962)[Sch96] FE Schroeck Jr Quantum Mechanics on Phase Space (Kluwer Dordrecht 1996)[Sch61] L Schwartz Meacutethodes matheacutematiques pour les sciences physiques (Hermann Paris
1961)[Scu97] MO Scully MS Zubairy Quantum Optics (Cambridge University Press Cam-
bridge 1997)[Sho50] JA Shohat JD Tamarkin The Problem of Moments (American Mathematical
Society Providence RI 1950)[Ste71] EM Stein G Weiss Introduction to Fourier Analysis on Euclidean Spaces (Prince-
ton University Press Princeton NJ 1971)[Str64] RF Streater AS Wightman PCT Spin and Statistics and All That (Benjamin New
York 1964)[Sug90] M Sugiura Unitary Representations and Harmonic Analysis An Introduction
(North-HollandKodansha Ltd Tokyo 1990)[Suv11] A Suvichakorn C Lemke A Schuck Jr J-P Antoine The continuous wavelet
transform in MRS Tutorial text Marie Curie Research Training Network FAST(2011) httpwwwfast-mariecurie-rtn-projecteuWavelet
[Tak79] M Takesaki Theory of Operator Algebras I (Springer New York 1979)[Ter88] A Terras Harmonic Analysis on Symmetric Spaces and Applications II (Springer
Berlin 1988)[Tho98] G Thonet New aspects of time-frequency analysis for biomedical signal processing
Thegravese de Doctorat EPFL Lausanne 1998[Tor95] B Torreacutesani Analyse continue par ondelettes (InterEacuteditionsCNRS Eacuteditions Paris
1995)[Unt87] A Unterberger Analyse harmonique et analyse pseudo-diffeacuterentielle du cocircne de
lumiegravere Asteacuterisque 156 1ndash201 (1987)[Unt91] A Unterberger Quantification relativiste Meacutem Soc Math France 44ndash45 1ndash215
(1991)[Van98] P Vandergheynst Ondelettes directionnelles et ondelettes sur la sphegravere Thegravese de
Doctorat Univ Cath Louvain Louvain-la-Neuve 1998[Var85] VS Varadarajan Geometry of Quantum Theory 2nd edn (Springer New York 1985)[Vet95] M Vetterli J Kovacevic Wavelets and Subband Coding (Prentice Hall Englewood
Cliffs NJ 1995)[Vil69] NJ Vilenkin Fonctions speacuteciales et theacuteorie de la repreacutesentation des groupes (Dunod
Paris 1969)[Wel03] GV Welland Beyond Wavelets (Academic New York 2003)[vWe86] C von Westenholz Differential Forms in Mathematical Physics (North-Holland
Amsterdam 1986)[Wey28] H Weyl Gruppentheorie und Quantenmechanik (Hirzel Leipzig 1928)[Wey31] H Weyl The Theory of Groups and Quantum Mechanics (Dover New York 1931)[Wic94] MV Wickerhauser Adapted Wavelet Analysis from Theory to Software (A K Peters
Wellesley MA 1994)
546 References
[Wis93] W Wisnoe Utilisation de la meacutethode de transformeacutee en ondelettes 2D pour lrsquoanalysede visualisation drsquoeacutecoulements Thegravese de Doctorat ENSAE Toulouse 1993
[Woj97] P Wojtaszczyk A Mathematical Introduction to Wavelets (Cambridge UniversityPress Cambridge 1997)
[Zac06] C Zachos D Fairlie T Curtright Quantum Mechanics in Phase Space An OverviewWith Selected Papers (World Scientific Publishing Singapore 2006)
B Articles
[1] P Abry R Baraniuk P Flandrin R Riedi D Veitch Multiscale nature of network trafficIEEE Signal Process Mag 19 28ndash46 (2002)
[2] MD Adams The JPEG-2000 still image compression standardhttpwwweceuvicca~frodopublicationsjpeg2000pdf
[3] SL Adler AC Millard Coherent states in quaternionic quantum mechanics J MathPhys 38 2117ndash2126 (1997)
[4] GS Agarwal K Tara Nonclassical properties of states generated by the excitation on acoherent state Phys Rev A 43 492ndash497 (1991)
[5] GS Agarwal E Wolf Calculus for functions of noncommuting operators and generalphase-space methods in quantum mechanics I Mapping theorems and ordering of func-tions of noncommuting operators Phys Rev D 2 2161ndash2186 (1970)
[6] GS Agarwal E Wolf Calculus for functions of noncommuting operators and generalphase-space methods in quantum mechanics II Quantum mechanics in phase space PhysRev D 2 2187ndash2205 (1970)
[7] GS Agarwal E Wolf Calculus for functions of noncommuting operators and generalphase-space methods in quantum mechanics III A generalized Wick theorem and multi-time mapping Phys Rev D 2 2206ndash2225 (1970)
[8] V Aldaya J Guerrero G Marmo Quantization on a Lie group Higher-order polariza-tions in Symmetry in Sciences X ed by B Gruber M Ramek (Plenum Press Nerw York1998) pp 1ndash36
[9] M Alexandrescu D Gibert G Hulot J-L Le Mouel G Saracco Worldwide waveletanalysis of geomagnetic jerks J Geophys Res B 101 21975ndash21994 (1996)
[10] G Alexanian A Pinzul A Stern Generalized coherent state approach to star productsand applications to the fuzzy sphere Nucl Phys B 600 531ndash547 (2001)
[11] ST Ali A geometrical property of POV-measures and systems of covariance in Differ-ential Geometric Methods in Mathematical Physics ed by HD Doebner SI AnderssonHR Petry Lecture Notes in Mathematics vol 905 (Springer Berlin 1982) pp 207ndash22
[12] ST Ali Commutative systems of covariance and a generalization of Mackeyrsquos imprimi-tivity theorem Canad Math Bull 27 390ndash397 (1984)
[13] ST Ali Stochastic localisation quantum mechanics on phase space and quantum space-time Riv Nuovo Cim 8(11) 1ndash128 (1985)
[14] ST Ali A general theorem on square-integrability Vector coherent states J Math Phys39 3954ndash3964 (1998)
[15] ST Ali J-P Antoine Coherent states of 1+1 dimensional Poincareacute group Squareintegrability and a relativistic Weyl transform Ann Inst H Poincareacute 51 23ndash44 (1989)
[16] ST Ali S De Biegravevre Coherent states and quantization on homogeneous spaces in GroupTheoretical Methods in Physics ed by H-D Doebner et al Lecture Notes in Mathematicsvol 313 (Springer Berlin 1988) pp 201ndash207
References 547
[17] ST Ali H-D Doebner Ordering problem in quantum mechanics Prime quantization anda physical interpretation Phys Rev A 41 1199ndash1210 (1990)
[18] ST Ali GG Emch Geometric quantization Modular reduction theory and coherentstates J Math Phys 27 2936ndash2943 (1986)
[19] ST Ali M Engliš J-P Gazeau Vector coherent states from Plancherelrsquos theorem andClifford algebras J Phys A 37 6067ndash6089 (2004)
[20] ST Ali MEH Ismail Some orthogonal polynomials arising from coherent states JPhys A 45 125203 (2012) (16pp)
[21] ST Ali UA Mueller Quantization of a classical system on a coadjoint orbit of thePoincareacute group in 1+1 dimensions J Math Phys 35 4405ndash4422 (1994)
[22] ST Ali E Prugovecki Systems of imprimitivity and representations of quantum mechan-ics on fuzzy phase spaces J Math Phys 18 219ndash228 (1977)
[23] ST Ali E Prugovecki Mathematical problems of stochastic quantum mechanics Har-monic analysis on phase space and quantum geometry Acta Appl Math 6 1ndash18 (1986)
[24] ST Ali E Prugovecki Extended harmonic analysis of phase space representation for theGalilei group Acta Appl Math 6 19ndash45 (1986)
[25] ST Ali E Prugovecki Harmonic analysis and systems of covariance for phase spacerepresentation of the Poincareacute group Acta Appl Math 6 47ndash62 (1986)
[26] ST Ali J-P Antoine J-P Gazeau De Sitter to Poincareacute contraction and relativisticcoherent states Ann Inst H Poincareacute 52 83ndash111 (1990)
[27] ST Ali J-P Antoine J-P Gazeau Square integrability of group representations onhomogeneous spaces I Reproducing triples and frames Ann Inst H Poincareacute 55 829ndash855 (1991)
[28] ST Ali J-P Antoine J-P Gazeau Square integrability of group representations onhomogeneous spaces II Coherent and quasi-coherent states The case of the Poincareacutegroup Ann Inst H Poincareacute 55 857ndash890 (1991)
[29] ST Ali J-P Antoine J-P Gazeau Continuous frames in Hilbert space Ann Phys(NY)222 1ndash37 (1993)
[30] ST Ali J-P Antoine J-P Gazeau Relativistic quantum frames Ann Phys(NY) 222 38ndash88 (1993)
[31] ST Ali J-P Antoine J-P Gazeau UA Mueller Coherent states and their generalizationsA mathematical overview Rev Math Phys 7 1013ndash1104 (1995)
[32] ST Ali J-P Gazeau MR Karim Frames the β -duality in Minkowski space and spincoherent states J Phys A Math Gen 29 5529ndash5549 (1996)
[33] ST Ali M Engliš Quantization methods A guide for physicists and analysts Rev MathPhys 17 391ndash490 (2005)
[34] ST Ali J-P Gazeau B Heller Coherent states and Bayesian duality J Phys A MathTheor 41 365302 (2008)
[35] ST Ali L Balkovaacute EMF Curado J-P Gazeau MA Rego-Monteiro LMCSRodrigues K Sekimoto Non-commutative reading of the complex plane through Delonesequences J Math Phys 50 043517 (2009)
[36] ST Ali C Carmeli T Heinosaari A Toigo Commutative POVMS and fuzzy observ-ables Found Phys 39 593ndash612 (2009)
[37] ST Ali T Bhattacharyya SS Roy Coherent states on Hilbert modules J Phys A MathTheor 44 275202 (2011)
[38] ST Ali J-P Antoine F Bagarello J-P Gazeau (Guest Editors) Coherent states Acontemporary panorama preface to a special issue on Coherent states Mathematical andphysical aspects J Phys A Math Gen 45(24) (2012)
[39] ST Ali F Bagarello J-P Gazeau Quantizations from reproducing kernel spaces AnnPhys (NY) 332 127ndash142 (2013)
[40] STAli K Goacuterska A Horzela F Szafraniec Squeezed states and Hermite polynomials ina complex variable Preprint (2013) arXiv13084730v1 [quant-phy]
[41] P Aniello G Cassinelli E De Vito A Levrero Square-integrability of induced represen-tations of semidirect products Rev Math Phys 10 301ndash313 (1998)
548 References
[42] P Aniello G Cassinelli E De Vito A Levrero Wavelet transforms and discrete framesassociated to semidirect products J Math Phys 39 3965ndash3973 (1998)
[43] J-P Antoine Remarques sur le vecteur de Runge-Lenz Ann Soc Scient Bruxelles 80160ndash168 (1966)
[44] J-P Antoine Etude de la deacutegeacuteneacuterescence orbitale du potentiel coulombien en theacuteorie desgroupes I II Ann Soc Scient Bruxelles 80 169ndash184 (1966)
[45] J-P Antoine Etude de la deacutegeacuteneacuterescence orbitale du potentiel coulombien en theacuteorie desgroupes I II Ann Soc Scient Bruxelles 81 49ndash68 (1967)
[46] J-P Antoine Dirac formalism and symmetry problems in quantum mechanics I Generaldirac formalism J Math Phys 10 53ndash69 (1969)
[47] J-P Antoine Dirac formalism and symmetry problems in quantum mechanics II Symme-try problems J Math Phys 10 2276ndash2290 (1969)
[48] J-P Antoine Quantum mechanics beyond Hilbert space in Irreversibility and Causality mdashSemigroups and Rigged Hilbert Spaces ed by A Boumlhm H-D Doebner P KielanowskiLecture Notes in Physics vol 504 (Springer Berlin 1998) pp 3ndash33
[49] J-P Antoine Discrete wavelets on abelian locally compact groups Rev Cien Math(Habana) 19 3ndash21 (2003)
[50] J-P Antoine Introduction to precursors in physics Affine coherent states in FundamentalPapers in Wavelet Theory ed by C Heil D Walnut (Princeton University Press PrincetonNJ 2006) pp 113ndash116
[51] J-P Antoine F Bagarello Wavelet-like orthonormal bases for the lowest Landau levelJ Phys A Math Gen 27 2471ndash2481 (1994)
[52] J-P Antoine P Balazs Frames and semi-frames J Phys A Math Theor 44 205201(2011) (25 pages) Corrigendum J-P Antoine P Balazs Frames and semi-frames J PhysA Math Theor 44 479501 (2011) (2 pages)
[53] J-P Antoine P Balazs Frames semi-frames and Hilbert scales Numer Funct AnalOptim 33 736ndash769 (2012)
[54] J-P Antoine A Coron Time-frequency and time-scale approach to magnetic resonancespectroscopy J Comput Methods Sci Eng (JCMSE) 1 327ndash352 (2001)
[55] J-P Antoine AL Hohoueacuteto Discrete frames of Poincareacute coherent states in 1+3 dimen-sions J Fourier Anal Appl 9 141ndash173 (2003)
[56] J-P Antoine I Mahara Galilean wavelets Coherent states for the affine Galilei groupJ Math Phys 40 5956ndash5971 (1999)
[57] J-P Antoine U Moschella Poincareacute coherent states The two-dimensional massless caseJ Phys A Math Gen 26 591ndash607 (1993)
[58] J-P Antoine R Murenzi Two-dimensional directional wavelets and the scale-anglerepresentation Signal Process 52 259ndash281 (1996)
[59] J-P Antoine R Murenzi Two-dimensional continuous wavelet transform as linear phasespace representation of two-dimensional signals in Wavelet Applications IV SPIE Pro-ceedings vol 3078 (SPIE Bellingham WA 1997) pp 206ndash217
[60] J-P Antoine D Rosca The wavelet transform on the two-sphere and related manifolds mdashA review in Optical and Digital Image Processing SPIE Proceedings vol 7000 (2008)pp 70000B-1ndash15
[61] J-P Antoine D Speiser Characters of irreducible representations of simple Lie groupsJ Math Phys 5 1226ndash1234 (1964)
[62] J-P Antoine P Vandergheynst Wavelets on the n-sphere and related manifolds J MathPhys 39 3987ndash4008 (1998)
[63] J-P Antoine P Vandergheynst Wavelets on the 2-sphere A group-theoretical approachAppl Comput Harmon Anal 7 262ndash291 (1999)
[64] J-P Antoine P Vandergheynst Wavelets on the two-sphere and other conic sections JFourier Anal Appl 13 369ndash386 (2007)
[65] J-P Antoine M Duval-Destin R Murenzi B Piette Image analysis with 2D wavelettransform Detection of position orientation and visual contrast of simple objects inWavelets and Applications (Proc Marseille 1989) ed by Y Meyer (Masson and SpringerParis and Berlin 1991) pp144ndash159
References 549
[66] J-P Antoine P Carrette R Murenzi B Piette Image analysis with 2D continuous wavelettransform Signal Process 31 241ndash272 (1993)
[67] J-P Antoine P Vandergheynst K Bouyoucef R Murenzi Alternative representations ofan image via the 2D wavelet transform Application to character recognition in VisualInformation Processing IV SPIE Proceedings vol 2488 (SPIE Bellingham WA 1995)pp 486ndash497
[68] J-P Antoine R Murenzi P Vandergheynst Two-dimensional directional wavelets inimage processing Int J Imaging Syst Tech 7 152ndash165 (1996)
[69] J-P Antoine D Barache RM Cesar Jr LF Costa Shape characterization with thewavelet transform Signal Process 62 265ndash290 (1997)
[70] J-P Antoine P Antoine B Piraux Wavelets in atomic physics in Spline Functions andthe Theory of Wavelets ed by S Dubuc G Deslauriers CRM Proceedings and LectureNotes vol 18 (AMS Providence RI 1999) pp261ndash276
[71] J-P Antoine P Antoine B Piraux Wavelets in atomic physics and in solid state physicsin Wavelets in Physics Chap 8 ed by JC van den Berg (Cambridge University PressCambridge 1999)
[72] J-P Antoine R Murenzi P Vandergheynst Directional wavelets revisited Cauchywavelets and symmetry detection in patterns Appl Comput Harmon Anal 6 314ndash345(1999)
[73] J-P Antoine L Jacques R Twarock Wavelet analysis of a quasiperiodic tiling withfivefold symmetry Phys Lett A 261 265ndash274 (1999)
[74] J-P Antoine L Jacques P Vandergheynst Penrose tilings quasicrystals and wavelets inWavelet Applications in Signal and Image Processing VII SPIE Proceedings vol 3813(SPIE Bellingham WA 1999) pp 28ndash39
[75] J-P Antoine YB Kouagou D Lambert B Torreacutesani An algebraic approach to discretedilations Application to discrete wavelet transforms J Fourier Anal Appl 6 113ndash141(2000)
[76] J-P Antoine A Coron J-M Dereppe Water peak suppression Time-frequency vs time-scale approach J Magn Reson 144 189ndash194 (2000)
[77] J-P Antoine J-P Gazeau P Monceau J R Klauder K Penson Temporally stablecoherent states for infinite well and Poumlschl-Teller potentials J Math Phys 42 2349ndash2387(2001)
[78] J-P Antoine A Coron C Chauvin Wavelets and related time-frequency techniques inmagnetic resonance spectroscopy NMR Biomed 14 265ndash270 (2001)
[79] J-P Antoine L Demanet J-F Hochedez L Jacques R Terrier E Verwichte Applicationof the 2-D wavelet transform to astrophysical images Phys Mag 24 93ndash116 (2002)
[80] J-P Antoine L Demanet L Jacques P Vandergheynst Wavelets on the sphere Imple-mentation and approximations Appl Comput Harmon Anal 13 177ndash200 (2002)
[81] J-P Antoine I Bogdanova P Vandergheynst The continuous wavelet transform on conicsections Int J Wavelets Multires Inform Proc 6 137ndash156 (2007)
[82] J-P Antoine D Rosca P Vandergheynst Wavelet transform on manifolds Old and newapproaches Appl Comput Harmon Anal 28 189ndash202 (2010)
[83] P Antoine B Piraux A Maquet Time profile of harmonics generated by a single atom ina strong electromagnetic field Phys Rev A 51 R1750ndashR1753 (1995)
[84] P Antoine B Piraux DB Miloševic M Gajda Generation of ultrashort pulses ofharmonics Phys Rev A 54 R1761ndashR1764 (1996)
[85] P Antoine B Piraux DB Miloševic M Gajda Temporal profile and time control ofharmonic generation Laser Phys 7 594ndash601 (1997)
[86] Apollonius see Wikipedia httpenwikipediaorgwikiApollonius_of_Perga[87] FT Arecchi E Courtens R Gilmore H Thomas Atomic coherent states in quantum
optics Phys Rev A 6 2211ndash2237 (1972)[88] I Aremua J-P Gazeau MN Hounkonnou Action-angle coherent states for quantum
systems with cylindric phase space J Phys A Math Theor 45 335302 (2012)
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[90] F Argoul A Arneacuteodo J Elezgaray G Grasseau R Murenzi Wavelet analysis of theself-similarity of diffusion-limited aggregates and electrodeposition clusters Phys Rev A41 5537ndash5560 (1990)
[91] TA Arias Multiresolution analysis of electronic structure Semicardinal and waveletbases Rev Mod Phys 71 267ndash312 (1999)
[92] A Arneacuteodo F Argoul E Bacry J Elezgaray E Freysz G Grasseau JF Muzy BPouligny Wavelet transform of fractals in Wavelets and Applications (Proc Marseille1989) ed by Y Meyer (Masson and Springer Paris and Berlin 1991) pp 286ndash352
[93] A Arneacuteodo E Bacry JF Muzy The thermodynamics of fractals revisited with waveletsPhysica A 213 232ndash275 (1995)
[94] A Arneacuteodo E Bacry JF Muzy Oscillating singularities in locally self-similar functionsPhys Rev Lett 74 4823ndash4826 (1995)
[95] A Arneacuteodo E Bacry PV Graves JF Muzy Characterizing long-range correlations inDNA sequences from wavelet analysis Phys Rev Lett 74 3293ndash3296 (1996)
[96] A Arneacuteodo Y drsquoAubenton E Bacry PV Graves JF Muzy C Thermes Wavelet basedfractal analysis of DNA sequences Physica D 96 291ndash320 (1996)
[97] A Arneacuteodo E Bacry S Jaffard JF Muzy Oscillating singularities on Cantor sets Agrand canonical multifractal formalism J Stat Phys 87 179ndash209 (1997)
[98] A Arneacuteodo E Bacry S Jaffard JF Muzy Singularity spectrum of multifractal functionsinvolving oscillating singularities J Fourier Anal Appl 4 159ndash174 (1998)
[99] N Aronszajn Theory of reproducing kernels Trans Amer Math Soc 66 337ndash404 (1950)[100] A Ashtekar J Lewandowski D Marolf J Mouratildeo T Thiemann Coherent state
transforms for spaces of connections J Funct Analysis 135 519ndash551 (1996)[101] A Askari-Hemmat MA Dehghan M Radjabalipour Generalized frames and their
redundancy Proc Amer Math Soc 129 1143ndash1147 (2001)[102] EW Aslaksen JR Klauder Unitary representations of the affine group J Math Phys 9
206ndash211 (1968)[103] EW Aslaksen JR Klauder Continuous representation theory using the affine group
J Math Phys 10 2267ndash2275 (1969)[104] D Astruc L Plantieacute R Murenzi Y Lebret D Vandromme On the use of the 3D
wavelet transform for the analysis of computational fluid dynamics results in Progressin Wavelet Analysis and Applications (Proc Toulouse 1992) ed by Y Meyer S Roques(Ed Frontiegraveres Gif-sur-Yvette 1993) pp 463ndash470
[105] PW Atkins JC Dobson Angular momentum coherent states Proc Roy Soc London A321 321ndash340 (1971)
[106] BW Atkinson DO Bruff JS Geronimo D P Hardin Wavelets centered on a knotsequence Piecewise polynomial wavelets on a quasi-crystal lattice preprint (2011)arXiv11024246v1 [mathNA]
[107] IS Averbuch NF Perelman Fractional revivals Universality in the long-term evolutionof quantum wave packets beyond the correspondence principle dynamics Phys Lett A139 449ndash453 (1989)
[108] H Bacry J-M Leacutevy-Leblond Possible kinematics J Math Phys 9 1605ndash1614 (1968)[109] H Bacry A Grossmann J Zak Proof of the completeness of lattice states in kq
representation Phys Rev B 12 1118ndash1120 (1975)[110] L Baggett KF Taylor Groups with completely reducible regular representation Proc
Amer Math Soc 72 593ndash600 (1978)[111] VG Bagrov J-P Gazeau D Gitman A Levine Coherent states and related quantizations
for unbounded motions J Phys A Math Theor 45 125306 (2012) arXiv12010955v2[quant-ph]
[112] P Balazs J-P Antoine A Grybos Weighted and controlled frames Mutual relationshipand first numerical properties Int J Wavelets Multires Inform Proc 8 109ndash132 (2010)
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[114] P Balazs D Bayer A Rahimi Multipliers for continuous frames in Hilbert spaces JPhys A Math Gen 45 244023 (2012)
[115] P Baldi G Kerkyacharian D Marinucci D Picard High frequency asymptotics forwavelet-based tests for Gaussianity and isotropy on the torus J Multivar Anal 99 606ndash636 (2008)
[116] P Baldi G Kerkyacharian D Marinucci D Picard Asymptotics for spherical needletsAnn of Stat 37 1150ndash1171 (2009)
[117] MC Baldiotti J-P Gazeau DM Gitman Coherent states of a particle in magnetic fieldand Stieltjes moment problem Phys Lett A 373 1916ndash1920 (2009) Erratum Phys LettA 373 2600 (2009)
[118] MC Baldiotti J-P Gazeau DM Gitman Semiclassical and quantum description ofmotion on the noncommutative plane Phys Lett A 373 3937ndash3943 (2009)
[119] R Balian Un principe drsquoincertitude fort en theacuteorie du signal ou en meacutecanique quantiqueCR Acad Sci(Paris) 292 1357ndash1362 (1981)
[120] M Bander C Itzykson Group theory and the hydrogen atom I II Rev Mod Phys 38330ndash345 346ndash358 (1966)
[121] D Barache S De Biegravevre J-P Gazeau Affine symmetry semigroups for quasicrystalsEurophys Lett 25 435ndash440 (1994)
[122] D Barache J-P Antoine J-M Dereppe The continuous wavelet transform a tool for NMRspectroscopy J Magn Reson 128 1ndash11 (1997)
[123] V Bargmann On a Hilbert space of analytic functions and an associated integral transformPart I Commun Pure Appl Math 14 187ndash214 (1961)
[124] V Bargmann On a Hilbert space of analytic functions and an associated integral transformPart II A family of related function spaces Application to distribution theory CommunPure Appl Math 20 1ndash101 (1967)
[125] V Bargmann P Butera L Girardello JR Klauder On the completeness of coherentstates Reports Math Phys 2 221ndash228 (1971)
[126] AO Barut L Girardello New ldquocoherentrdquo states associated with non compact groupsCommun Math Phys 21 41ndash55 (1971)
[127] AO Barut H Kleinert Transition probabilities of the hydrogen atom from noncompactdynamical groups Phys Rev 156 1541ndash1545 (1967)
[128] AO Barut BW Xu Non-spreading coherent states riding on Kepler orbits Helv PhysActa 66 711ndash720 (1993)
[129] G Battle Wavelets A renormalization group point of view in Wavelets and TheirApplications ed by MB Ruskai G Beylkin R Coifman I Daubechies S Mallat YMeyer L Raphael (Jones and Bartlett Boston 1992) pp 323ndash349
[130] P Bellomo CR Stroud Jr Dispersion of Klauderrsquos temporally stable coherent states forthe hydrogen atom J Phys A Math Gen 31 L445ndashL450 (1998)
[131] J Ben Geloun J R Klauder Ladder operators and coherent states for continuous spectraJ Phys A Math Theor 42 375209 (2009)
[132] J Ben Geloun J Hnybida JR Klauder Coherent states for continuous spectrum operatorswith non-normalizable fiducial states J Phys A Math Theor 45 085301 (2012)
[133] JJ Benedetto TD Andrews Intrinsic wavelet and frame applications in IndependentComponent Analyses Wavelets Neural Networks Biosystems and Nanoengineering IXed by H Szu L Dai SPIE Proceedings vol 8058 (SPIE Bellingham WA 2011) p805802
[134] JJ Benedetto A Teolis A wavelet auditory model and data compression Appl ComputHarmon Anal 1 3ndash28 (1993)
[135] FA Berezin Quantization Math USSR Izvestija 8 1109ndash1165 (1974)[136] FA Berezin General concept of quantization Commun Math Phys 40 153ndash174 (1975)[137] H Bergeron From classical to quantum mechanics How to translate physical ideas into
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[139] H Bergeron and J-P Gazeau Integral quantization with two basic examples Preprint(2013) arXiv13082348v1
[140] H Bergeron A Valance Overcomplete basis for one dimensional Hamiltonians J MathPhys 36 1572ndash1592 (1995)
[141] H Bergeron J-P Gazeau P Siegl A Youssef Semi-classical behavior of Poumlschl-Tellercoherent states Eur Phys Lett 92 60003 (2010)
[142] H Bergeron P Siegl A Youssef New SUSYQM coherent states for Poumlschl-Tellerpotentials A detailed mathematical analysis J Phys A Math Theor 45 244028 (2012)
[143] H Bergeron J-P Gazeau A Youssef Are the Weyl and coherent state descriptionsphysically equivalent Phys Lett A 377 598ndash605 (2013)
[144] H Bergeron A Dapor J-P Gazeau P Małkiewicz Wavelet quantum cosmology preprint(2013) arXiv13050653 [gr-qc]
[145] S Bergman Uumlber die Kernfunktion eines Bereiches und ihr Verhalten am Rande I ReineAngw Math 169 1ndash42 (1933)
[146] D Bernier KF Taylor Wavelets from square-integrable representations SIAM J MathAnal 27 594ndash608 (1996)
[147] G Bernuau Wavelet bases associated to a self-similar quasicrystal J Math Phys 394213ndash4225 (1998)
[148] A Bertrand Deacuteveloppements en base de Pisot et reacutepartition modulo 1 C R Acad SciParis 285 419ndash421 (1977)
[149] J Bertrand P Bertrand Classification of affine Wigner functions via an extendedcovariance principle in Group Theoretical Methods in Physics (Proc Sainte-Adegravele 1988)ed by Y Saint-Aubin L Vinet (World Scientific Singapore 1989) pp 1380ndash1383
[150] Z Białynicka-Birula I Białynicki-Birula Space-time description of squeezing J OptSoc Am B4 1621ndash1626 (1987)
[151] E Bianchi E Magliaro C Perini Coherent spin-networks Phys Rev D 82 024012(2010)
[152] S Biskri J-P Antoine B Inhester F Mekideche Extraction of Solar coronal magneticloops with the 2-D Morlet wavelet transform Solar Phys 262 373ndash385 (2010)
[153] R Bluhm VA Kostelecky JA Porter The evolution and revival structure of localizedquantum wave packets Am J Phys 64 944ndash953 (1996)
[154] I Bogdanova P Vandergheynst J-P Antoine L Jacques M Morvidone Stereographicwavelet frames on the sphere Appl Comput Harmon Anal 19 223ndash252 (2005)
[155] I Bogdanova X Bresson J-P Thiran P Vandergheynst Scale space analysis and activecontours for omnidirectional images IEEE Trans Image Process 16 1888ndash1901 (2007)
[156] I Bogdanova P Vandergheynst J-P Gazeau Continuous wavelet transform on thehyperboloid Appl Comput Harmon Anal 23 (2007) 286ndash306 (2007)
[157] P Boggiatto E Cordero Anti-Wick quantization of tempered distributions in Progress inAnalysis Berlin (2001) vol I II (World Sci Publ River Edge NJ 2003) pp 655ndash662
[158] P Boggiatto E Cordero K Groumlchenig Generalized Anti-Wick operators with symbols indistributional Sobolev spaces Int Equ Oper Theory 48 427ndash442 (2004)
[159] A Boumlhm The Rigged Hilbert Space in quantum mechanics in Lectures in TheoreticalPhysics vol IX A ed by WA Brittin et al (Gordon amp Breach New York 1967) pp255ndash315
[160] G Bohnkeacute Treillis drsquoondelettes associeacutes aux groupes de Lorentz Ann Inst H Poincareacute54 245ndash259 (1991)
[161] WR Bomstad JR Klauder Linearized quantum gravity using the projection operatorformalism Class Quantum Grav 23 5961ndash5981 (2006)
[162] VV Borzov Orthogonal polynomials and generalized oscillator algebras Int TransformSpec Funct 12 115ndash138 (2001)
[163] VV Borzov EV Damaskinsky Generalized coherent states for classical orthogonalpolynomials Day on Diffraction (2002) arXivmathQA0209181v1 (SPb 2002)
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[165] A Bouzouina S De Biegravevre Equipartition of the eigenfunctions of quantized ergodic mapson the torus Commun Math Phys 178 83ndash105 (1996)
[166] P Brault J-P Antoine A spatio-temporal Gaussian-Conical wavelet with high apertureselectivity for motion and speed analysis Appl Comput Harmon Anal 34 148ndash161(2012)
[167] A Briguet S Cavassila D Graveron-Demilly Suppression of huge signals using theCadzow enhancement procedure The NMR Newslett 440 26 (1995)
[168] CM Brislawn Fingerprints go digital Notices Amer Math Soc 42 1278ndash1283 (1995)[169] CM Brislawn On the group-theoretic structure of lifted filter banks in Excursions in
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[170] F Bruhat Sur les repreacutesentations induites des groupes de Lie Bull Soc Math France 8497ndash205 (1956)
[171] T Buumllow Multiscale image processing on the sphere in DAGM-Symposium (2002) pp609ndash617
[172] C Burdik C Frougny J-P Gazeau R Krejcar Beta-integers as natural counting systemsfor quasicrystals J Phys A Math Gen 31 6449ndash6472 (1998)
[173] KE Cahill Coherent-state representations for the photon density Phys Rev 138 B1566ndash1576 (1965)
[174] KE Cahill R Glauber Density operators and quasiprobability distributions Phys Rev177 1882ndash1902 (1969)
[175] KE Cahill R Glauber Ordered expansions in boson amplitude operators Phys Rev 1771857ndash1881 (1969)
[176] AR Calderbank I Daubechies W Sweldens BL Yeo Wavelets that map integers tointegers Appl Comput Harmon Anal 5 332ndash369 (1998)
[177] M Calixto J Guerrero Wavelet transform on the circle and the real line A unified group-theoretical treatment Appl Comput Harmon Anal 21 204ndash229 (2006)
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[179] M Calixto J Guerrero D Rosca Wavelet transform on the torus A group-theoreticalapproach preprint (2013)
[180] EJ Candegraves Harmonic analysis of neural networks Appl Comput Harmon Anal 6 197ndash218 (1999)
[181] EJ Candegraves Ridgelets and the representation of mutilated Sobolev functions SIAM JMath Anal 33 347ndash368 (2001)
[182] EJ Candegraves L Demanet Curvelets and Fourier integral operators CR Acad Sci ParisSeacuter I Math 336 395ndash398 (2003)
[183] EJ Candegraves L Demanet The curvelet representation of wave propagators is optimallysparse Commun Pure Appl Math 58 1472ndash1528 (2004)
[184] EJ Candegraves L Demanet The curvelet representation of wave propagators is optimallysparse Commun Pure Appl Math 58 1472ndash1528 (2005)
[185] EJ Candegraves DL Donoho Curvelets ndash A surprisingly effective nonadaptive representationfor objects with edges in Curves and Surfaces ed by LL Schumaker et al (VanderbiltUniversity Press Nashville TN 1999)
[186] EJ Candegraves DL Donoho Ridgelets A key to higher-dimensional intermittency PhilTrans R Soc Lond A 357 2495ndash2509 (1999)
[187] EJ Candegraves DL Donoho Curvelets multiresolution representation and scaling laws inWavelet Applications in Signal and Image Processing VIII ed by A Aldroubi A LaineM Unser SPIE Proceedings vol 4119 (SPIE Bellingham WA 2000) pp 1ndash12
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[189] EJ Candegraves DL Donoho New tight frames of curvelets and optimal representations ofobjects with piecewise C2 singularities Commun Pure Appl Math 57 219ndash266 (2004)
[190] EJ Candegraves DL Donoho Continuous curvelet transform I Resolution of the wavefrontset II Discretization and frames Appl Comput Harmon Anal 19 162ndash197 198ndash222(2005)
[191] EJ Candegraves F Guo New multiscale transforms minimum total variationsynthesisApplications to edge-preserving image reconstruction Signal Proc 82 1519ndash1543 (2002)
[192] EJ Candegraves L Demanet D Donoho L Ying Fast discrete curvelet transforms MultiscaleModel Simul 5 861ndash899 (2006)
[193] AL Carey Square integrable representations of non-unimodular groups Bull AustrMath Soc 15 1ndash12 (1976)
[194] AL Carey Group representations in reproducing kernel Hilbert spaces Rep Math Phys14 247ndash259 (1978)
[195] P Carruthers MM Nieto Phase and angle variables in quantum mechanics Rev ModPhys 40 411ndash440 (1968)
[196] PG Casazza G Kutyniok Frames of subspaces in Wavelets Frames and Operator The-ory Contemporary Mathematics vol 345 (American Mathematical Society ProvidenceRI 2004) pp 87ndash113
[197] PG Casazza D Han DR Larson Frames for Banach spaces Contemp Math 247 149ndash182 (1999)
[198] P Casazza O Christensen S Li A Lindner Riesz-Fischer sequences and lower framebounds Z Anal Anwend 21 305ndash314 (2002)
[199] PG Casazza G Kutyniok S Li Fusion frames and distributed processing ApplComputHarmon Anal 25 114ndash132 (2008)
[200] DPL Castrigiano RW Henrichs Systems of covariance and subrepresentations ofinduced representations Lett Math Phys 4 169ndash175 (1980)
[201] U Cattaneo Densities of covariant observables J Math Phys 23 659ndash664 (1982)[202] A Cerioni L Genovese I Duchemin Th Deutsch Accurate complex scaling of three
dimensional numerical potentials Preprint (2013) arXiv13036439v2[203] S-J Chang K-J Shi Evolution and exact eigenstates of a resonant quantum system Phys
Rev A 34 7ndash22 (1986)[204] SHH Chowdhury ST Ali All the groups of signal analysis from the (1+1) affine Galilei
group J Math Phys 52 103504 (2011)[205] SL Chown Antarctic marine biodiversity and deep-sea hydrothermal vents PLoS Biol
10 1ndash4 (2012)[206] C Cishahayo S De Biegravevre On the contraction of the discrete series of SU(11) Ann Inst
Fourier (Grenoble) 43 551ndash567 (1993)[207] M Clerc and S Mallat Shape from texture and shading with wavelets in Dynamical
Systems Control Coding Computer Vision Progress in Systems and Control Theory 25393ndash417 (1999)
[208] L Cohen General phase-space distribution functions J Math Phys 7 781ndash786 (1966)[209] A Cohen I Daubechies J-C Feauveau Biorthogonal bases of compactly supported
wavelets Commun Pure Appl Math 45 485ndash560 (1992)[210] R Coifman Y Meyer MV Wickerhauser Wavelet analysis and signal processing
in Wavelets and Their Applications ed by MB Ruskai G Beylkin R CoifmanI Daubechies S Mallat Y Meyer L Raphael (Jones and Bartlett Boston 1992)pp 153ndash178
[211] R Coifman Y Meyer MV Wickerhauser Entropy-based algorithms for best basisselection IEEE Trans Inform Theory 38 713ndash718 (1992)
[212] R Coquereaux A Jadczyk Conformal theories curved spaces relativistic wavelets andthe geometry of complex domains Rev Math Phys 2 1ndash44 (1990)
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[213] A Coron L Vanhamme J-P Antoine P Van Hecke S Van Huffel The filtering approachto solvent peak suppression in MRS A critical review J Magn Reson 152 26ndash40 (2001)
[214] N Cotfas J-P Gazeau Finite tight frames and some applications (topical review) J PhysA Math Theor 43 193001 (2010)
[215] N Cotfas J-P Gazeau K Goacuterska Complex and real Hermite polynomials and relatedquantizations J Phys A Math Theor 43 305304 (2010)
[216] N Cotfas J-P Gazeau A Vourdas Finite-dimensional Hilbert space and frame quantiza-tion J Phys A Math Gen 44 175303 (2011)
[217] EMF Curado MA Rego-Monteiro LMCS Rodrigues Y Hassouni Coherent statesfor a degenerate system The hydrogen atom Physica A 371 16ndash19 (2006)
[218] S Dahlke P Maass The affine uncertainty principle in one and two dimensions CompMath Appl 30 293ndash305 (1995)
[219] S Dahlke W Dahmen E Schmidt I Weinreich Multiresolution analysis and wavelets onS
2 and S3 Numer Funct Anal Optim 16 19ndash41 (1995)
[220] S Dahlke V Lehmann G Teschke Applications of wavelet methods to the analysis ofmeteorological radar data - An overview Arabian J Sci Eng 28 3ndash44 (2003)
[221] S Dahlke G Kutyniok P Maass C Sagiv H-G Stark G Teschke The uncertaintyprinciple associated with the continuous shearlet transform Int J Wavelets MultiresolutInf Process 6 157ndash181 (2008)
[222] S Dahlke G Kutyniok G Steidl G Teschke Shearlet coorbit spaces and associatedBanach frames Appl Comput Harmon Anal 27 195ndash214 (2009)
[223] S Dahlke G Steidl G Teschke The continuous shearlet transform in arbitrary spacedimensions J Fourier Anal Appl 16 340ndash364 (2010)
[224] S Dahlke G Steidl G Teschke Shearlet coorbit spaces Compactly supported analyzingshearlets traces and embeddings J Fourier Anal Appl 17 1232ndash1355 (2011)
[225] T Dallard GR Spedding 2-D wavelet transforms Generalisation of the Hardy space andapplication to experimental studies Eur J Mech BFluids 12 107ndash134 (1993)
[226] C Daskaloyannis Generalized deformed oscillator and nonlinear algebras J Phys AMath Gen 24 L789ndashL794 (1991)
[227] C Daskaloyannis K Ypsilantis A deformed oscillator with Coulomb energy spectrumJ Phys A Math Gen 25 4157ndash4166 (1992)
[228] I Daubechies On the distributions corresponding to bounded operators in the Weylquantization Commun Math Phys 75 229ndash238 (1980)
[229] I Daubechies and A Grossmann An integral transform related to quantization I J MathPhys 21 2080ndash2090 (1980)
[230] I Daubechies A Grossmann J Reignier An integral transform related to quantization IIJ Math Phys 24 239ndash254 (1983)
[231] I Daubechies Orthonormal bases of compactly supported wavelets Commun Pure ApplMath 41 909ndash996 (1988)
[232] I Daubechies The wavelet transform time-frequency localisation and signal analysisIEEE Trans Inform Theory 36 961ndash1005 (1990)
[233] I Daubechies S Maes A nonlinear squeezing of the continuous wavelet transform basedon auditory nerve models in Wavelets in Medicine and Biology ed by A Aldroubi MUnser (CRC Press Boca Raton 1996) pp 527ndash546
[234] I Daubechies A Grossmann Y Meyer Painless nonorthogonal expansions J Math Phys27 1271ndash1283 (1986)
[235] ER Davies Introduction to texture analysis in Handbook of texture analysis ed by MMirmehdi X Xie J Suri (World Scientific Singapore 2008) pp 1ndash31
[236] R De Beer D van Ormondt FTAW Wajer S Cavassila D Graveron-Demilly S VanHuffel SVD-based modelling of medical NMR signals in SVD and Signal ProcessingIII Algorithms Architectures and Applications ed by M Moonen B De Moor (Elsevier(North-Holland) Amsterdam 1995) pp 467ndash474
[237] S De Biegravevre Coherent states over symplectic homogeneous spaces J Math Phys 301401ndash1407 (1989)
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[238] S De Biegravevre JA Gonzalez Semi-classical behaviour of the Weyl correspondence on thecircle in Group-Theoretical Methods in Physics (Proc Salamanca 1992) ed by M delOlmo M Santander J Mateos Guilarte (CIEMAT Madrid 1993) pp 343ndash346
[239] S De Biegravevre JA Gonzaacutelez Semiclassical behaviour of coherent states on the circle inQuantization and Coherent States Methods in Physics ed by A Odzijewicz et al (WorldScientific Singapore 1993)
[240] S De Biegravevre AE Gradechi Quantum mechanics and coherent states on the anti-de Sitterspace-time and their Poincareacute contraction Ann Inst H Poincareacute 57 403ndash428 (1992)
[241] J Deenen C Quesne Dynamical group of collective states I II III J Math Phys 23878ndash889 2004ndash2015 (1982)
[242] J Deenen C Quesne Dynamical group of collective states I II III J Math Phys 251638ndash1650 (1984)
[243] J Deenen C Quesne Partially coherent states of the real symplectic group J Math Phys25 2354ndash2366 (1984)
[244] J Deenen C Quesne Boson representations of the real symplectic group and theirapplication to the nuclear collective model J Math Phys 26 2705ndash2716 (1985)
[245] R Delbourgo Minimal uncertainty states for the rotation and allied groups J Phys AMath Gen 10 1837ndash1846 (1977)
[246] R Delbourgo J R Fox Maximum weight vectors possess minimal uncertainty J PhysA Math Gen 10 L233ndashL235 (1977)
[247] V Delouille J de Patoul J-F Hochedez L Jacques J-P Antoine Wavelet spectrumanalysis of EITSoHO images Solar Phys 228 301ndash321 (2005)
[248] N Delprat B Escudieacute P Guillemain R Kronland-Martinet P Tchamitchian B Tor-reacutesani Asymptotic wavelet and Gabor analysis Extraction of instantaneous frequenciesIEEE Trans Inform Theory 38 644ndash664 (1992)
[249] Th Deutsch L Genovese Wavelets for electronic structure calculations Collection SocFr Neut 12 33ndash76 (2011)
[250] B Dewitt Quantum theory of gravity I The canonical theory Phys Rev 160 1113ndash1148(1967)
[251] RH Dicke Coherence in spontaneous radiation processes Phys Rev 93 99ndash110 (1954)[252] AN Dinkelaker AL MacKinnon Wavelets intermittency and solar flare hard X-rays 1
Local intermittency measure in cascade and avalanche scenarios Solar Phys 282 471ndash481(2013)
[253] AN Dinkelaker AL MacKinnon Wavelets intermittency and solar flare hard X-rays 2LIM analysis of high time resolution BATSE data Solar Phys 282 483ndash501 (2013)
[254] MN Do M Vetterli Contourlets in Beyond Wavelets ed by GV Welland (AcademicSan Diego 2003) pp 83ndash105
[255] MN Do M Vetterli The contourlet transform An efficient directional multiresolutionimage representation IEEE Trans Image Process 14 2091ndash2106 (2005)
[256] VV Dodonov Nonclassical states in quantum optics A ldquosqueezedrdquo review of the first 75years J Opt B Quant Semiclass Opot 4 R1ndashR33 (2002)
[257] DL Donoho Nonlinear wavelet methods for recovery of signals densities and spectrafrom indirect and noisy data in Different Perspectives on Wavelets Proceedings ofSymposia in Applied Mathematics vol 38 ed by I Daubechies (American MathematicalSociety Providence RI 1993) pp 173ndash205
[258] DL Donoho Wedgelets Nearly minimax estimation of edges Ann Stat 27 859ndash897(1999)
[259] DL Donoho X Huo Beamlet pyramids A new form of multiresolution analysis suitedfor extracting lines curves and objects from very noisy image data in SPIE Proceedingsvol 5914 (SPIE Bellingham WA 2005) pp 1ndash12
References 557
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[261] AH Dooley JW Rice Contractions of rotation groups and their representations MathProc Camb Phil Soc 94 509ndash517 (1983)
[262] AH Dooley JW Rice On contractions of semisimple Lie groups Trans Amer MathSoc 289 185ndash202 (1985)
[263] JR Driscoll DM Healy Computing Fourier transforms and convolutions on the 2-sphereAdv Appl Math 15 202ndash250 (1994)
[264] H Drissi F Regragui J-P Antoine M Bennouna Wavelet transform analysis of visualevoked potentials Some preliminary results ITBM-RBM 21 84ndash91 (2000)
[265] RJ Duffin AC Schaeffer A class of nonharmonic Fourier series Trans Amer MathSoc 72 341ndash366 (1952)
[266] M Duflo CC Moore On the regular representation of a nonunimodular locally compactgroup J Funct Anal 21 209ndash243 (1976)
[267] M Duval-Destin R Murenzi Spatio-temporal wavelets Application to the analysis ofmoving patterns in Progress in Wavelet Analysis and Applications (Proc Toulouse 1992)ed by Y Meyer S Roques (Ed Frontiegraveres Gif-sur-Yvette 1993) pp 399ndash408
[268] M Duval-Destin M-A Muschietti B Torreacutesani Continuous wavelet decompositionsmultiresolution and contrast analysis SIAM J Math Anal 24 739ndash755 (1993)
[269] SJL van Eindhoven JLH Meyers New orthogonality relations for the Hermitepolynomials and related Hilbert spaces J Math Anal Appl 146 89ndash98 (1990)
[270] M ElBaz R Fresneda J-P Gazeau Y Hassouni Coherent state quantization of para-grassmann algebras J Phys A Math Theor 43 385202 (2010) Corrigendum J PhysA Math Theor 45 (2012)
[271] A Elkharrat J-P Gazeau F Deacutenoyer Multiresolution of quasicrystal diffraction spectraActa Cryst A65 466ndash489 (2009)
[272] Q Fan Phase space analysis of the identity decompositions J Math Phys 34 3471ndash3477(1993)
[273] M Fanuel S Zonetti Affine quantization and the initial cosmological singularity Euro-phys Lett 101 10001 (2013)
[274] M Farge Wavelet transforms and their applications to turbulence Annu Rev Fluid Mech24 395ndash457 (1992)
[275] M Farge N Kevlahan V Perrier E Goirand Wavelets and turbulence Proc IEEE 84639ndash669 (1996)
[276] M Farge NK-R Kevlahan V Perrier K Schneider Turbulence analysis modellingand computing using wavelets in Wavelets in Physics Chap 4 ed by JC van den Berg(Cambridge University Press Cambridge 1999)
[277] HG Feichtinger Coherent frames and irregular sampling in Recent Advances in FourierAnalysis and Its applications ed by JS Byrnes JL Byrnes (Kluwer Dordrecht 1990)pp 427ndash440
[278] HG Feichtinger KH Groumlchenig Banach spaces related to integrable group representa-tions and their atomic decompositions I J Funct Anal 86 307ndash340 (1989)
[279] HG Feichtinger KH Groumlchenig Banach spaces related to integrable group representa-tions and their atomic decompositions II Mh Math 108 129ndash148 (1989)
[280] M Flensted-Jensen Discrete series for semisimple symmetric spaces Ann of Math 111253ndash311 (1980)
[281] K Flornes A Grossmann M Holschneider B Torreacutesani Wavelets on discrete fieldsAppl Comput Harmon Anal 1 137ndash146 (1994)
[282] V Fock Zur Theorie der Wasserstoffatoms Zs f Physik 98 145ndash54 (1936)[283] M Fornasier H Rauhut Continuous frames function spaces and the discretization
problem J Fourier Anal Appl 11 245ndash287 (2005)
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[284] W Freeden M Schreiner Orthogonal and non-orthogonal multiresolution analysis scalediscrete and exact fully discrete wavelet transform on the sphere Constr Approx 14 493ndash515 (1997)
[285] W Freeden U Windheuser Combined spherical harmonic and wavelet expansion mdash Afuture concept in Earthrsquos gravitational determination Appl Comput Harmon Anal 4 1ndash37 (1997)
[286] W Freeden T Maier S Zimmermann A survey on wavelet methods for (geo)applicationsRevista Mathematica Complutense 16 (2003) 277ndash310
[287] W Freeden M Schreiner Biorthogonal locally supported wavelets on the sphere based onzonal kernel functions J Fourier Anal Appl 13 693ndash709 (2007)
[288] WT Freeman EH Adelson The design and use of steerable filters IEEE Trans PatternAnal Machine Intell 13 891ndash906 (1991)
[289] L Freidel ER Livine U(N) coherent states for loop quantum gravity J Math Phys 52052502 (2011)
[290] J Froment S Mallat Arbitrary low bit rate image compression using wavelets in Progressin Wavelet Analysis and Applications (Proc Toulouse 1992) ed by Y Meyer S Roques(Ed Frontiegraveres Gif-sur-Yvette 1993) pp 413ndash418 and references therein
[291] L Freidel S Speziale Twisted geometries A geometric parameterisation of SU(2) phasespace Phys Rev D 82 084040 (2010)
[292] H Fuumlhr Wavelet frames and admissibility in higher dimensions J Math Phys 37 6353ndash6366 (1996)
[293] H Fuumlhr M Mayer Continuous wavelet transforms from semidirect products Cyclicrepresentations and Plancherel measure J Fourier Anal Appl 8 375ndash396 (2002)
[294] D Gabor Theory of communication J Inst Electr Engrg(London) 93 429ndash457 (1946)[295] J-P Gabardo D Han Frames associated with measurable spaces Adv Comput Math 18
127ndash147 (2003)[296] E Galapon Paulirsquos theorem and quantum canonical pairs The consistency of a bounded
self-adjoint time operator canonically conjugate to a Hamiltonian with non-empty pointspectrum Proc R Soc Lond A 458 451ndash472 (2002)
[297] PL Garciacutea de Leacuteon J-P Gazeau Coherent state quantization and phase operator PhysLett A 361 301ndash304 (2007)
[298] L Garciacutea de Leoacuten J-P Gazeau J Queacuteva The infinite well revisited Coherent states andquantization Phys Lett A 372 3597ndash3607 (2008)
[299] T Garidi J-P Gazeau E Huguet M Lachiegraveze Rey J Renaud Fuzzy spheres frominequivalent coherent states quantization J Phys A Math Theor 40 10225ndash10249 (2007)
[300] J-P Gazeau Four Euclidean conformal group in atomic calculations Exact analyticalexpressions for the bound-bound two-photon transition matrix elements in the H atomJ Math Phys 19 1041ndash1048 (1978)
[301] J-P Gazeau On the four Euclidean conformal group structure of the sturmian operatorLett Math Phys 3 285ndash292 (1979)
[302] J-P Gazeau Technique Sturmienne pour le spectre discret de lrsquoeacutequation de SchroumldingerJ Phys A Math Gen 13 3605ndash3617 (1980)
[303] J-P Gazeau Four Euclidean conformal group approach to the multiphoton processes in theH atom J Math Phys 23 156ndash164 (1982)
[304] J-P Gazeau A remarkable duality in one particle quantum mechanics between someconfining potentials and (R+Linfin
ε ) potentials Phys Lett 75A 159ndash163 (1980)[305] J-P Gazeau SL(2R)-coherent states and integrable systems in classical and quantum
physics in Quantization Coherent States and Complex Structures ed by J-P AntoineST Ali W Lisiecki IM Mladenov A Odzijewicz (Plenum Press New York and London1995) pp 147ndash158
[306] J-P Gazeau S Graffi Quantum harmonic oscillator A relativistic and statistical point ofview Boll Unione Mat Ital 11-A 815ndash839 (1997)
[307] J-P Gazeau V Hussin Poincareacute contraction of SU(11) Fock-Bargmann structure J PhysA Math Gen 25 1549ndash1573 (1992)
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[309] J-P Gazeau JR Klauder Coherent states for systems with discrete and continuousspectrum J Phys A Math Gen 32 123ndash132 (1999)
[310] J-P Gazeau P Monceau Generalized coherent states for arbitrary quantum systems inColloquium M Flato (Dijon Sept 99) vol II (Kluumlwer Dordrecht 2000) pp 131ndash144
[311] J-P Gazeau M Novello The question of mass in (Anti-) de Sitter space-times J Phys AMath Theor 41 304008 (2008)
[312] J-P Gazeau M del Olmo q-coherent states quantization of the harmonic oscillator AnnPhys (NY) 330 220ndash245 (2013) arXiv12071200 [quant-ph]
[313] J-P Gazeau J Patera Tau-wavelets of Haar J Phys A Math Gen 29 4549ndash4559 (1996)[314] J-P Gazeau W Piechocki Coherent states quantization of a particle in de Sitter space
J Phys A Math Gen 37 6977ndash6986 (2004)[315] J-P Gazeau J Renaud Lie algorithm for an interacting SU(11) elementary system and its
contraction Ann Phys (NY) 222 89ndash121 (1993)[316] J-P Gazeau J Renaud Relativistic harmonic oscillator and space curvature Phys Lett A
179 67ndash71 (1993)[317] J-P Gazeau V Spiridonov Toward discrete wavelets with irrational scaling factor J Math
plane J Phys A Math Theor 44 495201 (2011)[319] J-P Gazeau J Patera E Pelantovaacute Tau-wavelets in the plane J Math Phys 39 4201ndash
4212 (1998)[320] J-P Gazeau M Andrle C Burdiacutek R Krejcar Wavelet multiresolutions for the Fibonacci
chain J Phys A Math Gen 33 L47ndashL51 (2000)[321] J-P Gazeau M Andrle C Burdiacutek Bernuau spline wavelets and sturmian sequences
J Fourier Anal Appl 10 269ndash300 (2004)[322] J-P Gazeau F-X Josse-Michaux P Monceau Finite dimensional quantizations of the
(q p) plane new space and momentum inequalities Int J Modern Phys B 20 1778ndash1791 (2006)
[323] J-P Gazeau J Mourad J Queacuteva Fuzzy de Sitter space-times via coherent statesquantization in Proceedings of the XXVIth Colloquium on Group Theoretical Methodsin Physics New York 2006 ed by J Birman S Catto B Nicolescu (Canopus PublishingLimited London 2009)
[324] D Geller A Mayeli Continuous wavelets on compact manifolds Math Z 262 895ndash927(2009)
[325] D Geller A Mayeli Nearly tight frames and space-frequency analysis on compactmanifolds Math Z 263 235ndash264 (2009)
[326] L Genovese B Videau M Ospici Th Deutsch S Goedecker J-F Mhaut Daubechieswavelets for high performance electronic structure calculations The BigDFT project CR Mecanique 339 149ndash164 (2011)
[327] G Gentili C Stoppato Power series and analyticity over the quaternions Math Ann 352113ndash131 (2012)
[328] G Gentili DC Struppa A new theory of regular functions of a quaternionic variable AdvMath 216 279ndash301 (2007)
[329] C Geyer K Daniilidis Catadioptric projective geometry Int J Comput Vision 45 223ndash243 (2001)
[330] R Gilmore Geometry of symmetrized states Ann Phys (NY) 74 391ndash463 (1972)[331] R Gilmore On properties of coherent states Rev Mex Fis 23 143ndash187 (1974)[332] J Ginibre Statistical ensembles of complex quaternion and real matrices J Math Phys
6 440ndash449 (1965)[333] RJ Glauber The quantum theory of optical coherence Phys Rev 130 2529ndash2539 (1963)
560 References
[334] RJ Glauber Coherent and incoherent states of radiation field Phys Rev 131 2766ndash2788(1963)
[335] J Glimm Locally compact transformation groups Trans Amer Math Soc 101 124ndash138(1961)
[336] R Godement Sur les relations drsquoorthogonaliteacute de V Bargmann C R Acad Sci Paris 255521ndash523 657ndash659 (1947)
[337] C Gonnet B Torreacutesani Local frequency analysis with two-dimensional wavelet trans-form Signal Proc 37 389ndash404 (1994)
[338] JA Gonzalez MA del Olmo Coherent states on the circle J Phys A Math Gen 318841ndash8857 (1998)
[339] XGonze B Amadon et al ABINIT First-principles approach to material and nanosystemproperties Computer Physics Comm 180 2582ndash2615 (2009)
[340] KM Gograverski E Hivon AJ Banday BD Wandelt FK Hansen M Reinecke MBartelmann HEALPix A framework for high-resolution discretization and fast analysisof data distributed on the sphere Astrophys J 622 759ndash771 (2005)
[341] P Goupillaud A Grossmann J Morlet Cycle-octave and related transforms in seismicsignal analysis Geoexploration 23 85ndash102 (1984)
[342] KH Groumlchenig A new approach to irregular sampling of band-limited functions in RecentAdvances in Fourier Analysis and Its applications ed by JS Byrnes JL Byrnes (KluwerDordrecht 1990) pp 251ndash260
[343] KH Groumlchenig Gabor analysis over LCA groups in Gabor Analysis and Algorithms ndashTheory and Applications ed by HG Feichtinger T Strohmer (Birkhaumluser Boston-Basel-Berlin 1998) pp 211ndash231
[344] HJ Groenewold On the principles of elementary quantum mechanics Physica 12 405ndash460 (1946)
[345] P Grohs Continuous shearlet tight frames J Fourier Anal Appl 17 506ndash518 (2011)[346] P Grohs G Kutyniok Parabolic molecules preprint TU Berlin (2012)[347] M Grosser A note on distribution spaces on manifolds Novi Sad J Math 38 121ndash128
(2008)[348] A Grossmann Parity operator and quantization of δ -functions Commun Math Phys 48
191ndash194 (1976)[349] A Grossmann J Morlet Decomposition of Hardy functions into square integrable
wavelets of constant shape SIAM J Math Anal 15 723ndash736 (1984)[350] A Grossmann J Morlet Decomposition of functions into wavelets of constant shape and
related transforms in Mathematics + Physics Lectures on recent results I ed by L Streit(World Scientific Singapore 1985) pp 135ndash166
[351] A Grossmann J Morlet T Paul Integral transforms associated to square integrablerepresentations I General results J Math Phys 26 2473ndash2479 (1985)
[352] A Grossmann J Morlet T Paul Integral transforms associated to square integrablerepresentations II Examples Ann Inst H Poincareacute 45 293ndash309 (1986)
[353] A Grossmann R Kronland-Martinet J Morlet Reading and understanding the contin-uous wavelet transform in Wavelets Time-Frequency Methods and Phase Space (ProcMarseille 1987) ed by J-M Combes A Grossmann P Tchamitchian 2nd edn (SpringerBerlin 1990) pp 2ndash20
[354] P Guillemain R Kronland-Martinet B Martens Estimation of spectral lines with helpof the wavelet transform Application in NMR spectroscopy in Wavelets and Applications(Proc Marseille 1989) ed by Y Meyer (Masson and Springer Paris and Berlin 1991) pp38ndash60
[355] H de Guise M Bertola Coherent state realizations of su(n+ 1) on the n-torus J MathPhys 43 3425ndash3444 (2002)
[356] K Guo D Labate Representation of Fourier Integral Operators using shearlets J FourierAnal Appl 14 327ndash371 (2008)
References 561
[357] K Guo G Kutyniok D Labate Sparse multidimensional representations usinganisotropic dilation and shear operators in Wavelets and Spines (Athens GA 2005)(Nashboro Press Nashville TN 2006) pp 189ndash201
[358] K Guo D Labate W-Q Lim G Weiss E Wilson Wavelets with composite dilationsand their MRA properties Appl Comput Harmon Anal 20 202ndash236 (2006)
[359] EA Gutkin Overcomplete subspace systems and operator symbols Funct Anal Appl 9260ndash261 (1975)
[360] G Gyoumlrgyi Integration of the dynamical symmetry groups for the 1r potential Acta PhysAcad Sci Hung 27 435ndash439 (1969)
[361] BC Hall The Segal-Bargmann ldquoCoherent Staterdquo transform for compact Lie groups JFunct Analysis 122 103ndash151 (1994)
[362] B Hall JJ Mitchell Coherent states on spheres J Math Phys 43 1211ndash1236 (2002)[363] DK Hammond P Vandergheynst R Gribonval Wavelets on graphs via spectral theory
Appl Comput Harmon Anal 30 129ndash150 (2011)[364] Y Hassouni EMF Curado MA Rego-Monteiro Construction of coherent states for
physical algebraic system Phys Rev A 71 022104 (2005)[365] J He H Liu Admissible wavelets associated with the affine automorphism group of the
Siegel upper half-plane J Math Anal Appl 208 58ndash70 (1997)[366] J He H Liu Admissible wavelets associated with the classical domain of type one
Approx Appl 14 (1998) 89ndash105[367] J He L Peng Wavelet transform on the symmetric matrix space preprint Beijing (1997)
(unpublished)[368] J He L Peng Admissible wavelets on the unit disk Complex Variables 35 109ndash119
(1998)[369] DM Healy Jr FE Schroeck Jr On informational completeness of covariant localization
observables and Wigner coefficients J Math Phys 36 453ndash507 (1995)[370] C Heil D Walnut Continuous and discrete wavelet transforms SIAM Review 31 628ndash
666 (1989)[371] K Hepp EH Lieb On the superradiant phase transition for molecules in a quantized
radiation field The Dicke maser model Ann Phys (NY) 76 360ndash404 (1973)[372] K Hepp EH Lieb Equilibrium statistical mechanics of matter interacting with the
quantized radiation field Phys Rev A 8 2517ndash2525 (1973)[373] JA Hogan JD Lakey Extensions of the Heisenberg group by dilations and frames Appl
Comput Harmon Anal 2 174ndash199 (1995)[374] AL Hohoueacuteto K Thirulogasanthar ST Ali J-P Antoine Coherent states lattices and
square integrability of representations J Phys A Math Gen36 11817ndash11835 (2003)[375] M Holschneider On the wavelet transformation of fractal objects J Stat Phys 50 963ndash
993 (1988)[376] M Holschneider Wavelet analysis on the circle J Math Phys 31 39ndash44 (1990)[377] M Holschneider Inverse Radon transforms through inverse wavelet transforms Inv Probl
7 853ndash861 (1991)[378] M Holschneider Localization properties of wavelet transforms J Math Phys 34 3227ndash
3244 (1993)[379] M Holschneider General inversion formulas for wavelet transforms J Math Phys 34
4190ndash4198 (1993)[380] M Holschneider Wavelet analysis over abelian groups Applied Comput Harmon Anal
2 52ndash60 (1995)[381] M Holschneider Continuous wavelet transforms on the sphere J Math Phys 37 4156ndash
4165 (1996)[382] M Holschneider I Iglewska-Nowak Poisson wavelets on the sphere J Fourier Anal
Appl 13 405ndash419 (2007)
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[383] M Holschneider R Kronland-Martinet J Morlet P Tchamitchian A real-time algorithmfor signal analysis with the help of wavelet transform in Wavelets Time-FrequencyMethods and Phase Space (Proc Marseille 1987) ed by J-M Combes A Grossmann PTchamitchian 2nd edn (Springer Berlin 1990) pp 286ndash297
[384] M Holschneider P Tchamitchian Pointwise analysis of Riemannrsquos ldquonondifferentiablerdquofunction Invent Math 105 157ndash175 (1991)
[385] GR Honarasa MK Tavassoly M Hatami R Roknizadeh Nonclassical properties ofcoherent states and excited coherent states for continuous spectra J Phys A Math Theor44 085303 (2011)
[386] M Hongoh Coherent states associated with the continuous spectrum of noncompactgroups J Math Phys 18 2081ndash2085 (1977)
[387] A Horzela FH Szafraniec A measure free approach to coherent states J Phys A MathGen 45 244018 (2012)
[388] W-L Hwang S Mallat Characterization of self-similar multifractals with waveletmaxima Appl Comput Harmon Anal 1 316ndash328 (1994)
[389] W-L Hwang C-S Lu P-C Chung Shape from texture Estimation of planar surfaceorientation through the ridge surfaces of continuous wavelet transform IEEE Trans ImageProc 7 773ndash780 (1998)
[390] I Iglewska-Nowak M Holschneider Frames of Poisson wavelets on the sphere ApplComput Harmon Anal 28 227ndash248 (2010)
[391] E Inoumlnuuml EP Wigner On the contraction of groups and their representations Proc NatAcad Sci U S 39 510ndash524 (1953)
[392] S Iqbal F Saif Generalized coherent states and their statistical characteristics in power-law potentials J Math Phys 52 082105 (2011)
[393] CJ Isham JR Klauder Coherent states for n-dimensional Euclidean groups E(n) andtheir application J MathPhys 32 607ndash620 (1991)
[394] L Jacques J-P Antoine Multiselective pyramidal decomposition of images Wavelets withadaptive angular selectivity Int J Wavelets Multires Inform Proc 5 785ndash814 (2007)
[395] L Jacques L Duval C Chaux G Peyreacute A panorama on multiscale geometric rep-resentations intertwining spatial directional and frequency selectivity Signal Proc 912699ndash2730 (2011)
[396] HR Jalali M K Tavassoly On the ladder operators and nonclassicality of generalizedcoherent state associated with a particle in an infinite square well preprint (2013)arXiv13034100v1 [quant-ph]
[397] C Johnston On the pseudo-dilation representations of Flornes Grossmann Holschneiderand Torreacutesani Appl Comput Harmon Anal 3 377ndash385 (1997)
[398] G Kaiser Phase-space approach to relativistic quantum mechanics I Coherent staterepresentation for massive scalar particles J MathPhys 18 952ndash959 (1977)
[399] G Kaiser Phase-space approach to relativistic quantum mechanics II Geometrical aspectsJ MathPhys 19 502ndash507 (1978)
[400] C Kalisa B Torreacutesani N-dimensional affine Weyl-Heisenberg wavelets Ann Inst HPoincareacute 59 201ndash236 (1993)
[401] W Kaminski J Lewandowski T Pawłowski Quantum constraints Dirac observables andevolution group averaging versus the Schroumldinger picture in LQC Class Quant Grav 26245016 (2009)
[402] MR Karim ST Ali A relativistic windowed Fourier transform preprint ConcordiaUniversity Montreacuteal (1997) (unpublished)
[403] M R Karim ST Ali M Bodruzzaman A relativistic windowed Fourier transform inProceedings of IEEE SoutheastCon 2000 Nashville Tennessee pp 253ndash260 (2000)
[404] T Kawazoe Wavelet transforms associated to a principal series representation of semisim-ple Lie groups I II Proc Japan Acad Ser A ndash Math Sci 71 154ndash157 158ndash160 (1995)
[405] T Kawazoe Wavelet transform associated to an induced representation of SL(n+ 2R)Ann Inst H Poincareacute 65 1ndash13 (1996)
References 563
[406] P Kittipoom G Kutyniok W-Q Lim Irregular shearlet frames Geometry and approxi-mation properties J Fourier Anal Appl 17 604ndash639 (2011)
[407] P Kittipoom G Kutyniok W-Q Lim Construction of compactly supported shearletframes Constr Approx 35 21ndash72 (2012)
[408] J Kiukas P Lahti K Ylinenc Phase space quantization and the operator moment problemJ Math Phys 47 072104 (2006)
[409] JR Klauder Continuous-representation theory I Postulates of continuous-representationtheory J Math Phys 4 1055ndash1058 (1963)
[410] JR Klauder Continuous-representation theory II Generalized relation between quantumand classical dynamics J Math Phys 4 1058ndash1073 (1963)
[411] JR Klauder Path integrals for affine variables in Functional Integration Theory andApplications ed by J-P Antoine E Tirapegui (Plenum Press New York and London1980) pp 101ndash119
[412] JR Klauder Are coherent states the natural language of quantum mechanics inFundamental Aspects of Quantum Theory ed by V Gorini A Frigerio NATO ASI Seriesvol B 144 (Plenum Press New York 1986) pp 1ndash12
[413] JR Klauder Quantization without quantization Ann Phys (NY) 237 147ndash160 (1995)[414] JR Klauder Coherent states for the hydrogen atom J Phys A Math Gen 29 L293ndash
L296 (1996)[415] JR Klauder An affinity for affine quantum gravity Proc Steklov Inst Math 272 169ndash176
(2011) and references therein[416] JR Klauder RF Streater A wavelet transform for the Poincareacute group J Math Phys 32
1609ndash1611 (1991)[417] JR Klauder RF Streater Wavelets and the Poincareacute half-plane J Math Phys 35 471ndash
478 (1994)[418] JR Klauder K Penson J-M Sixdeniers Constructing coherent states through solutions
of Stieltjes and Hausdorff moment problems Phys Rev A 64 013817 (2001)[419] A Kleppner RL Lipsman The Plancherel formula for group extensions Ann Ec Norm
Sup 5 459ndash516 (1972)[420] AB Klimov C Muntildeoz Coherent isotropic and squeezed states in a N-qubit system Phys
Scr 87 038110 (2013)[421] A Klyashko Dynamical symmetry approach to entanglement in Physics and Theoretical
Computer Science From Numbers and Languages to (Quantum) Cryptography - NATOSecurity through Science Series D - Information and Communication Security vol 7 edby J-P Gazeau J Nesetril B Rovan (IOS Press Washington DC 2007) pp 25ndash54
[422] S Kobayashi Irreducibility of certain unitary representations J Math Soc Japan 20 638ndash642 (1968)
[423] K Kowalski J Rembielinski LC Papaloucas Coherent states for a quantum particle ona circle J Phys A Math Gen 29 4149ndash4167 (1996)
[424] K Kowalski J Rembielinski Quantum mechanics on a sphere and coherent states J PhysA Math Gen 33 6035ndash6048 (2000)
[425] K Kowalski J Rembielinski The Bargmann representation for the quantum mechanicson a sphere J Math Phys 42 4138ndash4147 (2001)
[426] C Kristjansen J Plefka GW Semenoff M Staudacher A new double-scaling limit ofN = 4 super-Yang-Mills theory and pp-wave strings Nuclear Phys B 643 3ndash30 (2002)
[427] M Kulesh M Holschneider MS Diallo Geophysical wavelet library Applications ofthe continuous wavelet transform to the polarization and dispersion analysis of signalsComput Geosci 34 1732ndash1752 (2008)
[428] R Kunze On the Frobenius reciprocity theorem for square integrable representationsPacific J Math 53 465ndash471 (1974)
[429] Y Kuroda A Wada T Yamazaki K Nagayama Postacquisition data processing methodfor suppression of the solvent signal I J Magn Reson 84 604ndash610 (1989)
564 References
[430] Y Kuroda A Wada T Yamazaki K Nagayama Postacquisition data processing methodfor suppression of the solvent signal II The weighted first derivative J Magn Reson 88141ndash145 (1990)
[431] G Kutyniok D Labate Resolution of the wavefront set using continuous shearlets TransAmer Math Soc 361 2719ndash2754 (2009)
[432] G Kutyniok W-Q Lim Compactly supported shearlets are optimally sparse J ApproxTheory 163 1564ndash1589 (2011)
[433] D Labate W-Q Lim G Kutyniok G Weiss Sparse multidimensional representationusing shearlets in Wavelets XI (San Diego CA 2005) ed by M Papadakis A Laine MUnser SPIE Proceedings vol 5914 (SPIE Bellingham WA 2005) pp 254ndash262
[434] P Lahti J-P Pellonpaumlauml Continuous variable tomographic measurements Phys Lett A373 3435ndash3438 (2009)
[435] Lambertrsquos projection see WikipediahttpenwikipediaorgwikiLambert_azimuthal_equal-area_projection
[436] J-P Leduc F Mujica R Murenzi MJT Smith Missile-tracking algorithm using target-adapted spatio-temporal wavelets in Automatic Object Recognition VII SPIE Proceedingsvol 5914 (SPIE Bellingham WA 1997) pp 400ndash411
[437] J-P Leduc F Mujica R Murenzi MJT Smith Spatio-temporal wavelet transforms formotion tracking in IEEE ICASSP 1997 vol 4 (1997) pp 3013ndash3016
[438] J-P Leduc F Mujica R Murenzi MJT Smith Spatio-temporal continuous waveletsapplied to missile warhead detection and tracking in SPIE VCIP rsquo97 vol 3024 ed byJ Biemond EJ Delp (1997) pp 787ndash798
[439] B Leistedt JD McEwen Exact wavelets on the ball IEEE Trans Signal Proc 60 1564ndash1589 (2012)
[440] PG Lemarieacute Y Meyer Ondelettes et bases hilbertiennes Rev Math Iberoamer 2 1ndash18(1986)
[441] C Lemke A Schuck Jr J-P Antoine D Sima Metabolite-sensitive analysis of magneticresonance spectroscopic signals using the continuous wavelet transform Meas SciTechnol 22 (2011) Art 114013
[442] J-M Leacutevy-Leblond Galilei group and non-relativistic quantum mechanics J Math Phys4 776-788 (1963)
[443] J-M Leacutevy-Leblond Galilei group and Galilean invariance in Group Theory and ItsApplications vol II ed by EM Loebl (Academic New York 1971) pp 221ndash299
[444] J-M Leacutevy-Leblond On the conceptual nature of the physical constants Riv Nuovo Cim7 187ndash214 (1977)
[445] EH Lieb The classical limit of quantum spin systems Commun Math Phys 31 327ndash340(1973)
[446] G Lindblad B Nagel Continuous bases for unitary irreducible representations of SU(11)Ann Inst H Poincareacute 13 27ndash56 (1970)
[447] W Lisiecki Kaumlhler coherent states orbits for representations of semisimple Lie groupsAnn Inst H Poincareacute 53 857ndash890 (1990)
[448] A Lisowska Moment-based fast wedgelet transform J Math Imaging Vis 39 180ndash192(2011)
[449] H Liu L Peng Admissible wavelets associated with the Heisenberg group Pacific JMath 180 101ndash123 (1997)
[450] E Livine S Speziale Physical boundary state for the quantum tetrahedron Class QuantGrav 25 085003 (2008)
[451] F Low Complete sets of wave packets in A Passion for Physics ndash Essay in Honor ofGeoffrey Chew ed by C DeTar (World Scientific Singapore 1985) pp 17ndash22
[452] G Mack All unitary ray representations of the conformal group SU(22) with positiveenergy Commun Math Phys 55 1ndash28 (1977)
[453] GW Mackey Imprimitivity for representations of locally compact groups I Proc NatAcad Sci 35 537ndash545 (1949)
References 565
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[455] M Mallalieu CR Stroud Jr Rydberg wave packets fractional revivals and classicalorbits in Coherent States Past Present and Future (Proc Oak Ridge 1993) ed by DHFeng JR Klauder M Strayer (World Scientific Singapore 1994) pp 301ndash314
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[457] SG Mallat A theory for multiresolution signal decomposition The wavelet representa-tion IEEE Trans Pattern Anal Machine Intell 11 674ndash693 (1989)
[458] S Mallat W-L Hwang Singularity detection and processing with wavelets IEEE TransInform Theory 38 617ndash643 (1992)
[459] S Mallat Z Zhang Matching pursuits with time frequency dictionaries IEEE TransSignal Proc 41 3397ndash3415 (1993)
[460] S Mallat S Zhong Wavelet maxima representation in Wavelets and Applications (ProcMarseille 1989) ed by Y Meyer (Masson and Springer Paris and Berlin 1991) pp 207ndash284
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[465] Y Meyer Principe drsquoincertitude bases hilbertiennes et algegravebres drsquoopeacuterateurs Asteacuterisque145ndash146 209ndash223 (1987)
[466] Y Meyer H Xu Wavelet analysis and chirps Appl Comput Harmon Anal 4 366ndash379(1997)
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[471] MI Monastyrsky AM Perelomov Coherent states and symmetric spaces II Ann InstH Poincareacute 23 23ndash48 (1975)
[472] B Moran S Howard D Cochran Positive-operator-valued measures A general settingfor frames in Excursions in Harmonic Analysis vol 1 2 ed by TD Andrews R BalanJJ Benedetto W Czaja KA Okoudjou (Birkhaumluser Boston 2013) pp 49ndash64
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[474] H Moscovici A Verona Coherent states and square integrable representations Ann InstH Poincareacute 29 139ndash156 (1978)
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[479] MA Naımark Dokl Akad Nauk SSSR 41 359ndash361 (1943) see also B Sz-NagyExtensions of linear transformations in Hilbert space which extend beyond this spaceAppendix to F Riesz B Sz-Nagy Functional Analysis (Frederick Ungar New York 1960)
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[483] H Neumann Transformation properties of observables Helv Phys Acta 45 811ndash819(1972)
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[537] D Rosca G Plonka Uniform spherical grids via area preserving projection from the cubeto the sphere J Comput Appl Math 236 1033ndash1041 (2011)
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[540] DJ Rotenberg Application of Sturmian functions to the Schroedinger three-body prob-lem Elastic e+ndashH scattering Ann Phys (NY) 19 262ndash278 (1962)
[541] C Rovelli Zakopane lectures on loop gravity in Proceedings of 3rd Quantum Gravityand Quantum Geometry School 28 Febndash13 March 2011 (Zakopane Poland 2011)arXiv11023660v5
[542] C Rovelli S Speziale A semiclassical tetrahedron Class Quant Grav 23 5861ndash5870(2006)
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[546] DJ Rowe J Repka Vector-coherent-state theory as a theory of induced representationsJ Math Phys 32 2614ndash2634 (1991)
[547] DJ Rowe G Rosensteel R Gilmore Vector coherent state representation theory J MathPhys 26 2787ndash2791 (1985)
[548] A Royer Phase states and phase operators for the quantum harmonic oscillator Phys RevA 53 70ndash108 (1996)
[549] J Saletan Contraction of Lie groups J Math Phys 2 1ndash21 (1961)[550] G Saracco A Grossmann P Tchamitchian Use of wavelet transforms in the study of
propagation of transient acoustic signals across a plane interface between two homoge-neous media in Wavelets Time-Frequency Methods and Phase Space (Proc Marseille1987) ed by J-M Combes A Grossmann P Tchamitchian 2nd edn (Springer Berlin1990) pp 139ndash146
[551] P Schroumlder W Sweldens Spherical wavelets Efficiently representing functions on thesphere in Computer Graphics Proceedings (SIGGRAPH95) (ACM Siggraph Los Angeles1995) pp 161ndash175
References 569
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[554] H Scutaru Coherent states and induced representations Lett Math Phys 2 101ndash107(1977)
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Math 137 82ndash203 (1998)[557] R Simon ECG Sudarshan N Mukunda Gaussian pure states in quantum mechanics
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R61ndashR75 (2000)[559] E Slezak A Bijaoui G Mars Identification of structures from galaxy counts Use of the
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Geometric Methods in Physics XXXI Workshop 2012 (Trends in Mathematics ed byP Kielanowski et al Birkhaumluser Verlag Basel 2013) pp 47ndash63
[562] SB Sontz Paragrassmann algebras as quantum spaces Part II Toeplitz operators J OperTh (2013 to appear) arXiv12055493
[563] SB Sontz A reproducing kernel and Toeplitz operators in the quantum plane Preprint(2013) arXiv13056986 [math-ph]
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[573] W Sweldens The lifting scheme A construction of second generation wavelets SIAM JMath Anal 29 511ndash546 (1998)
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[575] FH Szafraniec Multipliers in the reproducing kernel Hilbert space subnormality andnoncommutative complex analysis in Reproducing Kernel Spaces and Applications edby D Alpay Operator Theory Advances and Applications vol 143 (Birkhaumluser Basel2003) pp 313ndash331
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[579] T Thiemann Gauge field theory coherent states (GCS) 1 General properties Class QuantGrav 18 2025ndash2064 (2001)
[580] T Thiemann O Winkler Gauge field theory coherent states (GCS) 2 Peakednessproperties Class Quant Grav 18 2561ndash2636 (2001)
[581] T Thiemann O Winkler Gauge field theory coherent states (GCS) 3 Ehrenfest theoremsClass Quant Grav 18 4629ndash4682 (2001)
[582] T Thiemann O Winkler Gauge field theory coherent states (GCS) 4 Infinite tensorproduct and thermodynamical limit Class Quant Grav 18 4997ndash5054 (2001)
[583] K Thirulagasanthar ST Ali Regular subspaces of a quaternionic Hilbert space fromquaternionic Hermite polynomials and associated coherent states J Math Phys 54013506 (2013)
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(1994)[590] AS Trushechkin IV Volovich Localization properties of squeezed quantum states in
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algorithms IEEE Trans Image Proc 11 363ndash372 (2002)[593] P Vandergheynst J-P Antoine E Van Vyve A Goldberg I Doghri Modelling and
simulation of an impact test using wavelets analytical and finite element models Int JSolids Struct 38 5481ndash5508 (2001)
[594] L Vanhamme RD Fierro S Van Huffel R de Beer Fast removal of residual water inproton spectra J Magn Reson 132 197ndash203 (1998)
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[596] J Voisin On some unitary representations of the Galilei group I Irreducible representa-tions J Math Phys 6 1519ndash1529 (1965)
[597] A Vourdas Analytic representations in quantum mechanics J Phys A Math Gen 39R65ndashR141 (2006)
[598] DF Walls Squeezed states of light Nature 306 141ndash146 (1983)[599] YK Wang FT Hioe Phase transition in the Dicke maser model Phys Rev A 7 831ndash836
(1973)[600] PSP Wang J Yang A review of wavelet-based edge detection methods Int J Patt
Recogn Artif Intell 26 1255011 (2012)[601] I Weinreich A construction of C1-wavelets on the two-dimensional sphere Appl Comput
Harmon Anal 10 1ndash26 (2001)[602] H Weyl Quantenmechanik und Gruppentheorie Z Phys 46 1ndash46 (1927)
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[606] WM Wieland Complex Ashtekar variables and reality conditions for Holstrsquos action AnnHenri Poincareacute 13 425ndash448 (2012)
[607] EP Wigner On the quantum correction for thermodynamic equilibrium Phys Rev 40749ndash759 (1932)
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[609] W Wisnoe P Gajan A Strzelecki C Lempereur J-M Matheacute The use of the two-dimensional wavelet transform in flow visualization processing in Progress in WaveletAnalysis and Applications (Proc Toulouse 1992) ed by Y Meyer S Roques (EdFrontiegraveres Gif-sur-Yvette 1993) pp 455ndash458
[610] K Woacutedkiewicz On the quantum mechanics of squeezed states J Modern Optics 34 941ndash948(1987)
[611] JA Yeazell M Mallalieu CR Stroud Jr Observation of the collapse and revival of aRydberg electronic wave packet Phys Rev Lett 64 2007ndash2010 (1990)
[612] JA Yeazell CR Stroud Jr Observation of fractional revivals in the evolution of aRydberg atomic wave packet Phys Rev A 43 5153ndash5156 (1991)
[613] HP Yuen Two-photon coherent states of the radiation field Phys Rev A 13 2226ndash2243(1976)
[614] J Zak Balian-Low theorem for Landau levels Phys Rev Lett 79 533ndash536 (1997)[615] J Zak Orthonormal sets of localized functions for a Landau level J Math Phys 39 4195ndash
4200 (1998) and references quoted there[616] AA Zakharova On the properties of generalized frames Math Notes 83 190ndash200 (2008)[617] W-M Zhang DH Feng R Gilmore Coherent states Theory and some applications Rev
Mod Phys 26 867ndash927 (1990)[618] I Zlatev W-M Zhang DH Feng Possibility that Schroumldingerrsquos conjecture for the
hydrogen atom coherent states is not attainable Phys Rev A 50 R1973ndashR1975 (1994)[619] WH Zurek Decoherence einselection and the quantum origins of the classical Rev Mod
Phys 75 715ndash775 (2003)[620] WH Zurek S Habib JP Paz Coherent states via decoherence Phys Rev Lett 70 1187ndash
1190 (1993)[621] K Zyczkowski Squeezed states in a quantum chaotic system J Phys A Math Theor 22
of SU(11) 81 296 297HilbertClowast-modules 164holomorphic 140nonholomorphic 151nonlinear 146of affine Galilei group 505of affine Poincareacute group 509of affine Weyl-Heisenberg group GaWH
497of compact semisimple Lie groups 174of Euclidean group E(n) 266of Galilei group G (11) 290of isochronous Galilei group 237of non-semisimple Lie groups 179of noncompact semisimple Lie groups 177of Poincareacute group Puarr
+(11) 283massless case 288
of Poincareacute group Puarr+(13) 279
of Schroumldinger group 508quasi-coherent states 186quaternionic 164
ST Ali et al Coherent States Wavelets and Their Generalizations Theoreticaland Mathematical Physics DOI 101007978-1-4614-8535-3copy Springer Science+Business Media New York 2014
573
574 Index
coherent states (CS) (cont)spin or SU(2) 175square integrable covariant 166 180 264vector (VCS) 73 108 112 170weighted 184 523
of affine Weyl-Heisenberg group GaWH497
of Poincareacute group Puarr+(11) 284
cohomology group 393 403coboundaries 403cochains 402cocycle 403
algebraic 387Cauchy 418Cauchy-Paul 354 419 425conical 418difference 417 462directional 416 440kinematical 499local 488metabolite-based 355 374minimal uncertainty 425multiselective 440on a graph 493on the sphere S
2 458on the sphere S
n 479on the torus T2 481steerable 439von Mises 440
wedgelet transform 455Wigner function 322Wigner-Ville transform 349Windowed Fourier or Gabor transform 349
ZZak transform 518
References
A Books and Theses
B Articles
Index
546 References
[Wis93] W Wisnoe Utilisation de la meacutethode de transformeacutee en ondelettes 2D pour lrsquoanalysede visualisation drsquoeacutecoulements Thegravese de Doctorat ENSAE Toulouse 1993
[Woj97] P Wojtaszczyk A Mathematical Introduction to Wavelets (Cambridge UniversityPress Cambridge 1997)
[Zac06] C Zachos D Fairlie T Curtright Quantum Mechanics in Phase Space An OverviewWith Selected Papers (World Scientific Publishing Singapore 2006)
B Articles
[1] P Abry R Baraniuk P Flandrin R Riedi D Veitch Multiscale nature of network trafficIEEE Signal Process Mag 19 28ndash46 (2002)
[2] MD Adams The JPEG-2000 still image compression standardhttpwwweceuvicca~frodopublicationsjpeg2000pdf
[3] SL Adler AC Millard Coherent states in quaternionic quantum mechanics J MathPhys 38 2117ndash2126 (1997)
[4] GS Agarwal K Tara Nonclassical properties of states generated by the excitation on acoherent state Phys Rev A 43 492ndash497 (1991)
[5] GS Agarwal E Wolf Calculus for functions of noncommuting operators and generalphase-space methods in quantum mechanics I Mapping theorems and ordering of func-tions of noncommuting operators Phys Rev D 2 2161ndash2186 (1970)
[6] GS Agarwal E Wolf Calculus for functions of noncommuting operators and generalphase-space methods in quantum mechanics II Quantum mechanics in phase space PhysRev D 2 2187ndash2205 (1970)
[7] GS Agarwal E Wolf Calculus for functions of noncommuting operators and generalphase-space methods in quantum mechanics III A generalized Wick theorem and multi-time mapping Phys Rev D 2 2206ndash2225 (1970)
[8] V Aldaya J Guerrero G Marmo Quantization on a Lie group Higher-order polariza-tions in Symmetry in Sciences X ed by B Gruber M Ramek (Plenum Press Nerw York1998) pp 1ndash36
[9] M Alexandrescu D Gibert G Hulot J-L Le Mouel G Saracco Worldwide waveletanalysis of geomagnetic jerks J Geophys Res B 101 21975ndash21994 (1996)
[10] G Alexanian A Pinzul A Stern Generalized coherent state approach to star productsand applications to the fuzzy sphere Nucl Phys B 600 531ndash547 (2001)
[11] ST Ali A geometrical property of POV-measures and systems of covariance in Differ-ential Geometric Methods in Mathematical Physics ed by HD Doebner SI AnderssonHR Petry Lecture Notes in Mathematics vol 905 (Springer Berlin 1982) pp 207ndash22
[12] ST Ali Commutative systems of covariance and a generalization of Mackeyrsquos imprimi-tivity theorem Canad Math Bull 27 390ndash397 (1984)
[13] ST Ali Stochastic localisation quantum mechanics on phase space and quantum space-time Riv Nuovo Cim 8(11) 1ndash128 (1985)
[14] ST Ali A general theorem on square-integrability Vector coherent states J Math Phys39 3954ndash3964 (1998)
[15] ST Ali J-P Antoine Coherent states of 1+1 dimensional Poincareacute group Squareintegrability and a relativistic Weyl transform Ann Inst H Poincareacute 51 23ndash44 (1989)
[16] ST Ali S De Biegravevre Coherent states and quantization on homogeneous spaces in GroupTheoretical Methods in Physics ed by H-D Doebner et al Lecture Notes in Mathematicsvol 313 (Springer Berlin 1988) pp 201ndash207
References 547
[17] ST Ali H-D Doebner Ordering problem in quantum mechanics Prime quantization anda physical interpretation Phys Rev A 41 1199ndash1210 (1990)
[18] ST Ali GG Emch Geometric quantization Modular reduction theory and coherentstates J Math Phys 27 2936ndash2943 (1986)
[19] ST Ali M Engliš J-P Gazeau Vector coherent states from Plancherelrsquos theorem andClifford algebras J Phys A 37 6067ndash6089 (2004)
[20] ST Ali MEH Ismail Some orthogonal polynomials arising from coherent states JPhys A 45 125203 (2012) (16pp)
[21] ST Ali UA Mueller Quantization of a classical system on a coadjoint orbit of thePoincareacute group in 1+1 dimensions J Math Phys 35 4405ndash4422 (1994)
[22] ST Ali E Prugovecki Systems of imprimitivity and representations of quantum mechan-ics on fuzzy phase spaces J Math Phys 18 219ndash228 (1977)
[23] ST Ali E Prugovecki Mathematical problems of stochastic quantum mechanics Har-monic analysis on phase space and quantum geometry Acta Appl Math 6 1ndash18 (1986)
[24] ST Ali E Prugovecki Extended harmonic analysis of phase space representation for theGalilei group Acta Appl Math 6 19ndash45 (1986)
[25] ST Ali E Prugovecki Harmonic analysis and systems of covariance for phase spacerepresentation of the Poincareacute group Acta Appl Math 6 47ndash62 (1986)
[26] ST Ali J-P Antoine J-P Gazeau De Sitter to Poincareacute contraction and relativisticcoherent states Ann Inst H Poincareacute 52 83ndash111 (1990)
[27] ST Ali J-P Antoine J-P Gazeau Square integrability of group representations onhomogeneous spaces I Reproducing triples and frames Ann Inst H Poincareacute 55 829ndash855 (1991)
[28] ST Ali J-P Antoine J-P Gazeau Square integrability of group representations onhomogeneous spaces II Coherent and quasi-coherent states The case of the Poincareacutegroup Ann Inst H Poincareacute 55 857ndash890 (1991)
[29] ST Ali J-P Antoine J-P Gazeau Continuous frames in Hilbert space Ann Phys(NY)222 1ndash37 (1993)
[30] ST Ali J-P Antoine J-P Gazeau Relativistic quantum frames Ann Phys(NY) 222 38ndash88 (1993)
[31] ST Ali J-P Antoine J-P Gazeau UA Mueller Coherent states and their generalizationsA mathematical overview Rev Math Phys 7 1013ndash1104 (1995)
[32] ST Ali J-P Gazeau MR Karim Frames the β -duality in Minkowski space and spincoherent states J Phys A Math Gen 29 5529ndash5549 (1996)
[33] ST Ali M Engliš Quantization methods A guide for physicists and analysts Rev MathPhys 17 391ndash490 (2005)
[34] ST Ali J-P Gazeau B Heller Coherent states and Bayesian duality J Phys A MathTheor 41 365302 (2008)
[35] ST Ali L Balkovaacute EMF Curado J-P Gazeau MA Rego-Monteiro LMCSRodrigues K Sekimoto Non-commutative reading of the complex plane through Delonesequences J Math Phys 50 043517 (2009)
[36] ST Ali C Carmeli T Heinosaari A Toigo Commutative POVMS and fuzzy observ-ables Found Phys 39 593ndash612 (2009)
[37] ST Ali T Bhattacharyya SS Roy Coherent states on Hilbert modules J Phys A MathTheor 44 275202 (2011)
[38] ST Ali J-P Antoine F Bagarello J-P Gazeau (Guest Editors) Coherent states Acontemporary panorama preface to a special issue on Coherent states Mathematical andphysical aspects J Phys A Math Gen 45(24) (2012)
[39] ST Ali F Bagarello J-P Gazeau Quantizations from reproducing kernel spaces AnnPhys (NY) 332 127ndash142 (2013)
[40] STAli K Goacuterska A Horzela F Szafraniec Squeezed states and Hermite polynomials ina complex variable Preprint (2013) arXiv13084730v1 [quant-phy]
[41] P Aniello G Cassinelli E De Vito A Levrero Square-integrability of induced represen-tations of semidirect products Rev Math Phys 10 301ndash313 (1998)
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[42] P Aniello G Cassinelli E De Vito A Levrero Wavelet transforms and discrete framesassociated to semidirect products J Math Phys 39 3965ndash3973 (1998)
[43] J-P Antoine Remarques sur le vecteur de Runge-Lenz Ann Soc Scient Bruxelles 80160ndash168 (1966)
[44] J-P Antoine Etude de la deacutegeacuteneacuterescence orbitale du potentiel coulombien en theacuteorie desgroupes I II Ann Soc Scient Bruxelles 80 169ndash184 (1966)
[45] J-P Antoine Etude de la deacutegeacuteneacuterescence orbitale du potentiel coulombien en theacuteorie desgroupes I II Ann Soc Scient Bruxelles 81 49ndash68 (1967)
[46] J-P Antoine Dirac formalism and symmetry problems in quantum mechanics I Generaldirac formalism J Math Phys 10 53ndash69 (1969)
[47] J-P Antoine Dirac formalism and symmetry problems in quantum mechanics II Symme-try problems J Math Phys 10 2276ndash2290 (1969)
[48] J-P Antoine Quantum mechanics beyond Hilbert space in Irreversibility and Causality mdashSemigroups and Rigged Hilbert Spaces ed by A Boumlhm H-D Doebner P KielanowskiLecture Notes in Physics vol 504 (Springer Berlin 1998) pp 3ndash33
[49] J-P Antoine Discrete wavelets on abelian locally compact groups Rev Cien Math(Habana) 19 3ndash21 (2003)
[50] J-P Antoine Introduction to precursors in physics Affine coherent states in FundamentalPapers in Wavelet Theory ed by C Heil D Walnut (Princeton University Press PrincetonNJ 2006) pp 113ndash116
[51] J-P Antoine F Bagarello Wavelet-like orthonormal bases for the lowest Landau levelJ Phys A Math Gen 27 2471ndash2481 (1994)
[52] J-P Antoine P Balazs Frames and semi-frames J Phys A Math Theor 44 205201(2011) (25 pages) Corrigendum J-P Antoine P Balazs Frames and semi-frames J PhysA Math Theor 44 479501 (2011) (2 pages)
[53] J-P Antoine P Balazs Frames semi-frames and Hilbert scales Numer Funct AnalOptim 33 736ndash769 (2012)
[54] J-P Antoine A Coron Time-frequency and time-scale approach to magnetic resonancespectroscopy J Comput Methods Sci Eng (JCMSE) 1 327ndash352 (2001)
[55] J-P Antoine AL Hohoueacuteto Discrete frames of Poincareacute coherent states in 1+3 dimen-sions J Fourier Anal Appl 9 141ndash173 (2003)
[56] J-P Antoine I Mahara Galilean wavelets Coherent states for the affine Galilei groupJ Math Phys 40 5956ndash5971 (1999)
[57] J-P Antoine U Moschella Poincareacute coherent states The two-dimensional massless caseJ Phys A Math Gen 26 591ndash607 (1993)
[58] J-P Antoine R Murenzi Two-dimensional directional wavelets and the scale-anglerepresentation Signal Process 52 259ndash281 (1996)
[59] J-P Antoine R Murenzi Two-dimensional continuous wavelet transform as linear phasespace representation of two-dimensional signals in Wavelet Applications IV SPIE Pro-ceedings vol 3078 (SPIE Bellingham WA 1997) pp 206ndash217
[60] J-P Antoine D Rosca The wavelet transform on the two-sphere and related manifolds mdashA review in Optical and Digital Image Processing SPIE Proceedings vol 7000 (2008)pp 70000B-1ndash15
[61] J-P Antoine D Speiser Characters of irreducible representations of simple Lie groupsJ Math Phys 5 1226ndash1234 (1964)
[62] J-P Antoine P Vandergheynst Wavelets on the n-sphere and related manifolds J MathPhys 39 3987ndash4008 (1998)
[63] J-P Antoine P Vandergheynst Wavelets on the 2-sphere A group-theoretical approachAppl Comput Harmon Anal 7 262ndash291 (1999)
[64] J-P Antoine P Vandergheynst Wavelets on the two-sphere and other conic sections JFourier Anal Appl 13 369ndash386 (2007)
[65] J-P Antoine M Duval-Destin R Murenzi B Piette Image analysis with 2D wavelettransform Detection of position orientation and visual contrast of simple objects inWavelets and Applications (Proc Marseille 1989) ed by Y Meyer (Masson and SpringerParis and Berlin 1991) pp144ndash159
References 549
[66] J-P Antoine P Carrette R Murenzi B Piette Image analysis with 2D continuous wavelettransform Signal Process 31 241ndash272 (1993)
[67] J-P Antoine P Vandergheynst K Bouyoucef R Murenzi Alternative representations ofan image via the 2D wavelet transform Application to character recognition in VisualInformation Processing IV SPIE Proceedings vol 2488 (SPIE Bellingham WA 1995)pp 486ndash497
[68] J-P Antoine R Murenzi P Vandergheynst Two-dimensional directional wavelets inimage processing Int J Imaging Syst Tech 7 152ndash165 (1996)
[69] J-P Antoine D Barache RM Cesar Jr LF Costa Shape characterization with thewavelet transform Signal Process 62 265ndash290 (1997)
[70] J-P Antoine P Antoine B Piraux Wavelets in atomic physics in Spline Functions andthe Theory of Wavelets ed by S Dubuc G Deslauriers CRM Proceedings and LectureNotes vol 18 (AMS Providence RI 1999) pp261ndash276
[71] J-P Antoine P Antoine B Piraux Wavelets in atomic physics and in solid state physicsin Wavelets in Physics Chap 8 ed by JC van den Berg (Cambridge University PressCambridge 1999)
[72] J-P Antoine R Murenzi P Vandergheynst Directional wavelets revisited Cauchywavelets and symmetry detection in patterns Appl Comput Harmon Anal 6 314ndash345(1999)
[73] J-P Antoine L Jacques R Twarock Wavelet analysis of a quasiperiodic tiling withfivefold symmetry Phys Lett A 261 265ndash274 (1999)
[74] J-P Antoine L Jacques P Vandergheynst Penrose tilings quasicrystals and wavelets inWavelet Applications in Signal and Image Processing VII SPIE Proceedings vol 3813(SPIE Bellingham WA 1999) pp 28ndash39
[75] J-P Antoine YB Kouagou D Lambert B Torreacutesani An algebraic approach to discretedilations Application to discrete wavelet transforms J Fourier Anal Appl 6 113ndash141(2000)
[76] J-P Antoine A Coron J-M Dereppe Water peak suppression Time-frequency vs time-scale approach J Magn Reson 144 189ndash194 (2000)
[77] J-P Antoine J-P Gazeau P Monceau J R Klauder K Penson Temporally stablecoherent states for infinite well and Poumlschl-Teller potentials J Math Phys 42 2349ndash2387(2001)
[78] J-P Antoine A Coron C Chauvin Wavelets and related time-frequency techniques inmagnetic resonance spectroscopy NMR Biomed 14 265ndash270 (2001)
[79] J-P Antoine L Demanet J-F Hochedez L Jacques R Terrier E Verwichte Applicationof the 2-D wavelet transform to astrophysical images Phys Mag 24 93ndash116 (2002)
[80] J-P Antoine L Demanet L Jacques P Vandergheynst Wavelets on the sphere Imple-mentation and approximations Appl Comput Harmon Anal 13 177ndash200 (2002)
[81] J-P Antoine I Bogdanova P Vandergheynst The continuous wavelet transform on conicsections Int J Wavelets Multires Inform Proc 6 137ndash156 (2007)
[82] J-P Antoine D Rosca P Vandergheynst Wavelet transform on manifolds Old and newapproaches Appl Comput Harmon Anal 28 189ndash202 (2010)
[83] P Antoine B Piraux A Maquet Time profile of harmonics generated by a single atom ina strong electromagnetic field Phys Rev A 51 R1750ndashR1753 (1995)
[84] P Antoine B Piraux DB Miloševic M Gajda Generation of ultrashort pulses ofharmonics Phys Rev A 54 R1761ndashR1764 (1996)
[85] P Antoine B Piraux DB Miloševic M Gajda Temporal profile and time control ofharmonic generation Laser Phys 7 594ndash601 (1997)
[86] Apollonius see Wikipedia httpenwikipediaorgwikiApollonius_of_Perga[87] FT Arecchi E Courtens R Gilmore H Thomas Atomic coherent states in quantum
optics Phys Rev A 6 2211ndash2237 (1972)[88] I Aremua J-P Gazeau MN Hounkonnou Action-angle coherent states for quantum
systems with cylindric phase space J Phys A Math Theor 45 335302 (2012)
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[90] F Argoul A Arneacuteodo J Elezgaray G Grasseau R Murenzi Wavelet analysis of theself-similarity of diffusion-limited aggregates and electrodeposition clusters Phys Rev A41 5537ndash5560 (1990)
[91] TA Arias Multiresolution analysis of electronic structure Semicardinal and waveletbases Rev Mod Phys 71 267ndash312 (1999)
[92] A Arneacuteodo F Argoul E Bacry J Elezgaray E Freysz G Grasseau JF Muzy BPouligny Wavelet transform of fractals in Wavelets and Applications (Proc Marseille1989) ed by Y Meyer (Masson and Springer Paris and Berlin 1991) pp 286ndash352
[93] A Arneacuteodo E Bacry JF Muzy The thermodynamics of fractals revisited with waveletsPhysica A 213 232ndash275 (1995)
[94] A Arneacuteodo E Bacry JF Muzy Oscillating singularities in locally self-similar functionsPhys Rev Lett 74 4823ndash4826 (1995)
[95] A Arneacuteodo E Bacry PV Graves JF Muzy Characterizing long-range correlations inDNA sequences from wavelet analysis Phys Rev Lett 74 3293ndash3296 (1996)
[96] A Arneacuteodo Y drsquoAubenton E Bacry PV Graves JF Muzy C Thermes Wavelet basedfractal analysis of DNA sequences Physica D 96 291ndash320 (1996)
[97] A Arneacuteodo E Bacry S Jaffard JF Muzy Oscillating singularities on Cantor sets Agrand canonical multifractal formalism J Stat Phys 87 179ndash209 (1997)
[98] A Arneacuteodo E Bacry S Jaffard JF Muzy Singularity spectrum of multifractal functionsinvolving oscillating singularities J Fourier Anal Appl 4 159ndash174 (1998)
[99] N Aronszajn Theory of reproducing kernels Trans Amer Math Soc 66 337ndash404 (1950)[100] A Ashtekar J Lewandowski D Marolf J Mouratildeo T Thiemann Coherent state
transforms for spaces of connections J Funct Analysis 135 519ndash551 (1996)[101] A Askari-Hemmat MA Dehghan M Radjabalipour Generalized frames and their
redundancy Proc Amer Math Soc 129 1143ndash1147 (2001)[102] EW Aslaksen JR Klauder Unitary representations of the affine group J Math Phys 9
206ndash211 (1968)[103] EW Aslaksen JR Klauder Continuous representation theory using the affine group
J Math Phys 10 2267ndash2275 (1969)[104] D Astruc L Plantieacute R Murenzi Y Lebret D Vandromme On the use of the 3D
wavelet transform for the analysis of computational fluid dynamics results in Progressin Wavelet Analysis and Applications (Proc Toulouse 1992) ed by Y Meyer S Roques(Ed Frontiegraveres Gif-sur-Yvette 1993) pp 463ndash470
[105] PW Atkins JC Dobson Angular momentum coherent states Proc Roy Soc London A321 321ndash340 (1971)
[106] BW Atkinson DO Bruff JS Geronimo D P Hardin Wavelets centered on a knotsequence Piecewise polynomial wavelets on a quasi-crystal lattice preprint (2011)arXiv11024246v1 [mathNA]
[107] IS Averbuch NF Perelman Fractional revivals Universality in the long-term evolutionof quantum wave packets beyond the correspondence principle dynamics Phys Lett A139 449ndash453 (1989)
[108] H Bacry J-M Leacutevy-Leblond Possible kinematics J Math Phys 9 1605ndash1614 (1968)[109] H Bacry A Grossmann J Zak Proof of the completeness of lattice states in kq
representation Phys Rev B 12 1118ndash1120 (1975)[110] L Baggett KF Taylor Groups with completely reducible regular representation Proc
Amer Math Soc 72 593ndash600 (1978)[111] VG Bagrov J-P Gazeau D Gitman A Levine Coherent states and related quantizations
for unbounded motions J Phys A Math Theor 45 125306 (2012) arXiv12010955v2[quant-ph]
[112] P Balazs J-P Antoine A Grybos Weighted and controlled frames Mutual relationshipand first numerical properties Int J Wavelets Multires Inform Proc 8 109ndash132 (2010)
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[114] P Balazs D Bayer A Rahimi Multipliers for continuous frames in Hilbert spaces JPhys A Math Gen 45 244023 (2012)
[115] P Baldi G Kerkyacharian D Marinucci D Picard High frequency asymptotics forwavelet-based tests for Gaussianity and isotropy on the torus J Multivar Anal 99 606ndash636 (2008)
[116] P Baldi G Kerkyacharian D Marinucci D Picard Asymptotics for spherical needletsAnn of Stat 37 1150ndash1171 (2009)
[117] MC Baldiotti J-P Gazeau DM Gitman Coherent states of a particle in magnetic fieldand Stieltjes moment problem Phys Lett A 373 1916ndash1920 (2009) Erratum Phys LettA 373 2600 (2009)
[118] MC Baldiotti J-P Gazeau DM Gitman Semiclassical and quantum description ofmotion on the noncommutative plane Phys Lett A 373 3937ndash3943 (2009)
[119] R Balian Un principe drsquoincertitude fort en theacuteorie du signal ou en meacutecanique quantiqueCR Acad Sci(Paris) 292 1357ndash1362 (1981)
[120] M Bander C Itzykson Group theory and the hydrogen atom I II Rev Mod Phys 38330ndash345 346ndash358 (1966)
[121] D Barache S De Biegravevre J-P Gazeau Affine symmetry semigroups for quasicrystalsEurophys Lett 25 435ndash440 (1994)
[122] D Barache J-P Antoine J-M Dereppe The continuous wavelet transform a tool for NMRspectroscopy J Magn Reson 128 1ndash11 (1997)
[123] V Bargmann On a Hilbert space of analytic functions and an associated integral transformPart I Commun Pure Appl Math 14 187ndash214 (1961)
[124] V Bargmann On a Hilbert space of analytic functions and an associated integral transformPart II A family of related function spaces Application to distribution theory CommunPure Appl Math 20 1ndash101 (1967)
[125] V Bargmann P Butera L Girardello JR Klauder On the completeness of coherentstates Reports Math Phys 2 221ndash228 (1971)
[126] AO Barut L Girardello New ldquocoherentrdquo states associated with non compact groupsCommun Math Phys 21 41ndash55 (1971)
[127] AO Barut H Kleinert Transition probabilities of the hydrogen atom from noncompactdynamical groups Phys Rev 156 1541ndash1545 (1967)
[128] AO Barut BW Xu Non-spreading coherent states riding on Kepler orbits Helv PhysActa 66 711ndash720 (1993)
[129] G Battle Wavelets A renormalization group point of view in Wavelets and TheirApplications ed by MB Ruskai G Beylkin R Coifman I Daubechies S Mallat YMeyer L Raphael (Jones and Bartlett Boston 1992) pp 323ndash349
[130] P Bellomo CR Stroud Jr Dispersion of Klauderrsquos temporally stable coherent states forthe hydrogen atom J Phys A Math Gen 31 L445ndashL450 (1998)
[131] J Ben Geloun J R Klauder Ladder operators and coherent states for continuous spectraJ Phys A Math Theor 42 375209 (2009)
[132] J Ben Geloun J Hnybida JR Klauder Coherent states for continuous spectrum operatorswith non-normalizable fiducial states J Phys A Math Theor 45 085301 (2012)
[133] JJ Benedetto TD Andrews Intrinsic wavelet and frame applications in IndependentComponent Analyses Wavelets Neural Networks Biosystems and Nanoengineering IXed by H Szu L Dai SPIE Proceedings vol 8058 (SPIE Bellingham WA 2011) p805802
[134] JJ Benedetto A Teolis A wavelet auditory model and data compression Appl ComputHarmon Anal 1 3ndash28 (1993)
[135] FA Berezin Quantization Math USSR Izvestija 8 1109ndash1165 (1974)[136] FA Berezin General concept of quantization Commun Math Phys 40 153ndash174 (1975)[137] H Bergeron From classical to quantum mechanics How to translate physical ideas into
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[139] H Bergeron and J-P Gazeau Integral quantization with two basic examples Preprint(2013) arXiv13082348v1
[140] H Bergeron A Valance Overcomplete basis for one dimensional Hamiltonians J MathPhys 36 1572ndash1592 (1995)
[141] H Bergeron J-P Gazeau P Siegl A Youssef Semi-classical behavior of Poumlschl-Tellercoherent states Eur Phys Lett 92 60003 (2010)
[142] H Bergeron P Siegl A Youssef New SUSYQM coherent states for Poumlschl-Tellerpotentials A detailed mathematical analysis J Phys A Math Theor 45 244028 (2012)
[143] H Bergeron J-P Gazeau A Youssef Are the Weyl and coherent state descriptionsphysically equivalent Phys Lett A 377 598ndash605 (2013)
[144] H Bergeron A Dapor J-P Gazeau P Małkiewicz Wavelet quantum cosmology preprint(2013) arXiv13050653 [gr-qc]
[145] S Bergman Uumlber die Kernfunktion eines Bereiches und ihr Verhalten am Rande I ReineAngw Math 169 1ndash42 (1933)
[146] D Bernier KF Taylor Wavelets from square-integrable representations SIAM J MathAnal 27 594ndash608 (1996)
[147] G Bernuau Wavelet bases associated to a self-similar quasicrystal J Math Phys 394213ndash4225 (1998)
[148] A Bertrand Deacuteveloppements en base de Pisot et reacutepartition modulo 1 C R Acad SciParis 285 419ndash421 (1977)
[149] J Bertrand P Bertrand Classification of affine Wigner functions via an extendedcovariance principle in Group Theoretical Methods in Physics (Proc Sainte-Adegravele 1988)ed by Y Saint-Aubin L Vinet (World Scientific Singapore 1989) pp 1380ndash1383
[150] Z Białynicka-Birula I Białynicki-Birula Space-time description of squeezing J OptSoc Am B4 1621ndash1626 (1987)
[151] E Bianchi E Magliaro C Perini Coherent spin-networks Phys Rev D 82 024012(2010)
[152] S Biskri J-P Antoine B Inhester F Mekideche Extraction of Solar coronal magneticloops with the 2-D Morlet wavelet transform Solar Phys 262 373ndash385 (2010)
[153] R Bluhm VA Kostelecky JA Porter The evolution and revival structure of localizedquantum wave packets Am J Phys 64 944ndash953 (1996)
[154] I Bogdanova P Vandergheynst J-P Antoine L Jacques M Morvidone Stereographicwavelet frames on the sphere Appl Comput Harmon Anal 19 223ndash252 (2005)
[155] I Bogdanova X Bresson J-P Thiran P Vandergheynst Scale space analysis and activecontours for omnidirectional images IEEE Trans Image Process 16 1888ndash1901 (2007)
[156] I Bogdanova P Vandergheynst J-P Gazeau Continuous wavelet transform on thehyperboloid Appl Comput Harmon Anal 23 (2007) 286ndash306 (2007)
[157] P Boggiatto E Cordero Anti-Wick quantization of tempered distributions in Progress inAnalysis Berlin (2001) vol I II (World Sci Publ River Edge NJ 2003) pp 655ndash662
[158] P Boggiatto E Cordero K Groumlchenig Generalized Anti-Wick operators with symbols indistributional Sobolev spaces Int Equ Oper Theory 48 427ndash442 (2004)
[159] A Boumlhm The Rigged Hilbert Space in quantum mechanics in Lectures in TheoreticalPhysics vol IX A ed by WA Brittin et al (Gordon amp Breach New York 1967) pp255ndash315
[160] G Bohnkeacute Treillis drsquoondelettes associeacutes aux groupes de Lorentz Ann Inst H Poincareacute54 245ndash259 (1991)
[161] WR Bomstad JR Klauder Linearized quantum gravity using the projection operatorformalism Class Quantum Grav 23 5961ndash5981 (2006)
[162] VV Borzov Orthogonal polynomials and generalized oscillator algebras Int TransformSpec Funct 12 115ndash138 (2001)
[163] VV Borzov EV Damaskinsky Generalized coherent states for classical orthogonalpolynomials Day on Diffraction (2002) arXivmathQA0209181v1 (SPb 2002)
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[165] A Bouzouina S De Biegravevre Equipartition of the eigenfunctions of quantized ergodic mapson the torus Commun Math Phys 178 83ndash105 (1996)
[166] P Brault J-P Antoine A spatio-temporal Gaussian-Conical wavelet with high apertureselectivity for motion and speed analysis Appl Comput Harmon Anal 34 148ndash161(2012)
[167] A Briguet S Cavassila D Graveron-Demilly Suppression of huge signals using theCadzow enhancement procedure The NMR Newslett 440 26 (1995)
[168] CM Brislawn Fingerprints go digital Notices Amer Math Soc 42 1278ndash1283 (1995)[169] CM Brislawn On the group-theoretic structure of lifted filter banks in Excursions in
Harmonic Analysis vol 1 2 ed by TD Andrews R Balan JJ Benedetto W CzajaKA Okoudjou (Birkhaumluser Boston 2013) pp 113ndash135
[170] F Bruhat Sur les repreacutesentations induites des groupes de Lie Bull Soc Math France 8497ndash205 (1956)
[171] T Buumllow Multiscale image processing on the sphere in DAGM-Symposium (2002) pp609ndash617
[172] C Burdik C Frougny J-P Gazeau R Krejcar Beta-integers as natural counting systemsfor quasicrystals J Phys A Math Gen 31 6449ndash6472 (1998)
[173] KE Cahill Coherent-state representations for the photon density Phys Rev 138 B1566ndash1576 (1965)
[174] KE Cahill R Glauber Density operators and quasiprobability distributions Phys Rev177 1882ndash1902 (1969)
[175] KE Cahill R Glauber Ordered expansions in boson amplitude operators Phys Rev 1771857ndash1881 (1969)
[176] AR Calderbank I Daubechies W Sweldens BL Yeo Wavelets that map integers tointegers Appl Comput Harmon Anal 5 332ndash369 (1998)
[177] M Calixto J Guerrero Wavelet transform on the circle and the real line A unified group-theoretical treatment Appl Comput Harmon Anal 21 204ndash229 (2006)
[178] M Calixto E Peacuterez-Romero Extended MacMahon-Schwingerrsquos master theorem andconformal wavelets in complex Minkowski space Appl Comput Harmon Anal 31 143ndash168 (2011)
[179] M Calixto J Guerrero D Rosca Wavelet transform on the torus A group-theoreticalapproach preprint (2013)
[180] EJ Candegraves Harmonic analysis of neural networks Appl Comput Harmon Anal 6 197ndash218 (1999)
[181] EJ Candegraves Ridgelets and the representation of mutilated Sobolev functions SIAM JMath Anal 33 347ndash368 (2001)
[182] EJ Candegraves L Demanet Curvelets and Fourier integral operators CR Acad Sci ParisSeacuter I Math 336 395ndash398 (2003)
[183] EJ Candegraves L Demanet The curvelet representation of wave propagators is optimallysparse Commun Pure Appl Math 58 1472ndash1528 (2004)
[184] EJ Candegraves L Demanet The curvelet representation of wave propagators is optimallysparse Commun Pure Appl Math 58 1472ndash1528 (2005)
[185] EJ Candegraves DL Donoho Curvelets ndash A surprisingly effective nonadaptive representationfor objects with edges in Curves and Surfaces ed by LL Schumaker et al (VanderbiltUniversity Press Nashville TN 1999)
[186] EJ Candegraves DL Donoho Ridgelets A key to higher-dimensional intermittency PhilTrans R Soc Lond A 357 2495ndash2509 (1999)
[187] EJ Candegraves DL Donoho Curvelets multiresolution representation and scaling laws inWavelet Applications in Signal and Image Processing VIII ed by A Aldroubi A LaineM Unser SPIE Proceedings vol 4119 (SPIE Bellingham WA 2000) pp 1ndash12
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[189] EJ Candegraves DL Donoho New tight frames of curvelets and optimal representations ofobjects with piecewise C2 singularities Commun Pure Appl Math 57 219ndash266 (2004)
[190] EJ Candegraves DL Donoho Continuous curvelet transform I Resolution of the wavefrontset II Discretization and frames Appl Comput Harmon Anal 19 162ndash197 198ndash222(2005)
[191] EJ Candegraves F Guo New multiscale transforms minimum total variationsynthesisApplications to edge-preserving image reconstruction Signal Proc 82 1519ndash1543 (2002)
[192] EJ Candegraves L Demanet D Donoho L Ying Fast discrete curvelet transforms MultiscaleModel Simul 5 861ndash899 (2006)
[193] AL Carey Square integrable representations of non-unimodular groups Bull AustrMath Soc 15 1ndash12 (1976)
[194] AL Carey Group representations in reproducing kernel Hilbert spaces Rep Math Phys14 247ndash259 (1978)
[195] P Carruthers MM Nieto Phase and angle variables in quantum mechanics Rev ModPhys 40 411ndash440 (1968)
[196] PG Casazza G Kutyniok Frames of subspaces in Wavelets Frames and Operator The-ory Contemporary Mathematics vol 345 (American Mathematical Society ProvidenceRI 2004) pp 87ndash113
[197] PG Casazza D Han DR Larson Frames for Banach spaces Contemp Math 247 149ndash182 (1999)
[198] P Casazza O Christensen S Li A Lindner Riesz-Fischer sequences and lower framebounds Z Anal Anwend 21 305ndash314 (2002)
[199] PG Casazza G Kutyniok S Li Fusion frames and distributed processing ApplComputHarmon Anal 25 114ndash132 (2008)
[200] DPL Castrigiano RW Henrichs Systems of covariance and subrepresentations ofinduced representations Lett Math Phys 4 169ndash175 (1980)
[201] U Cattaneo Densities of covariant observables J Math Phys 23 659ndash664 (1982)[202] A Cerioni L Genovese I Duchemin Th Deutsch Accurate complex scaling of three
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Rev A 34 7ndash22 (1986)[204] SHH Chowdhury ST Ali All the groups of signal analysis from the (1+1) affine Galilei
group J Math Phys 52 103504 (2011)[205] SL Chown Antarctic marine biodiversity and deep-sea hydrothermal vents PLoS Biol
10 1ndash4 (2012)[206] C Cishahayo S De Biegravevre On the contraction of the discrete series of SU(11) Ann Inst
Fourier (Grenoble) 43 551ndash567 (1993)[207] M Clerc and S Mallat Shape from texture and shading with wavelets in Dynamical
Systems Control Coding Computer Vision Progress in Systems and Control Theory 25393ndash417 (1999)
[208] L Cohen General phase-space distribution functions J Math Phys 7 781ndash786 (1966)[209] A Cohen I Daubechies J-C Feauveau Biorthogonal bases of compactly supported
wavelets Commun Pure Appl Math 45 485ndash560 (1992)[210] R Coifman Y Meyer MV Wickerhauser Wavelet analysis and signal processing
in Wavelets and Their Applications ed by MB Ruskai G Beylkin R CoifmanI Daubechies S Mallat Y Meyer L Raphael (Jones and Bartlett Boston 1992)pp 153ndash178
[211] R Coifman Y Meyer MV Wickerhauser Entropy-based algorithms for best basisselection IEEE Trans Inform Theory 38 713ndash718 (1992)
[212] R Coquereaux A Jadczyk Conformal theories curved spaces relativistic wavelets andthe geometry of complex domains Rev Math Phys 2 1ndash44 (1990)
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[213] A Coron L Vanhamme J-P Antoine P Van Hecke S Van Huffel The filtering approachto solvent peak suppression in MRS A critical review J Magn Reson 152 26ndash40 (2001)
[214] N Cotfas J-P Gazeau Finite tight frames and some applications (topical review) J PhysA Math Theor 43 193001 (2010)
[215] N Cotfas J-P Gazeau K Goacuterska Complex and real Hermite polynomials and relatedquantizations J Phys A Math Theor 43 305304 (2010)
[216] N Cotfas J-P Gazeau A Vourdas Finite-dimensional Hilbert space and frame quantiza-tion J Phys A Math Gen 44 175303 (2011)
[217] EMF Curado MA Rego-Monteiro LMCS Rodrigues Y Hassouni Coherent statesfor a degenerate system The hydrogen atom Physica A 371 16ndash19 (2006)
[218] S Dahlke P Maass The affine uncertainty principle in one and two dimensions CompMath Appl 30 293ndash305 (1995)
[219] S Dahlke W Dahmen E Schmidt I Weinreich Multiresolution analysis and wavelets onS
2 and S3 Numer Funct Anal Optim 16 19ndash41 (1995)
[220] S Dahlke V Lehmann G Teschke Applications of wavelet methods to the analysis ofmeteorological radar data - An overview Arabian J Sci Eng 28 3ndash44 (2003)
[221] S Dahlke G Kutyniok P Maass C Sagiv H-G Stark G Teschke The uncertaintyprinciple associated with the continuous shearlet transform Int J Wavelets MultiresolutInf Process 6 157ndash181 (2008)
[222] S Dahlke G Kutyniok G Steidl G Teschke Shearlet coorbit spaces and associatedBanach frames Appl Comput Harmon Anal 27 195ndash214 (2009)
[223] S Dahlke G Steidl G Teschke The continuous shearlet transform in arbitrary spacedimensions J Fourier Anal Appl 16 340ndash364 (2010)
[224] S Dahlke G Steidl G Teschke Shearlet coorbit spaces Compactly supported analyzingshearlets traces and embeddings J Fourier Anal Appl 17 1232ndash1355 (2011)
[225] T Dallard GR Spedding 2-D wavelet transforms Generalisation of the Hardy space andapplication to experimental studies Eur J Mech BFluids 12 107ndash134 (1993)
[226] C Daskaloyannis Generalized deformed oscillator and nonlinear algebras J Phys AMath Gen 24 L789ndashL794 (1991)
[227] C Daskaloyannis K Ypsilantis A deformed oscillator with Coulomb energy spectrumJ Phys A Math Gen 25 4157ndash4166 (1992)
[228] I Daubechies On the distributions corresponding to bounded operators in the Weylquantization Commun Math Phys 75 229ndash238 (1980)
[229] I Daubechies and A Grossmann An integral transform related to quantization I J MathPhys 21 2080ndash2090 (1980)
[230] I Daubechies A Grossmann J Reignier An integral transform related to quantization IIJ Math Phys 24 239ndash254 (1983)
[231] I Daubechies Orthonormal bases of compactly supported wavelets Commun Pure ApplMath 41 909ndash996 (1988)
[232] I Daubechies The wavelet transform time-frequency localisation and signal analysisIEEE Trans Inform Theory 36 961ndash1005 (1990)
[233] I Daubechies S Maes A nonlinear squeezing of the continuous wavelet transform basedon auditory nerve models in Wavelets in Medicine and Biology ed by A Aldroubi MUnser (CRC Press Boca Raton 1996) pp 527ndash546
[234] I Daubechies A Grossmann Y Meyer Painless nonorthogonal expansions J Math Phys27 1271ndash1283 (1986)
[235] ER Davies Introduction to texture analysis in Handbook of texture analysis ed by MMirmehdi X Xie J Suri (World Scientific Singapore 2008) pp 1ndash31
[236] R De Beer D van Ormondt FTAW Wajer S Cavassila D Graveron-Demilly S VanHuffel SVD-based modelling of medical NMR signals in SVD and Signal ProcessingIII Algorithms Architectures and Applications ed by M Moonen B De Moor (Elsevier(North-Holland) Amsterdam 1995) pp 467ndash474
[237] S De Biegravevre Coherent states over symplectic homogeneous spaces J Math Phys 301401ndash1407 (1989)
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[238] S De Biegravevre JA Gonzalez Semi-classical behaviour of the Weyl correspondence on thecircle in Group-Theoretical Methods in Physics (Proc Salamanca 1992) ed by M delOlmo M Santander J Mateos Guilarte (CIEMAT Madrid 1993) pp 343ndash346
[239] S De Biegravevre JA Gonzaacutelez Semiclassical behaviour of coherent states on the circle inQuantization and Coherent States Methods in Physics ed by A Odzijewicz et al (WorldScientific Singapore 1993)
[240] S De Biegravevre AE Gradechi Quantum mechanics and coherent states on the anti-de Sitterspace-time and their Poincareacute contraction Ann Inst H Poincareacute 57 403ndash428 (1992)
[241] J Deenen C Quesne Dynamical group of collective states I II III J Math Phys 23878ndash889 2004ndash2015 (1982)
[242] J Deenen C Quesne Dynamical group of collective states I II III J Math Phys 251638ndash1650 (1984)
[243] J Deenen C Quesne Partially coherent states of the real symplectic group J Math Phys25 2354ndash2366 (1984)
[244] J Deenen C Quesne Boson representations of the real symplectic group and theirapplication to the nuclear collective model J Math Phys 26 2705ndash2716 (1985)
[245] R Delbourgo Minimal uncertainty states for the rotation and allied groups J Phys AMath Gen 10 1837ndash1846 (1977)
[246] R Delbourgo J R Fox Maximum weight vectors possess minimal uncertainty J PhysA Math Gen 10 L233ndashL235 (1977)
[247] V Delouille J de Patoul J-F Hochedez L Jacques J-P Antoine Wavelet spectrumanalysis of EITSoHO images Solar Phys 228 301ndash321 (2005)
[248] N Delprat B Escudieacute P Guillemain R Kronland-Martinet P Tchamitchian B Tor-reacutesani Asymptotic wavelet and Gabor analysis Extraction of instantaneous frequenciesIEEE Trans Inform Theory 38 644ndash664 (1992)
[249] Th Deutsch L Genovese Wavelets for electronic structure calculations Collection SocFr Neut 12 33ndash76 (2011)
[250] B Dewitt Quantum theory of gravity I The canonical theory Phys Rev 160 1113ndash1148(1967)
[251] RH Dicke Coherence in spontaneous radiation processes Phys Rev 93 99ndash110 (1954)[252] AN Dinkelaker AL MacKinnon Wavelets intermittency and solar flare hard X-rays 1
Local intermittency measure in cascade and avalanche scenarios Solar Phys 282 471ndash481(2013)
[253] AN Dinkelaker AL MacKinnon Wavelets intermittency and solar flare hard X-rays 2LIM analysis of high time resolution BATSE data Solar Phys 282 483ndash501 (2013)
[254] MN Do M Vetterli Contourlets in Beyond Wavelets ed by GV Welland (AcademicSan Diego 2003) pp 83ndash105
[255] MN Do M Vetterli The contourlet transform An efficient directional multiresolutionimage representation IEEE Trans Image Process 14 2091ndash2106 (2005)
[256] VV Dodonov Nonclassical states in quantum optics A ldquosqueezedrdquo review of the first 75years J Opt B Quant Semiclass Opot 4 R1ndashR33 (2002)
[257] DL Donoho Nonlinear wavelet methods for recovery of signals densities and spectrafrom indirect and noisy data in Different Perspectives on Wavelets Proceedings ofSymposia in Applied Mathematics vol 38 ed by I Daubechies (American MathematicalSociety Providence RI 1993) pp 173ndash205
[258] DL Donoho Wedgelets Nearly minimax estimation of edges Ann Stat 27 859ndash897(1999)
[259] DL Donoho X Huo Beamlet pyramids A new form of multiresolution analysis suitedfor extracting lines curves and objects from very noisy image data in SPIE Proceedingsvol 5914 (SPIE Bellingham WA 2005) pp 1ndash12
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[261] AH Dooley JW Rice Contractions of rotation groups and their representations MathProc Camb Phil Soc 94 509ndash517 (1983)
[262] AH Dooley JW Rice On contractions of semisimple Lie groups Trans Amer MathSoc 289 185ndash202 (1985)
[263] JR Driscoll DM Healy Computing Fourier transforms and convolutions on the 2-sphereAdv Appl Math 15 202ndash250 (1994)
[264] H Drissi F Regragui J-P Antoine M Bennouna Wavelet transform analysis of visualevoked potentials Some preliminary results ITBM-RBM 21 84ndash91 (2000)
[265] RJ Duffin AC Schaeffer A class of nonharmonic Fourier series Trans Amer MathSoc 72 341ndash366 (1952)
[266] M Duflo CC Moore On the regular representation of a nonunimodular locally compactgroup J Funct Anal 21 209ndash243 (1976)
[267] M Duval-Destin R Murenzi Spatio-temporal wavelets Application to the analysis ofmoving patterns in Progress in Wavelet Analysis and Applications (Proc Toulouse 1992)ed by Y Meyer S Roques (Ed Frontiegraveres Gif-sur-Yvette 1993) pp 399ndash408
[268] M Duval-Destin M-A Muschietti B Torreacutesani Continuous wavelet decompositionsmultiresolution and contrast analysis SIAM J Math Anal 24 739ndash755 (1993)
[269] SJL van Eindhoven JLH Meyers New orthogonality relations for the Hermitepolynomials and related Hilbert spaces J Math Anal Appl 146 89ndash98 (1990)
[270] M ElBaz R Fresneda J-P Gazeau Y Hassouni Coherent state quantization of para-grassmann algebras J Phys A Math Theor 43 385202 (2010) Corrigendum J PhysA Math Theor 45 (2012)
[271] A Elkharrat J-P Gazeau F Deacutenoyer Multiresolution of quasicrystal diffraction spectraActa Cryst A65 466ndash489 (2009)
[272] Q Fan Phase space analysis of the identity decompositions J Math Phys 34 3471ndash3477(1993)
[273] M Fanuel S Zonetti Affine quantization and the initial cosmological singularity Euro-phys Lett 101 10001 (2013)
[274] M Farge Wavelet transforms and their applications to turbulence Annu Rev Fluid Mech24 395ndash457 (1992)
[275] M Farge N Kevlahan V Perrier E Goirand Wavelets and turbulence Proc IEEE 84639ndash669 (1996)
[276] M Farge NK-R Kevlahan V Perrier K Schneider Turbulence analysis modellingand computing using wavelets in Wavelets in Physics Chap 4 ed by JC van den Berg(Cambridge University Press Cambridge 1999)
[277] HG Feichtinger Coherent frames and irregular sampling in Recent Advances in FourierAnalysis and Its applications ed by JS Byrnes JL Byrnes (Kluwer Dordrecht 1990)pp 427ndash440
[278] HG Feichtinger KH Groumlchenig Banach spaces related to integrable group representa-tions and their atomic decompositions I J Funct Anal 86 307ndash340 (1989)
[279] HG Feichtinger KH Groumlchenig Banach spaces related to integrable group representa-tions and their atomic decompositions II Mh Math 108 129ndash148 (1989)
[280] M Flensted-Jensen Discrete series for semisimple symmetric spaces Ann of Math 111253ndash311 (1980)
[281] K Flornes A Grossmann M Holschneider B Torreacutesani Wavelets on discrete fieldsAppl Comput Harmon Anal 1 137ndash146 (1994)
[282] V Fock Zur Theorie der Wasserstoffatoms Zs f Physik 98 145ndash54 (1936)[283] M Fornasier H Rauhut Continuous frames function spaces and the discretization
problem J Fourier Anal Appl 11 245ndash287 (2005)
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[286] W Freeden T Maier S Zimmermann A survey on wavelet methods for (geo)applicationsRevista Mathematica Complutense 16 (2003) 277ndash310
[287] W Freeden M Schreiner Biorthogonal locally supported wavelets on the sphere based onzonal kernel functions J Fourier Anal Appl 13 693ndash709 (2007)
[288] WT Freeman EH Adelson The design and use of steerable filters IEEE Trans PatternAnal Machine Intell 13 891ndash906 (1991)
[289] L Freidel ER Livine U(N) coherent states for loop quantum gravity J Math Phys 52052502 (2011)
[290] J Froment S Mallat Arbitrary low bit rate image compression using wavelets in Progressin Wavelet Analysis and Applications (Proc Toulouse 1992) ed by Y Meyer S Roques(Ed Frontiegraveres Gif-sur-Yvette 1993) pp 413ndash418 and references therein
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[292] H Fuumlhr Wavelet frames and admissibility in higher dimensions J Math Phys 37 6353ndash6366 (1996)
[293] H Fuumlhr M Mayer Continuous wavelet transforms from semidirect products Cyclicrepresentations and Plancherel measure J Fourier Anal Appl 8 375ndash396 (2002)
[294] D Gabor Theory of communication J Inst Electr Engrg(London) 93 429ndash457 (1946)[295] J-P Gabardo D Han Frames associated with measurable spaces Adv Comput Math 18
127ndash147 (2003)[296] E Galapon Paulirsquos theorem and quantum canonical pairs The consistency of a bounded
self-adjoint time operator canonically conjugate to a Hamiltonian with non-empty pointspectrum Proc R Soc Lond A 458 451ndash472 (2002)
[297] PL Garciacutea de Leacuteon J-P Gazeau Coherent state quantization and phase operator PhysLett A 361 301ndash304 (2007)
[298] L Garciacutea de Leoacuten J-P Gazeau J Queacuteva The infinite well revisited Coherent states andquantization Phys Lett A 372 3597ndash3607 (2008)
[299] T Garidi J-P Gazeau E Huguet M Lachiegraveze Rey J Renaud Fuzzy spheres frominequivalent coherent states quantization J Phys A Math Theor 40 10225ndash10249 (2007)
[300] J-P Gazeau Four Euclidean conformal group in atomic calculations Exact analyticalexpressions for the bound-bound two-photon transition matrix elements in the H atomJ Math Phys 19 1041ndash1048 (1978)
[301] J-P Gazeau On the four Euclidean conformal group structure of the sturmian operatorLett Math Phys 3 285ndash292 (1979)
[302] J-P Gazeau Technique Sturmienne pour le spectre discret de lrsquoeacutequation de SchroumldingerJ Phys A Math Gen 13 3605ndash3617 (1980)
[303] J-P Gazeau Four Euclidean conformal group approach to the multiphoton processes in theH atom J Math Phys 23 156ndash164 (1982)
[304] J-P Gazeau A remarkable duality in one particle quantum mechanics between someconfining potentials and (R+Linfin
ε ) potentials Phys Lett 75A 159ndash163 (1980)[305] J-P Gazeau SL(2R)-coherent states and integrable systems in classical and quantum
physics in Quantization Coherent States and Complex Structures ed by J-P AntoineST Ali W Lisiecki IM Mladenov A Odzijewicz (Plenum Press New York and London1995) pp 147ndash158
[306] J-P Gazeau S Graffi Quantum harmonic oscillator A relativistic and statistical point ofview Boll Unione Mat Ital 11-A 815ndash839 (1997)
[307] J-P Gazeau V Hussin Poincareacute contraction of SU(11) Fock-Bargmann structure J PhysA Math Gen 25 1549ndash1573 (1992)
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[310] J-P Gazeau P Monceau Generalized coherent states for arbitrary quantum systems inColloquium M Flato (Dijon Sept 99) vol II (Kluumlwer Dordrecht 2000) pp 131ndash144
[311] J-P Gazeau M Novello The question of mass in (Anti-) de Sitter space-times J Phys AMath Theor 41 304008 (2008)
[312] J-P Gazeau M del Olmo q-coherent states quantization of the harmonic oscillator AnnPhys (NY) 330 220ndash245 (2013) arXiv12071200 [quant-ph]
[313] J-P Gazeau J Patera Tau-wavelets of Haar J Phys A Math Gen 29 4549ndash4559 (1996)[314] J-P Gazeau W Piechocki Coherent states quantization of a particle in de Sitter space
J Phys A Math Gen 37 6977ndash6986 (2004)[315] J-P Gazeau J Renaud Lie algorithm for an interacting SU(11) elementary system and its
contraction Ann Phys (NY) 222 89ndash121 (1993)[316] J-P Gazeau J Renaud Relativistic harmonic oscillator and space curvature Phys Lett A
179 67ndash71 (1993)[317] J-P Gazeau V Spiridonov Toward discrete wavelets with irrational scaling factor J Math
plane J Phys A Math Theor 44 495201 (2011)[319] J-P Gazeau J Patera E Pelantovaacute Tau-wavelets in the plane J Math Phys 39 4201ndash
4212 (1998)[320] J-P Gazeau M Andrle C Burdiacutek R Krejcar Wavelet multiresolutions for the Fibonacci
chain J Phys A Math Gen 33 L47ndashL51 (2000)[321] J-P Gazeau M Andrle C Burdiacutek Bernuau spline wavelets and sturmian sequences
J Fourier Anal Appl 10 269ndash300 (2004)[322] J-P Gazeau F-X Josse-Michaux P Monceau Finite dimensional quantizations of the
(q p) plane new space and momentum inequalities Int J Modern Phys B 20 1778ndash1791 (2006)
[323] J-P Gazeau J Mourad J Queacuteva Fuzzy de Sitter space-times via coherent statesquantization in Proceedings of the XXVIth Colloquium on Group Theoretical Methodsin Physics New York 2006 ed by J Birman S Catto B Nicolescu (Canopus PublishingLimited London 2009)
[324] D Geller A Mayeli Continuous wavelets on compact manifolds Math Z 262 895ndash927(2009)
[325] D Geller A Mayeli Nearly tight frames and space-frequency analysis on compactmanifolds Math Z 263 235ndash264 (2009)
[326] L Genovese B Videau M Ospici Th Deutsch S Goedecker J-F Mhaut Daubechieswavelets for high performance electronic structure calculations The BigDFT project CR Mecanique 339 149ndash164 (2011)
[327] G Gentili C Stoppato Power series and analyticity over the quaternions Math Ann 352113ndash131 (2012)
[328] G Gentili DC Struppa A new theory of regular functions of a quaternionic variable AdvMath 216 279ndash301 (2007)
[329] C Geyer K Daniilidis Catadioptric projective geometry Int J Comput Vision 45 223ndash243 (2001)
[330] R Gilmore Geometry of symmetrized states Ann Phys (NY) 74 391ndash463 (1972)[331] R Gilmore On properties of coherent states Rev Mex Fis 23 143ndash187 (1974)[332] J Ginibre Statistical ensembles of complex quaternion and real matrices J Math Phys
6 440ndash449 (1965)[333] RJ Glauber The quantum theory of optical coherence Phys Rev 130 2529ndash2539 (1963)
560 References
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[335] J Glimm Locally compact transformation groups Trans Amer Math Soc 101 124ndash138(1961)
[336] R Godement Sur les relations drsquoorthogonaliteacute de V Bargmann C R Acad Sci Paris 255521ndash523 657ndash659 (1947)
[337] C Gonnet B Torreacutesani Local frequency analysis with two-dimensional wavelet trans-form Signal Proc 37 389ndash404 (1994)
[338] JA Gonzalez MA del Olmo Coherent states on the circle J Phys A Math Gen 318841ndash8857 (1998)
[339] XGonze B Amadon et al ABINIT First-principles approach to material and nanosystemproperties Computer Physics Comm 180 2582ndash2615 (2009)
[340] KM Gograverski E Hivon AJ Banday BD Wandelt FK Hansen M Reinecke MBartelmann HEALPix A framework for high-resolution discretization and fast analysisof data distributed on the sphere Astrophys J 622 759ndash771 (2005)
[341] P Goupillaud A Grossmann J Morlet Cycle-octave and related transforms in seismicsignal analysis Geoexploration 23 85ndash102 (1984)
[342] KH Groumlchenig A new approach to irregular sampling of band-limited functions in RecentAdvances in Fourier Analysis and Its applications ed by JS Byrnes JL Byrnes (KluwerDordrecht 1990) pp 251ndash260
[343] KH Groumlchenig Gabor analysis over LCA groups in Gabor Analysis and Algorithms ndashTheory and Applications ed by HG Feichtinger T Strohmer (Birkhaumluser Boston-Basel-Berlin 1998) pp 211ndash231
[344] HJ Groenewold On the principles of elementary quantum mechanics Physica 12 405ndash460 (1946)
[345] P Grohs Continuous shearlet tight frames J Fourier Anal Appl 17 506ndash518 (2011)[346] P Grohs G Kutyniok Parabolic molecules preprint TU Berlin (2012)[347] M Grosser A note on distribution spaces on manifolds Novi Sad J Math 38 121ndash128
(2008)[348] A Grossmann Parity operator and quantization of δ -functions Commun Math Phys 48
191ndash194 (1976)[349] A Grossmann J Morlet Decomposition of Hardy functions into square integrable
wavelets of constant shape SIAM J Math Anal 15 723ndash736 (1984)[350] A Grossmann J Morlet Decomposition of functions into wavelets of constant shape and
related transforms in Mathematics + Physics Lectures on recent results I ed by L Streit(World Scientific Singapore 1985) pp 135ndash166
[351] A Grossmann J Morlet T Paul Integral transforms associated to square integrablerepresentations I General results J Math Phys 26 2473ndash2479 (1985)
[352] A Grossmann J Morlet T Paul Integral transforms associated to square integrablerepresentations II Examples Ann Inst H Poincareacute 45 293ndash309 (1986)
[353] A Grossmann R Kronland-Martinet J Morlet Reading and understanding the contin-uous wavelet transform in Wavelets Time-Frequency Methods and Phase Space (ProcMarseille 1987) ed by J-M Combes A Grossmann P Tchamitchian 2nd edn (SpringerBerlin 1990) pp 2ndash20
[354] P Guillemain R Kronland-Martinet B Martens Estimation of spectral lines with helpof the wavelet transform Application in NMR spectroscopy in Wavelets and Applications(Proc Marseille 1989) ed by Y Meyer (Masson and Springer Paris and Berlin 1991) pp38ndash60
[355] H de Guise M Bertola Coherent state realizations of su(n+ 1) on the n-torus J MathPhys 43 3425ndash3444 (2002)
[356] K Guo D Labate Representation of Fourier Integral Operators using shearlets J FourierAnal Appl 14 327ndash371 (2008)
References 561
[357] K Guo G Kutyniok D Labate Sparse multidimensional representations usinganisotropic dilation and shear operators in Wavelets and Spines (Athens GA 2005)(Nashboro Press Nashville TN 2006) pp 189ndash201
[358] K Guo D Labate W-Q Lim G Weiss E Wilson Wavelets with composite dilationsand their MRA properties Appl Comput Harmon Anal 20 202ndash236 (2006)
[359] EA Gutkin Overcomplete subspace systems and operator symbols Funct Anal Appl 9260ndash261 (1975)
[360] G Gyoumlrgyi Integration of the dynamical symmetry groups for the 1r potential Acta PhysAcad Sci Hung 27 435ndash439 (1969)
[361] BC Hall The Segal-Bargmann ldquoCoherent Staterdquo transform for compact Lie groups JFunct Analysis 122 103ndash151 (1994)
[362] B Hall JJ Mitchell Coherent states on spheres J Math Phys 43 1211ndash1236 (2002)[363] DK Hammond P Vandergheynst R Gribonval Wavelets on graphs via spectral theory
Appl Comput Harmon Anal 30 129ndash150 (2011)[364] Y Hassouni EMF Curado MA Rego-Monteiro Construction of coherent states for
physical algebraic system Phys Rev A 71 022104 (2005)[365] J He H Liu Admissible wavelets associated with the affine automorphism group of the
Siegel upper half-plane J Math Anal Appl 208 58ndash70 (1997)[366] J He H Liu Admissible wavelets associated with the classical domain of type one
Approx Appl 14 (1998) 89ndash105[367] J He L Peng Wavelet transform on the symmetric matrix space preprint Beijing (1997)
(unpublished)[368] J He L Peng Admissible wavelets on the unit disk Complex Variables 35 109ndash119
(1998)[369] DM Healy Jr FE Schroeck Jr On informational completeness of covariant localization
observables and Wigner coefficients J Math Phys 36 453ndash507 (1995)[370] C Heil D Walnut Continuous and discrete wavelet transforms SIAM Review 31 628ndash
666 (1989)[371] K Hepp EH Lieb On the superradiant phase transition for molecules in a quantized
radiation field The Dicke maser model Ann Phys (NY) 76 360ndash404 (1973)[372] K Hepp EH Lieb Equilibrium statistical mechanics of matter interacting with the
quantized radiation field Phys Rev A 8 2517ndash2525 (1973)[373] JA Hogan JD Lakey Extensions of the Heisenberg group by dilations and frames Appl
Comput Harmon Anal 2 174ndash199 (1995)[374] AL Hohoueacuteto K Thirulogasanthar ST Ali J-P Antoine Coherent states lattices and
square integrability of representations J Phys A Math Gen36 11817ndash11835 (2003)[375] M Holschneider On the wavelet transformation of fractal objects J Stat Phys 50 963ndash
993 (1988)[376] M Holschneider Wavelet analysis on the circle J Math Phys 31 39ndash44 (1990)[377] M Holschneider Inverse Radon transforms through inverse wavelet transforms Inv Probl
7 853ndash861 (1991)[378] M Holschneider Localization properties of wavelet transforms J Math Phys 34 3227ndash
3244 (1993)[379] M Holschneider General inversion formulas for wavelet transforms J Math Phys 34
4190ndash4198 (1993)[380] M Holschneider Wavelet analysis over abelian groups Applied Comput Harmon Anal
2 52ndash60 (1995)[381] M Holschneider Continuous wavelet transforms on the sphere J Math Phys 37 4156ndash
4165 (1996)[382] M Holschneider I Iglewska-Nowak Poisson wavelets on the sphere J Fourier Anal
Appl 13 405ndash419 (2007)
562 References
[383] M Holschneider R Kronland-Martinet J Morlet P Tchamitchian A real-time algorithmfor signal analysis with the help of wavelet transform in Wavelets Time-FrequencyMethods and Phase Space (Proc Marseille 1987) ed by J-M Combes A Grossmann PTchamitchian 2nd edn (Springer Berlin 1990) pp 286ndash297
[384] M Holschneider P Tchamitchian Pointwise analysis of Riemannrsquos ldquonondifferentiablerdquofunction Invent Math 105 157ndash175 (1991)
[385] GR Honarasa MK Tavassoly M Hatami R Roknizadeh Nonclassical properties ofcoherent states and excited coherent states for continuous spectra J Phys A Math Theor44 085303 (2011)
[386] M Hongoh Coherent states associated with the continuous spectrum of noncompactgroups J Math Phys 18 2081ndash2085 (1977)
[387] A Horzela FH Szafraniec A measure free approach to coherent states J Phys A MathGen 45 244018 (2012)
[388] W-L Hwang S Mallat Characterization of self-similar multifractals with waveletmaxima Appl Comput Harmon Anal 1 316ndash328 (1994)
[389] W-L Hwang C-S Lu P-C Chung Shape from texture Estimation of planar surfaceorientation through the ridge surfaces of continuous wavelet transform IEEE Trans ImageProc 7 773ndash780 (1998)
[390] I Iglewska-Nowak M Holschneider Frames of Poisson wavelets on the sphere ApplComput Harmon Anal 28 227ndash248 (2010)
[391] E Inoumlnuuml EP Wigner On the contraction of groups and their representations Proc NatAcad Sci U S 39 510ndash524 (1953)
[392] S Iqbal F Saif Generalized coherent states and their statistical characteristics in power-law potentials J Math Phys 52 082105 (2011)
[393] CJ Isham JR Klauder Coherent states for n-dimensional Euclidean groups E(n) andtheir application J MathPhys 32 607ndash620 (1991)
[394] L Jacques J-P Antoine Multiselective pyramidal decomposition of images Wavelets withadaptive angular selectivity Int J Wavelets Multires Inform Proc 5 785ndash814 (2007)
[395] L Jacques L Duval C Chaux G Peyreacute A panorama on multiscale geometric rep-resentations intertwining spatial directional and frequency selectivity Signal Proc 912699ndash2730 (2011)
[396] HR Jalali M K Tavassoly On the ladder operators and nonclassicality of generalizedcoherent state associated with a particle in an infinite square well preprint (2013)arXiv13034100v1 [quant-ph]
[397] C Johnston On the pseudo-dilation representations of Flornes Grossmann Holschneiderand Torreacutesani Appl Comput Harmon Anal 3 377ndash385 (1997)
[398] G Kaiser Phase-space approach to relativistic quantum mechanics I Coherent staterepresentation for massive scalar particles J MathPhys 18 952ndash959 (1977)
[399] G Kaiser Phase-space approach to relativistic quantum mechanics II Geometrical aspectsJ MathPhys 19 502ndash507 (1978)
[400] C Kalisa B Torreacutesani N-dimensional affine Weyl-Heisenberg wavelets Ann Inst HPoincareacute 59 201ndash236 (1993)
[401] W Kaminski J Lewandowski T Pawłowski Quantum constraints Dirac observables andevolution group averaging versus the Schroumldinger picture in LQC Class Quant Grav 26245016 (2009)
[402] MR Karim ST Ali A relativistic windowed Fourier transform preprint ConcordiaUniversity Montreacuteal (1997) (unpublished)
[403] M R Karim ST Ali M Bodruzzaman A relativistic windowed Fourier transform inProceedings of IEEE SoutheastCon 2000 Nashville Tennessee pp 253ndash260 (2000)
[404] T Kawazoe Wavelet transforms associated to a principal series representation of semisim-ple Lie groups I II Proc Japan Acad Ser A ndash Math Sci 71 154ndash157 158ndash160 (1995)
[405] T Kawazoe Wavelet transform associated to an induced representation of SL(n+ 2R)Ann Inst H Poincareacute 65 1ndash13 (1996)
References 563
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[407] P Kittipoom G Kutyniok W-Q Lim Construction of compactly supported shearletframes Constr Approx 35 21ndash72 (2012)
[408] J Kiukas P Lahti K Ylinenc Phase space quantization and the operator moment problemJ Math Phys 47 072104 (2006)
[409] JR Klauder Continuous-representation theory I Postulates of continuous-representationtheory J Math Phys 4 1055ndash1058 (1963)
[410] JR Klauder Continuous-representation theory II Generalized relation between quantumand classical dynamics J Math Phys 4 1058ndash1073 (1963)
[411] JR Klauder Path integrals for affine variables in Functional Integration Theory andApplications ed by J-P Antoine E Tirapegui (Plenum Press New York and London1980) pp 101ndash119
[412] JR Klauder Are coherent states the natural language of quantum mechanics inFundamental Aspects of Quantum Theory ed by V Gorini A Frigerio NATO ASI Seriesvol B 144 (Plenum Press New York 1986) pp 1ndash12
[413] JR Klauder Quantization without quantization Ann Phys (NY) 237 147ndash160 (1995)[414] JR Klauder Coherent states for the hydrogen atom J Phys A Math Gen 29 L293ndash
L296 (1996)[415] JR Klauder An affinity for affine quantum gravity Proc Steklov Inst Math 272 169ndash176
(2011) and references therein[416] JR Klauder RF Streater A wavelet transform for the Poincareacute group J Math Phys 32
1609ndash1611 (1991)[417] JR Klauder RF Streater Wavelets and the Poincareacute half-plane J Math Phys 35 471ndash
478 (1994)[418] JR Klauder K Penson J-M Sixdeniers Constructing coherent states through solutions
of Stieltjes and Hausdorff moment problems Phys Rev A 64 013817 (2001)[419] A Kleppner RL Lipsman The Plancherel formula for group extensions Ann Ec Norm
Sup 5 459ndash516 (1972)[420] AB Klimov C Muntildeoz Coherent isotropic and squeezed states in a N-qubit system Phys
Scr 87 038110 (2013)[421] A Klyashko Dynamical symmetry approach to entanglement in Physics and Theoretical
Computer Science From Numbers and Languages to (Quantum) Cryptography - NATOSecurity through Science Series D - Information and Communication Security vol 7 edby J-P Gazeau J Nesetril B Rovan (IOS Press Washington DC 2007) pp 25ndash54
[422] S Kobayashi Irreducibility of certain unitary representations J Math Soc Japan 20 638ndash642 (1968)
[423] K Kowalski J Rembielinski LC Papaloucas Coherent states for a quantum particle ona circle J Phys A Math Gen 29 4149ndash4167 (1996)
[424] K Kowalski J Rembielinski Quantum mechanics on a sphere and coherent states J PhysA Math Gen 33 6035ndash6048 (2000)
[425] K Kowalski J Rembielinski The Bargmann representation for the quantum mechanicson a sphere J Math Phys 42 4138ndash4147 (2001)
[426] C Kristjansen J Plefka GW Semenoff M Staudacher A new double-scaling limit ofN = 4 super-Yang-Mills theory and pp-wave strings Nuclear Phys B 643 3ndash30 (2002)
[427] M Kulesh M Holschneider MS Diallo Geophysical wavelet library Applications ofthe continuous wavelet transform to the polarization and dispersion analysis of signalsComput Geosci 34 1732ndash1752 (2008)
[428] R Kunze On the Frobenius reciprocity theorem for square integrable representationsPacific J Math 53 465ndash471 (1974)
[429] Y Kuroda A Wada T Yamazaki K Nagayama Postacquisition data processing methodfor suppression of the solvent signal I J Magn Reson 84 604ndash610 (1989)
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[431] G Kutyniok D Labate Resolution of the wavefront set using continuous shearlets TransAmer Math Soc 361 2719ndash2754 (2009)
[432] G Kutyniok W-Q Lim Compactly supported shearlets are optimally sparse J ApproxTheory 163 1564ndash1589 (2011)
[433] D Labate W-Q Lim G Kutyniok G Weiss Sparse multidimensional representationusing shearlets in Wavelets XI (San Diego CA 2005) ed by M Papadakis A Laine MUnser SPIE Proceedings vol 5914 (SPIE Bellingham WA 2005) pp 254ndash262
[434] P Lahti J-P Pellonpaumlauml Continuous variable tomographic measurements Phys Lett A373 3435ndash3438 (2009)
[435] Lambertrsquos projection see WikipediahttpenwikipediaorgwikiLambert_azimuthal_equal-area_projection
[436] J-P Leduc F Mujica R Murenzi MJT Smith Missile-tracking algorithm using target-adapted spatio-temporal wavelets in Automatic Object Recognition VII SPIE Proceedingsvol 5914 (SPIE Bellingham WA 1997) pp 400ndash411
[437] J-P Leduc F Mujica R Murenzi MJT Smith Spatio-temporal wavelet transforms formotion tracking in IEEE ICASSP 1997 vol 4 (1997) pp 3013ndash3016
[438] J-P Leduc F Mujica R Murenzi MJT Smith Spatio-temporal continuous waveletsapplied to missile warhead detection and tracking in SPIE VCIP rsquo97 vol 3024 ed byJ Biemond EJ Delp (1997) pp 787ndash798
[439] B Leistedt JD McEwen Exact wavelets on the ball IEEE Trans Signal Proc 60 1564ndash1589 (2012)
[440] PG Lemarieacute Y Meyer Ondelettes et bases hilbertiennes Rev Math Iberoamer 2 1ndash18(1986)
[441] C Lemke A Schuck Jr J-P Antoine D Sima Metabolite-sensitive analysis of magneticresonance spectroscopic signals using the continuous wavelet transform Meas SciTechnol 22 (2011) Art 114013
[442] J-M Leacutevy-Leblond Galilei group and non-relativistic quantum mechanics J Math Phys4 776-788 (1963)
[443] J-M Leacutevy-Leblond Galilei group and Galilean invariance in Group Theory and ItsApplications vol II ed by EM Loebl (Academic New York 1971) pp 221ndash299
[444] J-M Leacutevy-Leblond On the conceptual nature of the physical constants Riv Nuovo Cim7 187ndash214 (1977)
[445] EH Lieb The classical limit of quantum spin systems Commun Math Phys 31 327ndash340(1973)
[446] G Lindblad B Nagel Continuous bases for unitary irreducible representations of SU(11)Ann Inst H Poincareacute 13 27ndash56 (1970)
[447] W Lisiecki Kaumlhler coherent states orbits for representations of semisimple Lie groupsAnn Inst H Poincareacute 53 857ndash890 (1990)
[448] A Lisowska Moment-based fast wedgelet transform J Math Imaging Vis 39 180ndash192(2011)
[449] H Liu L Peng Admissible wavelets associated with the Heisenberg group Pacific JMath 180 101ndash123 (1997)
[450] E Livine S Speziale Physical boundary state for the quantum tetrahedron Class QuantGrav 25 085003 (2008)
[451] F Low Complete sets of wave packets in A Passion for Physics ndash Essay in Honor ofGeoffrey Chew ed by C DeTar (World Scientific Singapore 1985) pp 17ndash22
[452] G Mack All unitary ray representations of the conformal group SU(22) with positiveenergy Commun Math Phys 55 1ndash28 (1977)
[453] GW Mackey Imprimitivity for representations of locally compact groups I Proc NatAcad Sci 35 537ndash545 (1949)
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[456] SG Mallat Multifrequency channel decompositions of images and wavelet models IEEETrans Acoust Speech Signal Proc 37 2091ndash2110 (1989)
[457] SG Mallat A theory for multiresolution signal decomposition The wavelet representa-tion IEEE Trans Pattern Anal Machine Intell 11 674ndash693 (1989)
[458] S Mallat W-L Hwang Singularity detection and processing with wavelets IEEE TransInform Theory 38 617ndash643 (1992)
[459] S Mallat Z Zhang Matching pursuits with time frequency dictionaries IEEE TransSignal Proc 41 3397ndash3415 (1993)
[460] S Mallat S Zhong Wavelet maxima representation in Wavelets and Applications (ProcMarseille 1989) ed by Y Meyer (Masson and Springer Paris and Berlin 1991) pp 207ndash284
[461] VI Manrsquoko G Marmo ECG Sudarshan F Zaccaria f -oscillators and non-linearcoherent states Phys Scr 55 528ndash541 (1997)
[462] D Marinucci D Pietrobon A Baldi P Baldi P Cabella G Kerkyacharian P Natoli DPicard N Vittorio Spherical needlets for CMB data analysis Mon Not R Astron Soc383 539ndash545 (2008)
[463] D Marion M Ikura A Bax Improved solvent suppression in one- and two-dimensionalNMR spectra by convolution of time-domain data J Magn Reson 84 425ndash430 (1989)
[464] Y Meyer Principe drsquoincertitude bases hilbertiennes et algegravebres drsquoopeacuterateurs SeacuteminaireBourbaki 662 (1985ndash1986)
[465] Y Meyer Principe drsquoincertitude bases hilbertiennes et algegravebres drsquoopeacuterateurs Asteacuterisque145ndash146 209ndash223 (1987)
[466] Y Meyer H Xu Wavelet analysis and chirps Appl Comput Harmon Anal 4 366ndash379(1997)
[467] L Michel Invariance in quantum mechanics and group extensions in Group TheoreticalConcepts and Methods in Elementary Particle Physics ed by F Guumlrsey (Gordon andBreach New York and London 1964) pp 135ndash200
[468] J Mickelsson J Niederle Contractions of representations of the de Sitter groupsCommun Math Phys 27 167ndash180 (1972)
[469] MM Miller Convergence of the Sudarshan expansion for the diagonal coherent-stateweight functional J Math Phys 9 1270ndash1274 (1968)
[470] V F Molchanov Harmonic analysis on homogeneous spaces in Representation Theoryand Noncommutative Harmonic Analysis II ed by AA Kirillov (Springer Berlin 1995)
[471] MI Monastyrsky AM Perelomov Coherent states and symmetric spaces II Ann InstH Poincareacute 23 23ndash48 (1975)
[472] B Moran S Howard D Cochran Positive-operator-valued measures A general settingfor frames in Excursions in Harmonic Analysis vol 1 2 ed by TD Andrews R BalanJJ Benedetto W Czaja KA Okoudjou (Birkhaumluser Boston 2013) pp 49ndash64
[473] H Moscovici Coherent states representations of nilpotent Lie groups Commun MathPhys 54 63ndash68 (1977)
[474] H Moscovici A Verona Coherent states and square integrable representations Ann InstH Poincareacute 29 139ndash156 (1978)
[475] F Mujica R Murenzi MJT Smith J-P Leduc Robust tracking in compressed imagesequences J Electr Imaging 7 746ndash754 (1998)
[476] R Murenzi Wavelet transforms associated to the n-dimensional Euclidean group withdilations Signals in more than one dimension in Wavelets Time-Frequency Methodsand Phase Space (Proc Marseille 1987) ed by J-M Combes A Grossmann PTchamitchian 2nd edn (Springer Berlin 1990) pp 239ndash246
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[479] MA Naımark Dokl Akad Nauk SSSR 41 359ndash361 (1943) see also B Sz-NagyExtensions of linear transformations in Hilbert space which extend beyond this spaceAppendix to F Riesz B Sz-Nagy Functional Analysis (Frederick Ungar New York 1960)
[480] FJ Narcowich P Petrushev JD Ward Localized tight frames on spheres SIAM J MathAnal 38 574ndash594 (2006)
[481] M Nauenberg Quantum wave packets on Kepler elliptic orbits Phys Rev A 40 1133ndash1136 (1989)
[482] M Nauenberg C Stroud J Yeazell The classical limit of an atom Scient Amer 27024ndash29 (1994)
[483] H Neumann Transformation properties of observables Helv Phys Acta 45 811ndash819(1972)
[484] U Niederer The maximal kinematical invariance group of the free Schroumldinger equationHelv Phys Acta 45 802ndash881 (1972)
[485] MM Nieto LM Simmons Jr Coherent states for general potentials I Formalism IIConfining one-dimensional examples III Nonconfining one-dimensional examples PhysRev D 20 1321ndash1331 1332ndash1341 1342ndash1350 (1979)
[486] MM Nieto LM Simmons Jr Coherent states for general potentials Phys Rev Lett 41207ndash210 (1987)
[487] A Odzijewicz On reproducing kernels and quantization of states Commun Math Phys114 577ndash597 (1988)
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[489] A Odzijewicz Quantum algebras and q-special functions related to coherent states mapsof the disc Commun Math Phys 192 183ndash215 (1998)
[490] A Odzijewicz M Horowski A Tereszkiewicz Integrable multi-boson systems andorthogonal polynomials J Phys A Math Gen 34 4353ndash4376 (2001)
[491] G Oacutelafsson B Oslashrsted The holomorphic discrete series for affine symmetric spaces JFunct Anal 81 126ndash159 (1988)
[492] G Oacutelafsson H Schlichtkrull Representation theory Radon transform and the heatequation on a Riemannian symmetric space Contemp Math 449 315ndash344 (2008)
[493] E Onofri A note on coherent state representations of Lie groups J Math Phys 16 1087ndash1089 (1975)
[494] E Onofri Dynamical quantization of the Kepler manifold J Math Phys 17 401ndash408(1976)
[495] D Oriti R Pereira L Sindoni Coherent states in quantum gravity A construction basedon the flux representation of loop quantum gravity J Phys A Math Theor 45 244004(2012)
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[498] Z Pasternak-Winiarski On reproducing kernels for holomorphic vector bundles inQuantization and Infinite Dimensional Systems (Proc Białowieza Poland 1993) ed by J-P Antoine ST Ali W Lisiecki IM Mladenov A Odzijewicz (Plenum Press New Yorkand London 1994) pp 109ndash112
[499] T Paul Affine coherent states and the radial Schroumldinger equation I preprint CPT-84P1710 (1984) (unpublished)
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[501] AM Perelomov On the completeness of a system of coherent states Theor Math Phys6 156ndash164 (1971)
[502] AM Perelomov Coherent states for arbitrary Lie group Commun Math Phys 26 222ndash236 (1972)
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[504] M Perroud Projective representations of the Schroumldinger group Helv Phys Acta 50 233ndash252 (1977)
[505] J Phillips A note on square-integrable representations J Funct Anal 20 83ndash92 (1975)[506] D Pietrobon P Baldi D Marinucci Integrated Sachs-Wolfe effect from the cross
correlation of WMAP3 year and the NRAO VLA sky survey data New results andconstraints on dark energy Phys Rev D 74 043524 (2006)
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[508] V Pop D Rosca Generalized piecewise constant orthogonal wavelet bases on 2D-domains Appl Anal 90 715ndash723 (2011)
[509] G Poumlschl E Teller Bemerkungen zur Quantenmechanik des anharmonischen OszillatorsZ Physik 83 143ndash151 (1933)
[510] D Potts G Steidl M Tasche Kernels of spherical harmonics and spherical frames inAdvanced Topics in Multivariate Approximation ed by F Fontanella K Jetter PJ Laurent(World Scientific Singapore 1996) pp 287ndash301
[511] E Prugovecki Consistent formulation of relativistic dynamics for massive spin-zeroparticles in external fields Phys Rev D 18 3655ndash3673 (1978) (Appendix C)
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[514] C Quesne Generalized vector coherent states of sp(2NR) vector operators and ofsp(2NR) sup u(N) reduced Wigner coefficients J Phys A Math Gen 24 2697ndash2714(1991)
[515] JM Radcliffe Some properties of spin coherent states J Phys A Math Gen 4 313ndash323(1971)
[516] A Rahimi A Najati YN Dehghan Continuous frames in Hilbert spaces Methods FunctAnal Topol 12 170ndash182 (2006)
[517] H Rauhut M Roumlsler Radial multiresolution in dimension three Constr Approx 22 193ndash218 (2005)
[518] JH Rawnsley Coherent states and Kaumlhler manifolds Quart J Math Oxford 28(2) 403ndash415 (1977)
[519] J Renaud The contraction of the SU(11) discrete series of representations by means ofcoherent states J Math Phys 37 3168ndash3179 (1996)
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[521] D Robert La coheacuterence dans tous ses eacutetats SMF Gazette 132 (2012)[522] JE Roberts The Dirac bra and ket formalism J Math Phys 7 1097ndash1104 (1966)[523] JE Roberts Rigged Hilbert spaces in quantum mechanics Commun Math Phys 3 98ndash
119 (1966)[524] S Roques F Bourzeix K Bouyoucef Soft-thresholding technique and restoration of
3C273 jet Astrophys Space Sci Nr 239 297ndash304 (1996)[525] D Rosca Haar wavelets on spherical triangulations in Advances in Multiresolution for
Geometric Modelling ed by NA Dogson MS Floater MA Sabin (Springer Berlin2005) pp 407ndash419
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501ndash511 (2007)[529] D Rosca Wavelet bases on the sphere obtained by radial projection J Fourier Anal Appl
13 421ndash434 (2007)[530] D Rosca Piecewise constant wavelets on triangulations obtained by 1ndash3 splitting Int J
Wavelets Multiresolut Inf Process 6 209ndash222 (2008)[531] D Rosca On a norm equivalence on L2(S2) Results Math 53 399ndash405 (2009)[532] D Rosca New uniform grids on the sphere Astron Astrophys 520 (2010) Art A63[533] D Rosca Uniform and refinable grids on elliptic domains and on some surfaces of
revolution Appl Math Comput 217 7812ndash7817 (2011)[534] D Rosca Wavelet analysis on some surfaces of revolution via area preserving projection
Appl Comput Harmon Anal 30 262ndash272 (2011)[535] D Rosca J-P Antoine Locally supported orthogonal wavelet bases on the sphere via
stereographic projection Math Probl Eng 2009 124904 (2009)[536] D Rosca J-P Antoine Constructing wavelet frames and orthogonal wavelet bases on the
sphere in Recent Advances in Signal Processing ed by S Miron (IN-TECH ViennaAustria and Rijeka Croatia 2010) pp 59ndash76
[537] D Rosca G Plonka Uniform spherical grids via area preserving projection from the cubeto the sphere J Comput Appl Math 236 1033ndash1041 (2011)
[538] D Rosca G Plonka An area preserving projection from the regular octahedron to thesphere Results Math 63 429ndash444 (2012)
[539] H Rossi M Vergne Analytic continuation of the holomorphic discrete series for a semi-simple Lie group Acta Math 136 1ndash59 (1976)
[540] DJ Rotenberg Application of Sturmian functions to the Schroedinger three-body prob-lem Elastic e+ndashH scattering Ann Phys (NY) 19 262ndash278 (1962)
[541] C Rovelli Zakopane lectures on loop gravity in Proceedings of 3rd Quantum Gravityand Quantum Geometry School 28 Febndash13 March 2011 (Zakopane Poland 2011)arXiv11023660v5
[542] C Rovelli S Speziale A semiclassical tetrahedron Class Quant Grav 23 5861ndash5870(2006)
[543] DJ Rowe Coherent state theory of the noncompact symplectic group J Math Phys 252662ndash2271 (1984)
[544] DJ Rowe Microscopic theory of the nuclear collective model Rep Prog Phys 48 1419ndash1480 (1985)
[545] DJ Rowe Vector coherent state representations and their inner products J Phys A MathGen 45 244003 (2012) (This paper belongs to the special issue [38])
[546] DJ Rowe J Repka Vector-coherent-state theory as a theory of induced representationsJ Math Phys 32 2614ndash2634 (1991)
[547] DJ Rowe G Rosensteel R Gilmore Vector coherent state representation theory J MathPhys 26 2787ndash2791 (1985)
[548] A Royer Phase states and phase operators for the quantum harmonic oscillator Phys RevA 53 70ndash108 (1996)
[549] J Saletan Contraction of Lie groups J Math Phys 2 1ndash21 (1961)[550] G Saracco A Grossmann P Tchamitchian Use of wavelet transforms in the study of
propagation of transient acoustic signals across a plane interface between two homoge-neous media in Wavelets Time-Frequency Methods and Phase Space (Proc Marseille1987) ed by J-M Combes A Grossmann P Tchamitchian 2nd edn (Springer Berlin1990) pp 139ndash146
[551] P Schroumlder W Sweldens Spherical wavelets Efficiently representing functions on thesphere in Computer Graphics Proceedings (SIGGRAPH95) (ACM Siggraph Los Angeles1995) pp 161ndash175
References 569
[552] E Schroumldinger Der stetige Uumlbergang von der Mikro- zur Makromechanik Naturwiss 14664ndash666 (1926)
[553] S Scodeller Oslash Rudjord FK Hansen D Marinucci D Geller A Mayeli IntroducingMexican needlets for CMB analysis Issues for practical applications and comparison withstandard needlets Astrophys J 733 (2011) Art 121
[554] H Scutaru Coherent states and induced representations Lett Math Phys 2 101ndash107(1977)
[555] B Simon Distributions and their Hermite expansions J Math Phys 12 140ndash148 (1971)[556] B Simon The classical moment problem as a self-adjoint finite difference operator Adv
Math 137 82ndash203 (1998)[557] R Simon ECG Sudarshan N Mukunda Gaussian pure states in quantum mechanics
and the symplectic group Phys Rev A37 3028ndash3038 (1988)[558] S Sivakumar Studies on nonlinear coherent states J Opt B Quant Semiclass Opt 2
R61ndashR75 (2000)[559] E Slezak A Bijaoui G Mars Identification of structures from galaxy counts Use of the
wavelet transform Astron Astroph 227 301ndash316 (1990)[560] A Solomon A characteristic functional for deformed photon phenomenology Phys Lett
A 196 29ndash34 (1994)[561] SB Sontz Paragrassmann algebras as quantum spaces Part I Reproducing kernels in
Geometric Methods in Physics XXXI Workshop 2012 (Trends in Mathematics ed byP Kielanowski et al Birkhaumluser Verlag Basel 2013) pp 47ndash63
[562] SB Sontz Paragrassmann algebras as quantum spaces Part II Toeplitz operators J OperTh (2013 to appear) arXiv12055493
[563] SB Sontz A reproducing kernel and Toeplitz operators in the quantum plane Preprint(2013) arXiv13056986 [math-ph]
[564] SB Sontz Toeplitz quantization of an algebra with conjugation Preprint (2013)arXiv13085454 [math-ph]
[565] M Spera On a generalized Uncertainty Principle coherent states and the moment mapJ Geom Phys 12 165ndash182 (1993)
[566] J-L Starck EJ Candegraves DL Donoho The curvelet transform for image denoising IEEETrans Image Proc 11 670ndash684 (2002)
[567] J-L Starck DL Donoho E J Candegraves Astronomical image representation by the curvelettransform Astron Astroph 398 785ndash800 (2003)
[568] J-L Starck Y Moudden P Abrial M Nguyen Wavelets ridgelets and curvelets on thesphere Astron Astroph 446 1191ndash1204 (2006)
[569] MB Stenzel The Segal-Bargmann transform on a symmetric space of compact type JFunct Analysis 165 44ndash58 (1994)
[570] ECG Sudarshan Equivalence of semiclassical and quantum mechanical descriptions ofstatistical light beams Phys Rev Lett 10 277ndash279 (1963)
[571] A Suvichakorn H Ratiney A Bucur S Cavassila J-P Antoine Toward a quantitativeanalysis of in vivo magnetic resonance proton spectroscopic signals using the continuousMorlet wavelet transform Meas Sci Technol 20 (2009) Art 104029
[572] W Sweldens The lifting scheme A custom-design construction of biorthogonal waveletsApplied Comput Harmon Anal 3 1186ndash1200 (1996)
[573] W Sweldens The lifting scheme A construction of second generation wavelets SIAM JMath Anal 29 511ndash546 (1998)
[574] FH Szafraniec The reproducing kernel Hilbert space and its multiplication operatorsin Complex Analysis and Related Topics ed by E Ramirez de Arellano et al OperatorTheory Advances and Applications vol 114 (Birkhaumluser Basel 2000) pp 254ndash263
[575] FH Szafraniec Multipliers in the reproducing kernel Hilbert space subnormality andnoncommutative complex analysis in Reproducing Kernel Spaces and Applications edby D Alpay Operator Theory Advances and Applications vol 143 (Birkhaumluser Basel2003) pp 313ndash331
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[577] MC Teich BEA Saleh Squeezed states of light Quantum Opt 1 152ndash191 (1989)[578] R Terrier L Demanet IA Grenier J-P Antoine Wavelet analysis of EGRET data in
Proceedings of the 27th International Cosmic Ray Conference (ICRC 2001) (CopernicusGesellschaft DE 2001) pp 2923ndash2926
[579] T Thiemann Gauge field theory coherent states (GCS) 1 General properties Class QuantGrav 18 2025ndash2064 (2001)
[580] T Thiemann O Winkler Gauge field theory coherent states (GCS) 2 Peakednessproperties Class Quant Grav 18 2561ndash2636 (2001)
[581] T Thiemann O Winkler Gauge field theory coherent states (GCS) 3 Ehrenfest theoremsClass Quant Grav 18 4629ndash4682 (2001)
[582] T Thiemann O Winkler Gauge field theory coherent states (GCS) 4 Infinite tensorproduct and thermodynamical limit Class Quant Grav 18 4997ndash5054 (2001)
[583] K Thirulagasanthar ST Ali Regular subspaces of a quaternionic Hilbert space fromquaternionic Hermite polynomials and associated coherent states J Math Phys 54013506 (2013)
[584] K Thirulogasanthar G Honnouvo A Krzyzak Coherent states and Hermite polynomialson quaternionic Hilbert spaces J Phys A Math Theor 43 385205 (2010)
[585] Tokamak see Wikipedia httpenwikipediaorgwikiTokamak[586] B Torreacutesani Wavelets associated with representations of the affine Weyl-Heisenberg
group J Math Phys 32 1273ndash1279 (1991)[587] B Torreacutesani Time-frequency representation Wavelet packets and optimal decomposition
Ann Inst H Poincareacute 56 215ndash234 (1992)[588] B Torreacutesani Position-frequency analysis for signals defined on spheres Signal Proc 43
341ndash346 (2005)[589] DA Trifonov Generalized intelligent states and squeezing J Math Phys 35 2297ndash2308
(1994)[590] AS Trushechkin IV Volovich Localization properties of squeezed quantum states in
nanoscale space domains preprint (2013) arXiv13046277v1 [quant-ph][591] M Unser N Chenouard A unifying parametric framework for 2D steerable wavelet
transforms SIAM J Imaging Sci 6 102ndash135 (2013)[592] P Vandergheynst J-F Gobbers Directional dyadic wavelet transforms Design and
algorithms IEEE Trans Image Proc 11 363ndash372 (2002)[593] P Vandergheynst J-P Antoine E Van Vyve A Goldberg I Doghri Modelling and
simulation of an impact test using wavelets analytical and finite element models Int JSolids Struct 38 5481ndash5508 (2001)
[594] L Vanhamme RD Fierro S Van Huffel R de Beer Fast removal of residual water inproton spectra J Magn Reson 132 197ndash203 (1998)
[595] J Ville Theacuteorie et applications de la notion de signal analytique Cacircbles et Trans 2 61ndash74(1948)
[596] J Voisin On some unitary representations of the Galilei group I Irreducible representa-tions J Math Phys 6 1519ndash1529 (1965)
[597] A Vourdas Analytic representations in quantum mechanics J Phys A Math Gen 39R65ndashR141 (2006)
[598] DF Walls Squeezed states of light Nature 306 141ndash146 (1983)[599] YK Wang FT Hioe Phase transition in the Dicke maser model Phys Rev A 7 831ndash836
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Recogn Artif Intell 26 1255011 (2012)[601] I Weinreich A construction of C1-wavelets on the two-dimensional sphere Appl Comput
Harmon Anal 10 1ndash26 (2001)[602] H Weyl Quantenmechanik und Gruppentheorie Z Phys 46 1ndash46 (1927)
References 571
[603] Y Wiaux L Jacques P Vandergheynst Correspondence principle between spherical andEuclidean wavelets Astrophys J 632 15ndash28 (2005)
[604] Y Wiaux L Jacques P Vielva P Vandergheynst Fast directional correlation on the spherewith steerable filters Astrophys J 652 820ndash832 (2006)
[605] Y Wiaux JD McEwen P Vandergheynst O Blanc Exact reconstruction with directionalwavelets on the sphere Mon Not R Astron Soc 388 770ndash788 (2008)
[606] WM Wieland Complex Ashtekar variables and reality conditions for Holstrsquos action AnnHenri Poincareacute 13 425ndash448 (2012)
[607] EP Wigner On the quantum correction for thermodynamic equilibrium Phys Rev 40749ndash759 (1932)
[608] RM Willette RD Nowak Platelets A multiscale approach for recovering edges andsurfaces in photon-limited medical imaging IEEE Trans Med Imaging 22 332ndash350(2003)
[609] W Wisnoe P Gajan A Strzelecki C Lempereur J-M Matheacute The use of the two-dimensional wavelet transform in flow visualization processing in Progress in WaveletAnalysis and Applications (Proc Toulouse 1992) ed by Y Meyer S Roques (EdFrontiegraveres Gif-sur-Yvette 1993) pp 455ndash458
[610] K Woacutedkiewicz On the quantum mechanics of squeezed states J Modern Optics 34 941ndash948(1987)
[611] JA Yeazell M Mallalieu CR Stroud Jr Observation of the collapse and revival of aRydberg electronic wave packet Phys Rev Lett 64 2007ndash2010 (1990)
[612] JA Yeazell CR Stroud Jr Observation of fractional revivals in the evolution of aRydberg atomic wave packet Phys Rev A 43 5153ndash5156 (1991)
[613] HP Yuen Two-photon coherent states of the radiation field Phys Rev A 13 2226ndash2243(1976)
[614] J Zak Balian-Low theorem for Landau levels Phys Rev Lett 79 533ndash536 (1997)[615] J Zak Orthonormal sets of localized functions for a Landau level J Math Phys 39 4195ndash
4200 (1998) and references quoted there[616] AA Zakharova On the properties of generalized frames Math Notes 83 190ndash200 (2008)[617] W-M Zhang DH Feng R Gilmore Coherent states Theory and some applications Rev
Mod Phys 26 867ndash927 (1990)[618] I Zlatev W-M Zhang DH Feng Possibility that Schroumldingerrsquos conjecture for the
hydrogen atom coherent states is not attainable Phys Rev A 50 R1973ndashR1975 (1994)[619] WH Zurek Decoherence einselection and the quantum origins of the classical Rev Mod
Phys 75 715ndash775 (2003)[620] WH Zurek S Habib JP Paz Coherent states via decoherence Phys Rev Lett 70 1187ndash
1190 (1993)[621] K Zyczkowski Squeezed states in a quantum chaotic system J Phys A Math Theor 22
of SU(11) 81 296 297HilbertClowast-modules 164holomorphic 140nonholomorphic 151nonlinear 146of affine Galilei group 505of affine Poincareacute group 509of affine Weyl-Heisenberg group GaWH
497of compact semisimple Lie groups 174of Euclidean group E(n) 266of Galilei group G (11) 290of isochronous Galilei group 237of non-semisimple Lie groups 179of noncompact semisimple Lie groups 177of Poincareacute group Puarr
+(11) 283massless case 288
of Poincareacute group Puarr+(13) 279
of Schroumldinger group 508quasi-coherent states 186quaternionic 164
ST Ali et al Coherent States Wavelets and Their Generalizations Theoreticaland Mathematical Physics DOI 101007978-1-4614-8535-3copy Springer Science+Business Media New York 2014
573
574 Index
coherent states (CS) (cont)spin or SU(2) 175square integrable covariant 166 180 264vector (VCS) 73 108 112 170weighted 184 523
of affine Weyl-Heisenberg group GaWH497
of Poincareacute group Puarr+(11) 284
cohomology group 393 403coboundaries 403cochains 402cocycle 403
algebraic 387Cauchy 418Cauchy-Paul 354 419 425conical 418difference 417 462directional 416 440kinematical 499local 488metabolite-based 355 374minimal uncertainty 425multiselective 440on a graph 493on the sphere S
2 458on the sphere S
n 479on the torus T2 481steerable 439von Mises 440
wedgelet transform 455Wigner function 322Wigner-Ville transform 349Windowed Fourier or Gabor transform 349
ZZak transform 518
References
A Books and Theses
B Articles
Index
References 547
[17] ST Ali H-D Doebner Ordering problem in quantum mechanics Prime quantization anda physical interpretation Phys Rev A 41 1199ndash1210 (1990)
[18] ST Ali GG Emch Geometric quantization Modular reduction theory and coherentstates J Math Phys 27 2936ndash2943 (1986)
[19] ST Ali M Engliš J-P Gazeau Vector coherent states from Plancherelrsquos theorem andClifford algebras J Phys A 37 6067ndash6089 (2004)
[20] ST Ali MEH Ismail Some orthogonal polynomials arising from coherent states JPhys A 45 125203 (2012) (16pp)
[21] ST Ali UA Mueller Quantization of a classical system on a coadjoint orbit of thePoincareacute group in 1+1 dimensions J Math Phys 35 4405ndash4422 (1994)
[22] ST Ali E Prugovecki Systems of imprimitivity and representations of quantum mechan-ics on fuzzy phase spaces J Math Phys 18 219ndash228 (1977)
[23] ST Ali E Prugovecki Mathematical problems of stochastic quantum mechanics Har-monic analysis on phase space and quantum geometry Acta Appl Math 6 1ndash18 (1986)
[24] ST Ali E Prugovecki Extended harmonic analysis of phase space representation for theGalilei group Acta Appl Math 6 19ndash45 (1986)
[25] ST Ali E Prugovecki Harmonic analysis and systems of covariance for phase spacerepresentation of the Poincareacute group Acta Appl Math 6 47ndash62 (1986)
[26] ST Ali J-P Antoine J-P Gazeau De Sitter to Poincareacute contraction and relativisticcoherent states Ann Inst H Poincareacute 52 83ndash111 (1990)
[27] ST Ali J-P Antoine J-P Gazeau Square integrability of group representations onhomogeneous spaces I Reproducing triples and frames Ann Inst H Poincareacute 55 829ndash855 (1991)
[28] ST Ali J-P Antoine J-P Gazeau Square integrability of group representations onhomogeneous spaces II Coherent and quasi-coherent states The case of the Poincareacutegroup Ann Inst H Poincareacute 55 857ndash890 (1991)
[29] ST Ali J-P Antoine J-P Gazeau Continuous frames in Hilbert space Ann Phys(NY)222 1ndash37 (1993)
[30] ST Ali J-P Antoine J-P Gazeau Relativistic quantum frames Ann Phys(NY) 222 38ndash88 (1993)
[31] ST Ali J-P Antoine J-P Gazeau UA Mueller Coherent states and their generalizationsA mathematical overview Rev Math Phys 7 1013ndash1104 (1995)
[32] ST Ali J-P Gazeau MR Karim Frames the β -duality in Minkowski space and spincoherent states J Phys A Math Gen 29 5529ndash5549 (1996)
[33] ST Ali M Engliš Quantization methods A guide for physicists and analysts Rev MathPhys 17 391ndash490 (2005)
[34] ST Ali J-P Gazeau B Heller Coherent states and Bayesian duality J Phys A MathTheor 41 365302 (2008)
[35] ST Ali L Balkovaacute EMF Curado J-P Gazeau MA Rego-Monteiro LMCSRodrigues K Sekimoto Non-commutative reading of the complex plane through Delonesequences J Math Phys 50 043517 (2009)
[36] ST Ali C Carmeli T Heinosaari A Toigo Commutative POVMS and fuzzy observ-ables Found Phys 39 593ndash612 (2009)
[37] ST Ali T Bhattacharyya SS Roy Coherent states on Hilbert modules J Phys A MathTheor 44 275202 (2011)
[38] ST Ali J-P Antoine F Bagarello J-P Gazeau (Guest Editors) Coherent states Acontemporary panorama preface to a special issue on Coherent states Mathematical andphysical aspects J Phys A Math Gen 45(24) (2012)
[39] ST Ali F Bagarello J-P Gazeau Quantizations from reproducing kernel spaces AnnPhys (NY) 332 127ndash142 (2013)
[40] STAli K Goacuterska A Horzela F Szafraniec Squeezed states and Hermite polynomials ina complex variable Preprint (2013) arXiv13084730v1 [quant-phy]
[41] P Aniello G Cassinelli E De Vito A Levrero Square-integrability of induced represen-tations of semidirect products Rev Math Phys 10 301ndash313 (1998)
548 References
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[43] J-P Antoine Remarques sur le vecteur de Runge-Lenz Ann Soc Scient Bruxelles 80160ndash168 (1966)
[44] J-P Antoine Etude de la deacutegeacuteneacuterescence orbitale du potentiel coulombien en theacuteorie desgroupes I II Ann Soc Scient Bruxelles 80 169ndash184 (1966)
[45] J-P Antoine Etude de la deacutegeacuteneacuterescence orbitale du potentiel coulombien en theacuteorie desgroupes I II Ann Soc Scient Bruxelles 81 49ndash68 (1967)
[46] J-P Antoine Dirac formalism and symmetry problems in quantum mechanics I Generaldirac formalism J Math Phys 10 53ndash69 (1969)
[47] J-P Antoine Dirac formalism and symmetry problems in quantum mechanics II Symme-try problems J Math Phys 10 2276ndash2290 (1969)
[48] J-P Antoine Quantum mechanics beyond Hilbert space in Irreversibility and Causality mdashSemigroups and Rigged Hilbert Spaces ed by A Boumlhm H-D Doebner P KielanowskiLecture Notes in Physics vol 504 (Springer Berlin 1998) pp 3ndash33
[49] J-P Antoine Discrete wavelets on abelian locally compact groups Rev Cien Math(Habana) 19 3ndash21 (2003)
[50] J-P Antoine Introduction to precursors in physics Affine coherent states in FundamentalPapers in Wavelet Theory ed by C Heil D Walnut (Princeton University Press PrincetonNJ 2006) pp 113ndash116
[51] J-P Antoine F Bagarello Wavelet-like orthonormal bases for the lowest Landau levelJ Phys A Math Gen 27 2471ndash2481 (1994)
[52] J-P Antoine P Balazs Frames and semi-frames J Phys A Math Theor 44 205201(2011) (25 pages) Corrigendum J-P Antoine P Balazs Frames and semi-frames J PhysA Math Theor 44 479501 (2011) (2 pages)
[53] J-P Antoine P Balazs Frames semi-frames and Hilbert scales Numer Funct AnalOptim 33 736ndash769 (2012)
[54] J-P Antoine A Coron Time-frequency and time-scale approach to magnetic resonancespectroscopy J Comput Methods Sci Eng (JCMSE) 1 327ndash352 (2001)
[55] J-P Antoine AL Hohoueacuteto Discrete frames of Poincareacute coherent states in 1+3 dimen-sions J Fourier Anal Appl 9 141ndash173 (2003)
[56] J-P Antoine I Mahara Galilean wavelets Coherent states for the affine Galilei groupJ Math Phys 40 5956ndash5971 (1999)
[57] J-P Antoine U Moschella Poincareacute coherent states The two-dimensional massless caseJ Phys A Math Gen 26 591ndash607 (1993)
[58] J-P Antoine R Murenzi Two-dimensional directional wavelets and the scale-anglerepresentation Signal Process 52 259ndash281 (1996)
[59] J-P Antoine R Murenzi Two-dimensional continuous wavelet transform as linear phasespace representation of two-dimensional signals in Wavelet Applications IV SPIE Pro-ceedings vol 3078 (SPIE Bellingham WA 1997) pp 206ndash217
[60] J-P Antoine D Rosca The wavelet transform on the two-sphere and related manifolds mdashA review in Optical and Digital Image Processing SPIE Proceedings vol 7000 (2008)pp 70000B-1ndash15
[61] J-P Antoine D Speiser Characters of irreducible representations of simple Lie groupsJ Math Phys 5 1226ndash1234 (1964)
[62] J-P Antoine P Vandergheynst Wavelets on the n-sphere and related manifolds J MathPhys 39 3987ndash4008 (1998)
[63] J-P Antoine P Vandergheynst Wavelets on the 2-sphere A group-theoretical approachAppl Comput Harmon Anal 7 262ndash291 (1999)
[64] J-P Antoine P Vandergheynst Wavelets on the two-sphere and other conic sections JFourier Anal Appl 13 369ndash386 (2007)
[65] J-P Antoine M Duval-Destin R Murenzi B Piette Image analysis with 2D wavelettransform Detection of position orientation and visual contrast of simple objects inWavelets and Applications (Proc Marseille 1989) ed by Y Meyer (Masson and SpringerParis and Berlin 1991) pp144ndash159
References 549
[66] J-P Antoine P Carrette R Murenzi B Piette Image analysis with 2D continuous wavelettransform Signal Process 31 241ndash272 (1993)
[67] J-P Antoine P Vandergheynst K Bouyoucef R Murenzi Alternative representations ofan image via the 2D wavelet transform Application to character recognition in VisualInformation Processing IV SPIE Proceedings vol 2488 (SPIE Bellingham WA 1995)pp 486ndash497
[68] J-P Antoine R Murenzi P Vandergheynst Two-dimensional directional wavelets inimage processing Int J Imaging Syst Tech 7 152ndash165 (1996)
[69] J-P Antoine D Barache RM Cesar Jr LF Costa Shape characterization with thewavelet transform Signal Process 62 265ndash290 (1997)
[70] J-P Antoine P Antoine B Piraux Wavelets in atomic physics in Spline Functions andthe Theory of Wavelets ed by S Dubuc G Deslauriers CRM Proceedings and LectureNotes vol 18 (AMS Providence RI 1999) pp261ndash276
[71] J-P Antoine P Antoine B Piraux Wavelets in atomic physics and in solid state physicsin Wavelets in Physics Chap 8 ed by JC van den Berg (Cambridge University PressCambridge 1999)
[72] J-P Antoine R Murenzi P Vandergheynst Directional wavelets revisited Cauchywavelets and symmetry detection in patterns Appl Comput Harmon Anal 6 314ndash345(1999)
[73] J-P Antoine L Jacques R Twarock Wavelet analysis of a quasiperiodic tiling withfivefold symmetry Phys Lett A 261 265ndash274 (1999)
[74] J-P Antoine L Jacques P Vandergheynst Penrose tilings quasicrystals and wavelets inWavelet Applications in Signal and Image Processing VII SPIE Proceedings vol 3813(SPIE Bellingham WA 1999) pp 28ndash39
[75] J-P Antoine YB Kouagou D Lambert B Torreacutesani An algebraic approach to discretedilations Application to discrete wavelet transforms J Fourier Anal Appl 6 113ndash141(2000)
[76] J-P Antoine A Coron J-M Dereppe Water peak suppression Time-frequency vs time-scale approach J Magn Reson 144 189ndash194 (2000)
[77] J-P Antoine J-P Gazeau P Monceau J R Klauder K Penson Temporally stablecoherent states for infinite well and Poumlschl-Teller potentials J Math Phys 42 2349ndash2387(2001)
[78] J-P Antoine A Coron C Chauvin Wavelets and related time-frequency techniques inmagnetic resonance spectroscopy NMR Biomed 14 265ndash270 (2001)
[79] J-P Antoine L Demanet J-F Hochedez L Jacques R Terrier E Verwichte Applicationof the 2-D wavelet transform to astrophysical images Phys Mag 24 93ndash116 (2002)
[80] J-P Antoine L Demanet L Jacques P Vandergheynst Wavelets on the sphere Imple-mentation and approximations Appl Comput Harmon Anal 13 177ndash200 (2002)
[81] J-P Antoine I Bogdanova P Vandergheynst The continuous wavelet transform on conicsections Int J Wavelets Multires Inform Proc 6 137ndash156 (2007)
[82] J-P Antoine D Rosca P Vandergheynst Wavelet transform on manifolds Old and newapproaches Appl Comput Harmon Anal 28 189ndash202 (2010)
[83] P Antoine B Piraux A Maquet Time profile of harmonics generated by a single atom ina strong electromagnetic field Phys Rev A 51 R1750ndashR1753 (1995)
[84] P Antoine B Piraux DB Miloševic M Gajda Generation of ultrashort pulses ofharmonics Phys Rev A 54 R1761ndashR1764 (1996)
[85] P Antoine B Piraux DB Miloševic M Gajda Temporal profile and time control ofharmonic generation Laser Phys 7 594ndash601 (1997)
[86] Apollonius see Wikipedia httpenwikipediaorgwikiApollonius_of_Perga[87] FT Arecchi E Courtens R Gilmore H Thomas Atomic coherent states in quantum
optics Phys Rev A 6 2211ndash2237 (1972)[88] I Aremua J-P Gazeau MN Hounkonnou Action-angle coherent states for quantum
systems with cylindric phase space J Phys A Math Theor 45 335302 (2012)
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[90] F Argoul A Arneacuteodo J Elezgaray G Grasseau R Murenzi Wavelet analysis of theself-similarity of diffusion-limited aggregates and electrodeposition clusters Phys Rev A41 5537ndash5560 (1990)
[91] TA Arias Multiresolution analysis of electronic structure Semicardinal and waveletbases Rev Mod Phys 71 267ndash312 (1999)
[92] A Arneacuteodo F Argoul E Bacry J Elezgaray E Freysz G Grasseau JF Muzy BPouligny Wavelet transform of fractals in Wavelets and Applications (Proc Marseille1989) ed by Y Meyer (Masson and Springer Paris and Berlin 1991) pp 286ndash352
[93] A Arneacuteodo E Bacry JF Muzy The thermodynamics of fractals revisited with waveletsPhysica A 213 232ndash275 (1995)
[94] A Arneacuteodo E Bacry JF Muzy Oscillating singularities in locally self-similar functionsPhys Rev Lett 74 4823ndash4826 (1995)
[95] A Arneacuteodo E Bacry PV Graves JF Muzy Characterizing long-range correlations inDNA sequences from wavelet analysis Phys Rev Lett 74 3293ndash3296 (1996)
[96] A Arneacuteodo Y drsquoAubenton E Bacry PV Graves JF Muzy C Thermes Wavelet basedfractal analysis of DNA sequences Physica D 96 291ndash320 (1996)
[97] A Arneacuteodo E Bacry S Jaffard JF Muzy Oscillating singularities on Cantor sets Agrand canonical multifractal formalism J Stat Phys 87 179ndash209 (1997)
[98] A Arneacuteodo E Bacry S Jaffard JF Muzy Singularity spectrum of multifractal functionsinvolving oscillating singularities J Fourier Anal Appl 4 159ndash174 (1998)
[99] N Aronszajn Theory of reproducing kernels Trans Amer Math Soc 66 337ndash404 (1950)[100] A Ashtekar J Lewandowski D Marolf J Mouratildeo T Thiemann Coherent state
transforms for spaces of connections J Funct Analysis 135 519ndash551 (1996)[101] A Askari-Hemmat MA Dehghan M Radjabalipour Generalized frames and their
redundancy Proc Amer Math Soc 129 1143ndash1147 (2001)[102] EW Aslaksen JR Klauder Unitary representations of the affine group J Math Phys 9
206ndash211 (1968)[103] EW Aslaksen JR Klauder Continuous representation theory using the affine group
J Math Phys 10 2267ndash2275 (1969)[104] D Astruc L Plantieacute R Murenzi Y Lebret D Vandromme On the use of the 3D
wavelet transform for the analysis of computational fluid dynamics results in Progressin Wavelet Analysis and Applications (Proc Toulouse 1992) ed by Y Meyer S Roques(Ed Frontiegraveres Gif-sur-Yvette 1993) pp 463ndash470
[105] PW Atkins JC Dobson Angular momentum coherent states Proc Roy Soc London A321 321ndash340 (1971)
[106] BW Atkinson DO Bruff JS Geronimo D P Hardin Wavelets centered on a knotsequence Piecewise polynomial wavelets on a quasi-crystal lattice preprint (2011)arXiv11024246v1 [mathNA]
[107] IS Averbuch NF Perelman Fractional revivals Universality in the long-term evolutionof quantum wave packets beyond the correspondence principle dynamics Phys Lett A139 449ndash453 (1989)
[108] H Bacry J-M Leacutevy-Leblond Possible kinematics J Math Phys 9 1605ndash1614 (1968)[109] H Bacry A Grossmann J Zak Proof of the completeness of lattice states in kq
representation Phys Rev B 12 1118ndash1120 (1975)[110] L Baggett KF Taylor Groups with completely reducible regular representation Proc
Amer Math Soc 72 593ndash600 (1978)[111] VG Bagrov J-P Gazeau D Gitman A Levine Coherent states and related quantizations
for unbounded motions J Phys A Math Theor 45 125306 (2012) arXiv12010955v2[quant-ph]
[112] P Balazs J-P Antoine A Grybos Weighted and controlled frames Mutual relationshipand first numerical properties Int J Wavelets Multires Inform Proc 8 109ndash132 (2010)
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[121] D Barache S De Biegravevre J-P Gazeau Affine symmetry semigroups for quasicrystalsEurophys Lett 25 435ndash440 (1994)
[122] D Barache J-P Antoine J-M Dereppe The continuous wavelet transform a tool for NMRspectroscopy J Magn Reson 128 1ndash11 (1997)
[123] V Bargmann On a Hilbert space of analytic functions and an associated integral transformPart I Commun Pure Appl Math 14 187ndash214 (1961)
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[125] V Bargmann P Butera L Girardello JR Klauder On the completeness of coherentstates Reports Math Phys 2 221ndash228 (1971)
[126] AO Barut L Girardello New ldquocoherentrdquo states associated with non compact groupsCommun Math Phys 21 41ndash55 (1971)
[127] AO Barut H Kleinert Transition probabilities of the hydrogen atom from noncompactdynamical groups Phys Rev 156 1541ndash1545 (1967)
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[130] P Bellomo CR Stroud Jr Dispersion of Klauderrsquos temporally stable coherent states forthe hydrogen atom J Phys A Math Gen 31 L445ndashL450 (1998)
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[134] JJ Benedetto A Teolis A wavelet auditory model and data compression Appl ComputHarmon Anal 1 3ndash28 (1993)
[135] FA Berezin Quantization Math USSR Izvestija 8 1109ndash1165 (1974)[136] FA Berezin General concept of quantization Commun Math Phys 40 153ndash174 (1975)[137] H Bergeron From classical to quantum mechanics How to translate physical ideas into
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[139] H Bergeron and J-P Gazeau Integral quantization with two basic examples Preprint(2013) arXiv13082348v1
[140] H Bergeron A Valance Overcomplete basis for one dimensional Hamiltonians J MathPhys 36 1572ndash1592 (1995)
[141] H Bergeron J-P Gazeau P Siegl A Youssef Semi-classical behavior of Poumlschl-Tellercoherent states Eur Phys Lett 92 60003 (2010)
[142] H Bergeron P Siegl A Youssef New SUSYQM coherent states for Poumlschl-Tellerpotentials A detailed mathematical analysis J Phys A Math Theor 45 244028 (2012)
[143] H Bergeron J-P Gazeau A Youssef Are the Weyl and coherent state descriptionsphysically equivalent Phys Lett A 377 598ndash605 (2013)
[144] H Bergeron A Dapor J-P Gazeau P Małkiewicz Wavelet quantum cosmology preprint(2013) arXiv13050653 [gr-qc]
[145] S Bergman Uumlber die Kernfunktion eines Bereiches und ihr Verhalten am Rande I ReineAngw Math 169 1ndash42 (1933)
[146] D Bernier KF Taylor Wavelets from square-integrable representations SIAM J MathAnal 27 594ndash608 (1996)
[147] G Bernuau Wavelet bases associated to a self-similar quasicrystal J Math Phys 394213ndash4225 (1998)
[148] A Bertrand Deacuteveloppements en base de Pisot et reacutepartition modulo 1 C R Acad SciParis 285 419ndash421 (1977)
[149] J Bertrand P Bertrand Classification of affine Wigner functions via an extendedcovariance principle in Group Theoretical Methods in Physics (Proc Sainte-Adegravele 1988)ed by Y Saint-Aubin L Vinet (World Scientific Singapore 1989) pp 1380ndash1383
[150] Z Białynicka-Birula I Białynicki-Birula Space-time description of squeezing J OptSoc Am B4 1621ndash1626 (1987)
[151] E Bianchi E Magliaro C Perini Coherent spin-networks Phys Rev D 82 024012(2010)
[152] S Biskri J-P Antoine B Inhester F Mekideche Extraction of Solar coronal magneticloops with the 2-D Morlet wavelet transform Solar Phys 262 373ndash385 (2010)
[153] R Bluhm VA Kostelecky JA Porter The evolution and revival structure of localizedquantum wave packets Am J Phys 64 944ndash953 (1996)
[154] I Bogdanova P Vandergheynst J-P Antoine L Jacques M Morvidone Stereographicwavelet frames on the sphere Appl Comput Harmon Anal 19 223ndash252 (2005)
[155] I Bogdanova X Bresson J-P Thiran P Vandergheynst Scale space analysis and activecontours for omnidirectional images IEEE Trans Image Process 16 1888ndash1901 (2007)
[156] I Bogdanova P Vandergheynst J-P Gazeau Continuous wavelet transform on thehyperboloid Appl Comput Harmon Anal 23 (2007) 286ndash306 (2007)
[157] P Boggiatto E Cordero Anti-Wick quantization of tempered distributions in Progress inAnalysis Berlin (2001) vol I II (World Sci Publ River Edge NJ 2003) pp 655ndash662
[158] P Boggiatto E Cordero K Groumlchenig Generalized Anti-Wick operators with symbols indistributional Sobolev spaces Int Equ Oper Theory 48 427ndash442 (2004)
[159] A Boumlhm The Rigged Hilbert Space in quantum mechanics in Lectures in TheoreticalPhysics vol IX A ed by WA Brittin et al (Gordon amp Breach New York 1967) pp255ndash315
[160] G Bohnkeacute Treillis drsquoondelettes associeacutes aux groupes de Lorentz Ann Inst H Poincareacute54 245ndash259 (1991)
[161] WR Bomstad JR Klauder Linearized quantum gravity using the projection operatorformalism Class Quantum Grav 23 5961ndash5981 (2006)
[162] VV Borzov Orthogonal polynomials and generalized oscillator algebras Int TransformSpec Funct 12 115ndash138 (2001)
[163] VV Borzov EV Damaskinsky Generalized coherent states for classical orthogonalpolynomials Day on Diffraction (2002) arXivmathQA0209181v1 (SPb 2002)
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[165] A Bouzouina S De Biegravevre Equipartition of the eigenfunctions of quantized ergodic mapson the torus Commun Math Phys 178 83ndash105 (1996)
[166] P Brault J-P Antoine A spatio-temporal Gaussian-Conical wavelet with high apertureselectivity for motion and speed analysis Appl Comput Harmon Anal 34 148ndash161(2012)
[167] A Briguet S Cavassila D Graveron-Demilly Suppression of huge signals using theCadzow enhancement procedure The NMR Newslett 440 26 (1995)
[168] CM Brislawn Fingerprints go digital Notices Amer Math Soc 42 1278ndash1283 (1995)[169] CM Brislawn On the group-theoretic structure of lifted filter banks in Excursions in
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[170] F Bruhat Sur les repreacutesentations induites des groupes de Lie Bull Soc Math France 8497ndash205 (1956)
[171] T Buumllow Multiscale image processing on the sphere in DAGM-Symposium (2002) pp609ndash617
[172] C Burdik C Frougny J-P Gazeau R Krejcar Beta-integers as natural counting systemsfor quasicrystals J Phys A Math Gen 31 6449ndash6472 (1998)
[173] KE Cahill Coherent-state representations for the photon density Phys Rev 138 B1566ndash1576 (1965)
[174] KE Cahill R Glauber Density operators and quasiprobability distributions Phys Rev177 1882ndash1902 (1969)
[175] KE Cahill R Glauber Ordered expansions in boson amplitude operators Phys Rev 1771857ndash1881 (1969)
[176] AR Calderbank I Daubechies W Sweldens BL Yeo Wavelets that map integers tointegers Appl Comput Harmon Anal 5 332ndash369 (1998)
[177] M Calixto J Guerrero Wavelet transform on the circle and the real line A unified group-theoretical treatment Appl Comput Harmon Anal 21 204ndash229 (2006)
[178] M Calixto E Peacuterez-Romero Extended MacMahon-Schwingerrsquos master theorem andconformal wavelets in complex Minkowski space Appl Comput Harmon Anal 31 143ndash168 (2011)
[179] M Calixto J Guerrero D Rosca Wavelet transform on the torus A group-theoreticalapproach preprint (2013)
[180] EJ Candegraves Harmonic analysis of neural networks Appl Comput Harmon Anal 6 197ndash218 (1999)
[181] EJ Candegraves Ridgelets and the representation of mutilated Sobolev functions SIAM JMath Anal 33 347ndash368 (2001)
[182] EJ Candegraves L Demanet Curvelets and Fourier integral operators CR Acad Sci ParisSeacuter I Math 336 395ndash398 (2003)
[183] EJ Candegraves L Demanet The curvelet representation of wave propagators is optimallysparse Commun Pure Appl Math 58 1472ndash1528 (2004)
[184] EJ Candegraves L Demanet The curvelet representation of wave propagators is optimallysparse Commun Pure Appl Math 58 1472ndash1528 (2005)
[185] EJ Candegraves DL Donoho Curvelets ndash A surprisingly effective nonadaptive representationfor objects with edges in Curves and Surfaces ed by LL Schumaker et al (VanderbiltUniversity Press Nashville TN 1999)
[186] EJ Candegraves DL Donoho Ridgelets A key to higher-dimensional intermittency PhilTrans R Soc Lond A 357 2495ndash2509 (1999)
[187] EJ Candegraves DL Donoho Curvelets multiresolution representation and scaling laws inWavelet Applications in Signal and Image Processing VIII ed by A Aldroubi A LaineM Unser SPIE Proceedings vol 4119 (SPIE Bellingham WA 2000) pp 1ndash12
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[190] EJ Candegraves DL Donoho Continuous curvelet transform I Resolution of the wavefrontset II Discretization and frames Appl Comput Harmon Anal 19 162ndash197 198ndash222(2005)
[191] EJ Candegraves F Guo New multiscale transforms minimum total variationsynthesisApplications to edge-preserving image reconstruction Signal Proc 82 1519ndash1543 (2002)
[192] EJ Candegraves L Demanet D Donoho L Ying Fast discrete curvelet transforms MultiscaleModel Simul 5 861ndash899 (2006)
[193] AL Carey Square integrable representations of non-unimodular groups Bull AustrMath Soc 15 1ndash12 (1976)
[194] AL Carey Group representations in reproducing kernel Hilbert spaces Rep Math Phys14 247ndash259 (1978)
[195] P Carruthers MM Nieto Phase and angle variables in quantum mechanics Rev ModPhys 40 411ndash440 (1968)
[196] PG Casazza G Kutyniok Frames of subspaces in Wavelets Frames and Operator The-ory Contemporary Mathematics vol 345 (American Mathematical Society ProvidenceRI 2004) pp 87ndash113
[197] PG Casazza D Han DR Larson Frames for Banach spaces Contemp Math 247 149ndash182 (1999)
[198] P Casazza O Christensen S Li A Lindner Riesz-Fischer sequences and lower framebounds Z Anal Anwend 21 305ndash314 (2002)
[199] PG Casazza G Kutyniok S Li Fusion frames and distributed processing ApplComputHarmon Anal 25 114ndash132 (2008)
[200] DPL Castrigiano RW Henrichs Systems of covariance and subrepresentations ofinduced representations Lett Math Phys 4 169ndash175 (1980)
[201] U Cattaneo Densities of covariant observables J Math Phys 23 659ndash664 (1982)[202] A Cerioni L Genovese I Duchemin Th Deutsch Accurate complex scaling of three
dimensional numerical potentials Preprint (2013) arXiv13036439v2[203] S-J Chang K-J Shi Evolution and exact eigenstates of a resonant quantum system Phys
Rev A 34 7ndash22 (1986)[204] SHH Chowdhury ST Ali All the groups of signal analysis from the (1+1) affine Galilei
group J Math Phys 52 103504 (2011)[205] SL Chown Antarctic marine biodiversity and deep-sea hydrothermal vents PLoS Biol
10 1ndash4 (2012)[206] C Cishahayo S De Biegravevre On the contraction of the discrete series of SU(11) Ann Inst
Fourier (Grenoble) 43 551ndash567 (1993)[207] M Clerc and S Mallat Shape from texture and shading with wavelets in Dynamical
Systems Control Coding Computer Vision Progress in Systems and Control Theory 25393ndash417 (1999)
[208] L Cohen General phase-space distribution functions J Math Phys 7 781ndash786 (1966)[209] A Cohen I Daubechies J-C Feauveau Biorthogonal bases of compactly supported
wavelets Commun Pure Appl Math 45 485ndash560 (1992)[210] R Coifman Y Meyer MV Wickerhauser Wavelet analysis and signal processing
in Wavelets and Their Applications ed by MB Ruskai G Beylkin R CoifmanI Daubechies S Mallat Y Meyer L Raphael (Jones and Bartlett Boston 1992)pp 153ndash178
[211] R Coifman Y Meyer MV Wickerhauser Entropy-based algorithms for best basisselection IEEE Trans Inform Theory 38 713ndash718 (1992)
[212] R Coquereaux A Jadczyk Conformal theories curved spaces relativistic wavelets andthe geometry of complex domains Rev Math Phys 2 1ndash44 (1990)
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[214] N Cotfas J-P Gazeau Finite tight frames and some applications (topical review) J PhysA Math Theor 43 193001 (2010)
[215] N Cotfas J-P Gazeau K Goacuterska Complex and real Hermite polynomials and relatedquantizations J Phys A Math Theor 43 305304 (2010)
[216] N Cotfas J-P Gazeau A Vourdas Finite-dimensional Hilbert space and frame quantiza-tion J Phys A Math Gen 44 175303 (2011)
[217] EMF Curado MA Rego-Monteiro LMCS Rodrigues Y Hassouni Coherent statesfor a degenerate system The hydrogen atom Physica A 371 16ndash19 (2006)
[218] S Dahlke P Maass The affine uncertainty principle in one and two dimensions CompMath Appl 30 293ndash305 (1995)
[219] S Dahlke W Dahmen E Schmidt I Weinreich Multiresolution analysis and wavelets onS
2 and S3 Numer Funct Anal Optim 16 19ndash41 (1995)
[220] S Dahlke V Lehmann G Teschke Applications of wavelet methods to the analysis ofmeteorological radar data - An overview Arabian J Sci Eng 28 3ndash44 (2003)
[221] S Dahlke G Kutyniok P Maass C Sagiv H-G Stark G Teschke The uncertaintyprinciple associated with the continuous shearlet transform Int J Wavelets MultiresolutInf Process 6 157ndash181 (2008)
[222] S Dahlke G Kutyniok G Steidl G Teschke Shearlet coorbit spaces and associatedBanach frames Appl Comput Harmon Anal 27 195ndash214 (2009)
[223] S Dahlke G Steidl G Teschke The continuous shearlet transform in arbitrary spacedimensions J Fourier Anal Appl 16 340ndash364 (2010)
[224] S Dahlke G Steidl G Teschke Shearlet coorbit spaces Compactly supported analyzingshearlets traces and embeddings J Fourier Anal Appl 17 1232ndash1355 (2011)
[225] T Dallard GR Spedding 2-D wavelet transforms Generalisation of the Hardy space andapplication to experimental studies Eur J Mech BFluids 12 107ndash134 (1993)
[226] C Daskaloyannis Generalized deformed oscillator and nonlinear algebras J Phys AMath Gen 24 L789ndashL794 (1991)
[227] C Daskaloyannis K Ypsilantis A deformed oscillator with Coulomb energy spectrumJ Phys A Math Gen 25 4157ndash4166 (1992)
[228] I Daubechies On the distributions corresponding to bounded operators in the Weylquantization Commun Math Phys 75 229ndash238 (1980)
[229] I Daubechies and A Grossmann An integral transform related to quantization I J MathPhys 21 2080ndash2090 (1980)
[230] I Daubechies A Grossmann J Reignier An integral transform related to quantization IIJ Math Phys 24 239ndash254 (1983)
[231] I Daubechies Orthonormal bases of compactly supported wavelets Commun Pure ApplMath 41 909ndash996 (1988)
[232] I Daubechies The wavelet transform time-frequency localisation and signal analysisIEEE Trans Inform Theory 36 961ndash1005 (1990)
[233] I Daubechies S Maes A nonlinear squeezing of the continuous wavelet transform basedon auditory nerve models in Wavelets in Medicine and Biology ed by A Aldroubi MUnser (CRC Press Boca Raton 1996) pp 527ndash546
[234] I Daubechies A Grossmann Y Meyer Painless nonorthogonal expansions J Math Phys27 1271ndash1283 (1986)
[235] ER Davies Introduction to texture analysis in Handbook of texture analysis ed by MMirmehdi X Xie J Suri (World Scientific Singapore 2008) pp 1ndash31
[236] R De Beer D van Ormondt FTAW Wajer S Cavassila D Graveron-Demilly S VanHuffel SVD-based modelling of medical NMR signals in SVD and Signal ProcessingIII Algorithms Architectures and Applications ed by M Moonen B De Moor (Elsevier(North-Holland) Amsterdam 1995) pp 467ndash474
[237] S De Biegravevre Coherent states over symplectic homogeneous spaces J Math Phys 301401ndash1407 (1989)
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[239] S De Biegravevre JA Gonzaacutelez Semiclassical behaviour of coherent states on the circle inQuantization and Coherent States Methods in Physics ed by A Odzijewicz et al (WorldScientific Singapore 1993)
[240] S De Biegravevre AE Gradechi Quantum mechanics and coherent states on the anti-de Sitterspace-time and their Poincareacute contraction Ann Inst H Poincareacute 57 403ndash428 (1992)
[241] J Deenen C Quesne Dynamical group of collective states I II III J Math Phys 23878ndash889 2004ndash2015 (1982)
[242] J Deenen C Quesne Dynamical group of collective states I II III J Math Phys 251638ndash1650 (1984)
[243] J Deenen C Quesne Partially coherent states of the real symplectic group J Math Phys25 2354ndash2366 (1984)
[244] J Deenen C Quesne Boson representations of the real symplectic group and theirapplication to the nuclear collective model J Math Phys 26 2705ndash2716 (1985)
[245] R Delbourgo Minimal uncertainty states for the rotation and allied groups J Phys AMath Gen 10 1837ndash1846 (1977)
[246] R Delbourgo J R Fox Maximum weight vectors possess minimal uncertainty J PhysA Math Gen 10 L233ndashL235 (1977)
[247] V Delouille J de Patoul J-F Hochedez L Jacques J-P Antoine Wavelet spectrumanalysis of EITSoHO images Solar Phys 228 301ndash321 (2005)
[248] N Delprat B Escudieacute P Guillemain R Kronland-Martinet P Tchamitchian B Tor-reacutesani Asymptotic wavelet and Gabor analysis Extraction of instantaneous frequenciesIEEE Trans Inform Theory 38 644ndash664 (1992)
[249] Th Deutsch L Genovese Wavelets for electronic structure calculations Collection SocFr Neut 12 33ndash76 (2011)
[250] B Dewitt Quantum theory of gravity I The canonical theory Phys Rev 160 1113ndash1148(1967)
[251] RH Dicke Coherence in spontaneous radiation processes Phys Rev 93 99ndash110 (1954)[252] AN Dinkelaker AL MacKinnon Wavelets intermittency and solar flare hard X-rays 1
Local intermittency measure in cascade and avalanche scenarios Solar Phys 282 471ndash481(2013)
[253] AN Dinkelaker AL MacKinnon Wavelets intermittency and solar flare hard X-rays 2LIM analysis of high time resolution BATSE data Solar Phys 282 483ndash501 (2013)
[254] MN Do M Vetterli Contourlets in Beyond Wavelets ed by GV Welland (AcademicSan Diego 2003) pp 83ndash105
[255] MN Do M Vetterli The contourlet transform An efficient directional multiresolutionimage representation IEEE Trans Image Process 14 2091ndash2106 (2005)
[256] VV Dodonov Nonclassical states in quantum optics A ldquosqueezedrdquo review of the first 75years J Opt B Quant Semiclass Opot 4 R1ndashR33 (2002)
[257] DL Donoho Nonlinear wavelet methods for recovery of signals densities and spectrafrom indirect and noisy data in Different Perspectives on Wavelets Proceedings ofSymposia in Applied Mathematics vol 38 ed by I Daubechies (American MathematicalSociety Providence RI 1993) pp 173ndash205
[258] DL Donoho Wedgelets Nearly minimax estimation of edges Ann Stat 27 859ndash897(1999)
[259] DL Donoho X Huo Beamlet pyramids A new form of multiresolution analysis suitedfor extracting lines curves and objects from very noisy image data in SPIE Proceedingsvol 5914 (SPIE Bellingham WA 2005) pp 1ndash12
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[261] AH Dooley JW Rice Contractions of rotation groups and their representations MathProc Camb Phil Soc 94 509ndash517 (1983)
[262] AH Dooley JW Rice On contractions of semisimple Lie groups Trans Amer MathSoc 289 185ndash202 (1985)
[263] JR Driscoll DM Healy Computing Fourier transforms and convolutions on the 2-sphereAdv Appl Math 15 202ndash250 (1994)
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[265] RJ Duffin AC Schaeffer A class of nonharmonic Fourier series Trans Amer MathSoc 72 341ndash366 (1952)
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[267] M Duval-Destin R Murenzi Spatio-temporal wavelets Application to the analysis ofmoving patterns in Progress in Wavelet Analysis and Applications (Proc Toulouse 1992)ed by Y Meyer S Roques (Ed Frontiegraveres Gif-sur-Yvette 1993) pp 399ndash408
[268] M Duval-Destin M-A Muschietti B Torreacutesani Continuous wavelet decompositionsmultiresolution and contrast analysis SIAM J Math Anal 24 739ndash755 (1993)
[269] SJL van Eindhoven JLH Meyers New orthogonality relations for the Hermitepolynomials and related Hilbert spaces J Math Anal Appl 146 89ndash98 (1990)
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[271] A Elkharrat J-P Gazeau F Deacutenoyer Multiresolution of quasicrystal diffraction spectraActa Cryst A65 466ndash489 (2009)
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[273] M Fanuel S Zonetti Affine quantization and the initial cosmological singularity Euro-phys Lett 101 10001 (2013)
[274] M Farge Wavelet transforms and their applications to turbulence Annu Rev Fluid Mech24 395ndash457 (1992)
[275] M Farge N Kevlahan V Perrier E Goirand Wavelets and turbulence Proc IEEE 84639ndash669 (1996)
[276] M Farge NK-R Kevlahan V Perrier K Schneider Turbulence analysis modellingand computing using wavelets in Wavelets in Physics Chap 4 ed by JC van den Berg(Cambridge University Press Cambridge 1999)
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[280] M Flensted-Jensen Discrete series for semisimple symmetric spaces Ann of Math 111253ndash311 (1980)
[281] K Flornes A Grossmann M Holschneider B Torreacutesani Wavelets on discrete fieldsAppl Comput Harmon Anal 1 137ndash146 (1994)
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[286] W Freeden T Maier S Zimmermann A survey on wavelet methods for (geo)applicationsRevista Mathematica Complutense 16 (2003) 277ndash310
[287] W Freeden M Schreiner Biorthogonal locally supported wavelets on the sphere based onzonal kernel functions J Fourier Anal Appl 13 693ndash709 (2007)
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[289] L Freidel ER Livine U(N) coherent states for loop quantum gravity J Math Phys 52052502 (2011)
[290] J Froment S Mallat Arbitrary low bit rate image compression using wavelets in Progressin Wavelet Analysis and Applications (Proc Toulouse 1992) ed by Y Meyer S Roques(Ed Frontiegraveres Gif-sur-Yvette 1993) pp 413ndash418 and references therein
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[292] H Fuumlhr Wavelet frames and admissibility in higher dimensions J Math Phys 37 6353ndash6366 (1996)
[293] H Fuumlhr M Mayer Continuous wavelet transforms from semidirect products Cyclicrepresentations and Plancherel measure J Fourier Anal Appl 8 375ndash396 (2002)
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127ndash147 (2003)[296] E Galapon Paulirsquos theorem and quantum canonical pairs The consistency of a bounded
self-adjoint time operator canonically conjugate to a Hamiltonian with non-empty pointspectrum Proc R Soc Lond A 458 451ndash472 (2002)
[297] PL Garciacutea de Leacuteon J-P Gazeau Coherent state quantization and phase operator PhysLett A 361 301ndash304 (2007)
[298] L Garciacutea de Leoacuten J-P Gazeau J Queacuteva The infinite well revisited Coherent states andquantization Phys Lett A 372 3597ndash3607 (2008)
[299] T Garidi J-P Gazeau E Huguet M Lachiegraveze Rey J Renaud Fuzzy spheres frominequivalent coherent states quantization J Phys A Math Theor 40 10225ndash10249 (2007)
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[301] J-P Gazeau On the four Euclidean conformal group structure of the sturmian operatorLett Math Phys 3 285ndash292 (1979)
[302] J-P Gazeau Technique Sturmienne pour le spectre discret de lrsquoeacutequation de SchroumldingerJ Phys A Math Gen 13 3605ndash3617 (1980)
[303] J-P Gazeau Four Euclidean conformal group approach to the multiphoton processes in theH atom J Math Phys 23 156ndash164 (1982)
[304] J-P Gazeau A remarkable duality in one particle quantum mechanics between someconfining potentials and (R+Linfin
ε ) potentials Phys Lett 75A 159ndash163 (1980)[305] J-P Gazeau SL(2R)-coherent states and integrable systems in classical and quantum
physics in Quantization Coherent States and Complex Structures ed by J-P AntoineST Ali W Lisiecki IM Mladenov A Odzijewicz (Plenum Press New York and London1995) pp 147ndash158
[306] J-P Gazeau S Graffi Quantum harmonic oscillator A relativistic and statistical point ofview Boll Unione Mat Ital 11-A 815ndash839 (1997)
[307] J-P Gazeau V Hussin Poincareacute contraction of SU(11) Fock-Bargmann structure J PhysA Math Gen 25 1549ndash1573 (1992)
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[310] J-P Gazeau P Monceau Generalized coherent states for arbitrary quantum systems inColloquium M Flato (Dijon Sept 99) vol II (Kluumlwer Dordrecht 2000) pp 131ndash144
[311] J-P Gazeau M Novello The question of mass in (Anti-) de Sitter space-times J Phys AMath Theor 41 304008 (2008)
[312] J-P Gazeau M del Olmo q-coherent states quantization of the harmonic oscillator AnnPhys (NY) 330 220ndash245 (2013) arXiv12071200 [quant-ph]
[313] J-P Gazeau J Patera Tau-wavelets of Haar J Phys A Math Gen 29 4549ndash4559 (1996)[314] J-P Gazeau W Piechocki Coherent states quantization of a particle in de Sitter space
J Phys A Math Gen 37 6977ndash6986 (2004)[315] J-P Gazeau J Renaud Lie algorithm for an interacting SU(11) elementary system and its
contraction Ann Phys (NY) 222 89ndash121 (1993)[316] J-P Gazeau J Renaud Relativistic harmonic oscillator and space curvature Phys Lett A
179 67ndash71 (1993)[317] J-P Gazeau V Spiridonov Toward discrete wavelets with irrational scaling factor J Math
plane J Phys A Math Theor 44 495201 (2011)[319] J-P Gazeau J Patera E Pelantovaacute Tau-wavelets in the plane J Math Phys 39 4201ndash
4212 (1998)[320] J-P Gazeau M Andrle C Burdiacutek R Krejcar Wavelet multiresolutions for the Fibonacci
chain J Phys A Math Gen 33 L47ndashL51 (2000)[321] J-P Gazeau M Andrle C Burdiacutek Bernuau spline wavelets and sturmian sequences
J Fourier Anal Appl 10 269ndash300 (2004)[322] J-P Gazeau F-X Josse-Michaux P Monceau Finite dimensional quantizations of the
(q p) plane new space and momentum inequalities Int J Modern Phys B 20 1778ndash1791 (2006)
[323] J-P Gazeau J Mourad J Queacuteva Fuzzy de Sitter space-times via coherent statesquantization in Proceedings of the XXVIth Colloquium on Group Theoretical Methodsin Physics New York 2006 ed by J Birman S Catto B Nicolescu (Canopus PublishingLimited London 2009)
[324] D Geller A Mayeli Continuous wavelets on compact manifolds Math Z 262 895ndash927(2009)
[325] D Geller A Mayeli Nearly tight frames and space-frequency analysis on compactmanifolds Math Z 263 235ndash264 (2009)
[326] L Genovese B Videau M Ospici Th Deutsch S Goedecker J-F Mhaut Daubechieswavelets for high performance electronic structure calculations The BigDFT project CR Mecanique 339 149ndash164 (2011)
[327] G Gentili C Stoppato Power series and analyticity over the quaternions Math Ann 352113ndash131 (2012)
[328] G Gentili DC Struppa A new theory of regular functions of a quaternionic variable AdvMath 216 279ndash301 (2007)
[329] C Geyer K Daniilidis Catadioptric projective geometry Int J Comput Vision 45 223ndash243 (2001)
[330] R Gilmore Geometry of symmetrized states Ann Phys (NY) 74 391ndash463 (1972)[331] R Gilmore On properties of coherent states Rev Mex Fis 23 143ndash187 (1974)[332] J Ginibre Statistical ensembles of complex quaternion and real matrices J Math Phys
6 440ndash449 (1965)[333] RJ Glauber The quantum theory of optical coherence Phys Rev 130 2529ndash2539 (1963)
560 References
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[335] J Glimm Locally compact transformation groups Trans Amer Math Soc 101 124ndash138(1961)
[336] R Godement Sur les relations drsquoorthogonaliteacute de V Bargmann C R Acad Sci Paris 255521ndash523 657ndash659 (1947)
[337] C Gonnet B Torreacutesani Local frequency analysis with two-dimensional wavelet trans-form Signal Proc 37 389ndash404 (1994)
[338] JA Gonzalez MA del Olmo Coherent states on the circle J Phys A Math Gen 318841ndash8857 (1998)
[339] XGonze B Amadon et al ABINIT First-principles approach to material and nanosystemproperties Computer Physics Comm 180 2582ndash2615 (2009)
[340] KM Gograverski E Hivon AJ Banday BD Wandelt FK Hansen M Reinecke MBartelmann HEALPix A framework for high-resolution discretization and fast analysisof data distributed on the sphere Astrophys J 622 759ndash771 (2005)
[341] P Goupillaud A Grossmann J Morlet Cycle-octave and related transforms in seismicsignal analysis Geoexploration 23 85ndash102 (1984)
[342] KH Groumlchenig A new approach to irregular sampling of band-limited functions in RecentAdvances in Fourier Analysis and Its applications ed by JS Byrnes JL Byrnes (KluwerDordrecht 1990) pp 251ndash260
[343] KH Groumlchenig Gabor analysis over LCA groups in Gabor Analysis and Algorithms ndashTheory and Applications ed by HG Feichtinger T Strohmer (Birkhaumluser Boston-Basel-Berlin 1998) pp 211ndash231
[344] HJ Groenewold On the principles of elementary quantum mechanics Physica 12 405ndash460 (1946)
[345] P Grohs Continuous shearlet tight frames J Fourier Anal Appl 17 506ndash518 (2011)[346] P Grohs G Kutyniok Parabolic molecules preprint TU Berlin (2012)[347] M Grosser A note on distribution spaces on manifolds Novi Sad J Math 38 121ndash128
(2008)[348] A Grossmann Parity operator and quantization of δ -functions Commun Math Phys 48
191ndash194 (1976)[349] A Grossmann J Morlet Decomposition of Hardy functions into square integrable
wavelets of constant shape SIAM J Math Anal 15 723ndash736 (1984)[350] A Grossmann J Morlet Decomposition of functions into wavelets of constant shape and
related transforms in Mathematics + Physics Lectures on recent results I ed by L Streit(World Scientific Singapore 1985) pp 135ndash166
[351] A Grossmann J Morlet T Paul Integral transforms associated to square integrablerepresentations I General results J Math Phys 26 2473ndash2479 (1985)
[352] A Grossmann J Morlet T Paul Integral transforms associated to square integrablerepresentations II Examples Ann Inst H Poincareacute 45 293ndash309 (1986)
[353] A Grossmann R Kronland-Martinet J Morlet Reading and understanding the contin-uous wavelet transform in Wavelets Time-Frequency Methods and Phase Space (ProcMarseille 1987) ed by J-M Combes A Grossmann P Tchamitchian 2nd edn (SpringerBerlin 1990) pp 2ndash20
[354] P Guillemain R Kronland-Martinet B Martens Estimation of spectral lines with helpof the wavelet transform Application in NMR spectroscopy in Wavelets and Applications(Proc Marseille 1989) ed by Y Meyer (Masson and Springer Paris and Berlin 1991) pp38ndash60
[355] H de Guise M Bertola Coherent state realizations of su(n+ 1) on the n-torus J MathPhys 43 3425ndash3444 (2002)
[356] K Guo D Labate Representation of Fourier Integral Operators using shearlets J FourierAnal Appl 14 327ndash371 (2008)
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[357] K Guo G Kutyniok D Labate Sparse multidimensional representations usinganisotropic dilation and shear operators in Wavelets and Spines (Athens GA 2005)(Nashboro Press Nashville TN 2006) pp 189ndash201
[358] K Guo D Labate W-Q Lim G Weiss E Wilson Wavelets with composite dilationsand their MRA properties Appl Comput Harmon Anal 20 202ndash236 (2006)
[359] EA Gutkin Overcomplete subspace systems and operator symbols Funct Anal Appl 9260ndash261 (1975)
[360] G Gyoumlrgyi Integration of the dynamical symmetry groups for the 1r potential Acta PhysAcad Sci Hung 27 435ndash439 (1969)
[361] BC Hall The Segal-Bargmann ldquoCoherent Staterdquo transform for compact Lie groups JFunct Analysis 122 103ndash151 (1994)
[362] B Hall JJ Mitchell Coherent states on spheres J Math Phys 43 1211ndash1236 (2002)[363] DK Hammond P Vandergheynst R Gribonval Wavelets on graphs via spectral theory
Appl Comput Harmon Anal 30 129ndash150 (2011)[364] Y Hassouni EMF Curado MA Rego-Monteiro Construction of coherent states for
physical algebraic system Phys Rev A 71 022104 (2005)[365] J He H Liu Admissible wavelets associated with the affine automorphism group of the
Siegel upper half-plane J Math Anal Appl 208 58ndash70 (1997)[366] J He H Liu Admissible wavelets associated with the classical domain of type one
Approx Appl 14 (1998) 89ndash105[367] J He L Peng Wavelet transform on the symmetric matrix space preprint Beijing (1997)
(unpublished)[368] J He L Peng Admissible wavelets on the unit disk Complex Variables 35 109ndash119
(1998)[369] DM Healy Jr FE Schroeck Jr On informational completeness of covariant localization
observables and Wigner coefficients J Math Phys 36 453ndash507 (1995)[370] C Heil D Walnut Continuous and discrete wavelet transforms SIAM Review 31 628ndash
666 (1989)[371] K Hepp EH Lieb On the superradiant phase transition for molecules in a quantized
radiation field The Dicke maser model Ann Phys (NY) 76 360ndash404 (1973)[372] K Hepp EH Lieb Equilibrium statistical mechanics of matter interacting with the
quantized radiation field Phys Rev A 8 2517ndash2525 (1973)[373] JA Hogan JD Lakey Extensions of the Heisenberg group by dilations and frames Appl
Comput Harmon Anal 2 174ndash199 (1995)[374] AL Hohoueacuteto K Thirulogasanthar ST Ali J-P Antoine Coherent states lattices and
square integrability of representations J Phys A Math Gen36 11817ndash11835 (2003)[375] M Holschneider On the wavelet transformation of fractal objects J Stat Phys 50 963ndash
993 (1988)[376] M Holschneider Wavelet analysis on the circle J Math Phys 31 39ndash44 (1990)[377] M Holschneider Inverse Radon transforms through inverse wavelet transforms Inv Probl
7 853ndash861 (1991)[378] M Holschneider Localization properties of wavelet transforms J Math Phys 34 3227ndash
3244 (1993)[379] M Holschneider General inversion formulas for wavelet transforms J Math Phys 34
4190ndash4198 (1993)[380] M Holschneider Wavelet analysis over abelian groups Applied Comput Harmon Anal
2 52ndash60 (1995)[381] M Holschneider Continuous wavelet transforms on the sphere J Math Phys 37 4156ndash
4165 (1996)[382] M Holschneider I Iglewska-Nowak Poisson wavelets on the sphere J Fourier Anal
Appl 13 405ndash419 (2007)
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[383] M Holschneider R Kronland-Martinet J Morlet P Tchamitchian A real-time algorithmfor signal analysis with the help of wavelet transform in Wavelets Time-FrequencyMethods and Phase Space (Proc Marseille 1987) ed by J-M Combes A Grossmann PTchamitchian 2nd edn (Springer Berlin 1990) pp 286ndash297
[384] M Holschneider P Tchamitchian Pointwise analysis of Riemannrsquos ldquonondifferentiablerdquofunction Invent Math 105 157ndash175 (1991)
[385] GR Honarasa MK Tavassoly M Hatami R Roknizadeh Nonclassical properties ofcoherent states and excited coherent states for continuous spectra J Phys A Math Theor44 085303 (2011)
[386] M Hongoh Coherent states associated with the continuous spectrum of noncompactgroups J Math Phys 18 2081ndash2085 (1977)
[387] A Horzela FH Szafraniec A measure free approach to coherent states J Phys A MathGen 45 244018 (2012)
[388] W-L Hwang S Mallat Characterization of self-similar multifractals with waveletmaxima Appl Comput Harmon Anal 1 316ndash328 (1994)
[389] W-L Hwang C-S Lu P-C Chung Shape from texture Estimation of planar surfaceorientation through the ridge surfaces of continuous wavelet transform IEEE Trans ImageProc 7 773ndash780 (1998)
[390] I Iglewska-Nowak M Holschneider Frames of Poisson wavelets on the sphere ApplComput Harmon Anal 28 227ndash248 (2010)
[391] E Inoumlnuuml EP Wigner On the contraction of groups and their representations Proc NatAcad Sci U S 39 510ndash524 (1953)
[392] S Iqbal F Saif Generalized coherent states and their statistical characteristics in power-law potentials J Math Phys 52 082105 (2011)
[393] CJ Isham JR Klauder Coherent states for n-dimensional Euclidean groups E(n) andtheir application J MathPhys 32 607ndash620 (1991)
[394] L Jacques J-P Antoine Multiselective pyramidal decomposition of images Wavelets withadaptive angular selectivity Int J Wavelets Multires Inform Proc 5 785ndash814 (2007)
[395] L Jacques L Duval C Chaux G Peyreacute A panorama on multiscale geometric rep-resentations intertwining spatial directional and frequency selectivity Signal Proc 912699ndash2730 (2011)
[396] HR Jalali M K Tavassoly On the ladder operators and nonclassicality of generalizedcoherent state associated with a particle in an infinite square well preprint (2013)arXiv13034100v1 [quant-ph]
[397] C Johnston On the pseudo-dilation representations of Flornes Grossmann Holschneiderand Torreacutesani Appl Comput Harmon Anal 3 377ndash385 (1997)
[398] G Kaiser Phase-space approach to relativistic quantum mechanics I Coherent staterepresentation for massive scalar particles J MathPhys 18 952ndash959 (1977)
[399] G Kaiser Phase-space approach to relativistic quantum mechanics II Geometrical aspectsJ MathPhys 19 502ndash507 (1978)
[400] C Kalisa B Torreacutesani N-dimensional affine Weyl-Heisenberg wavelets Ann Inst HPoincareacute 59 201ndash236 (1993)
[401] W Kaminski J Lewandowski T Pawłowski Quantum constraints Dirac observables andevolution group averaging versus the Schroumldinger picture in LQC Class Quant Grav 26245016 (2009)
[402] MR Karim ST Ali A relativistic windowed Fourier transform preprint ConcordiaUniversity Montreacuteal (1997) (unpublished)
[403] M R Karim ST Ali M Bodruzzaman A relativistic windowed Fourier transform inProceedings of IEEE SoutheastCon 2000 Nashville Tennessee pp 253ndash260 (2000)
[404] T Kawazoe Wavelet transforms associated to a principal series representation of semisim-ple Lie groups I II Proc Japan Acad Ser A ndash Math Sci 71 154ndash157 158ndash160 (1995)
[405] T Kawazoe Wavelet transform associated to an induced representation of SL(n+ 2R)Ann Inst H Poincareacute 65 1ndash13 (1996)
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[407] P Kittipoom G Kutyniok W-Q Lim Construction of compactly supported shearletframes Constr Approx 35 21ndash72 (2012)
[408] J Kiukas P Lahti K Ylinenc Phase space quantization and the operator moment problemJ Math Phys 47 072104 (2006)
[409] JR Klauder Continuous-representation theory I Postulates of continuous-representationtheory J Math Phys 4 1055ndash1058 (1963)
[410] JR Klauder Continuous-representation theory II Generalized relation between quantumand classical dynamics J Math Phys 4 1058ndash1073 (1963)
[411] JR Klauder Path integrals for affine variables in Functional Integration Theory andApplications ed by J-P Antoine E Tirapegui (Plenum Press New York and London1980) pp 101ndash119
[412] JR Klauder Are coherent states the natural language of quantum mechanics inFundamental Aspects of Quantum Theory ed by V Gorini A Frigerio NATO ASI Seriesvol B 144 (Plenum Press New York 1986) pp 1ndash12
[413] JR Klauder Quantization without quantization Ann Phys (NY) 237 147ndash160 (1995)[414] JR Klauder Coherent states for the hydrogen atom J Phys A Math Gen 29 L293ndash
L296 (1996)[415] JR Klauder An affinity for affine quantum gravity Proc Steklov Inst Math 272 169ndash176
(2011) and references therein[416] JR Klauder RF Streater A wavelet transform for the Poincareacute group J Math Phys 32
1609ndash1611 (1991)[417] JR Klauder RF Streater Wavelets and the Poincareacute half-plane J Math Phys 35 471ndash
478 (1994)[418] JR Klauder K Penson J-M Sixdeniers Constructing coherent states through solutions
of Stieltjes and Hausdorff moment problems Phys Rev A 64 013817 (2001)[419] A Kleppner RL Lipsman The Plancherel formula for group extensions Ann Ec Norm
Sup 5 459ndash516 (1972)[420] AB Klimov C Muntildeoz Coherent isotropic and squeezed states in a N-qubit system Phys
Scr 87 038110 (2013)[421] A Klyashko Dynamical symmetry approach to entanglement in Physics and Theoretical
Computer Science From Numbers and Languages to (Quantum) Cryptography - NATOSecurity through Science Series D - Information and Communication Security vol 7 edby J-P Gazeau J Nesetril B Rovan (IOS Press Washington DC 2007) pp 25ndash54
[422] S Kobayashi Irreducibility of certain unitary representations J Math Soc Japan 20 638ndash642 (1968)
[423] K Kowalski J Rembielinski LC Papaloucas Coherent states for a quantum particle ona circle J Phys A Math Gen 29 4149ndash4167 (1996)
[424] K Kowalski J Rembielinski Quantum mechanics on a sphere and coherent states J PhysA Math Gen 33 6035ndash6048 (2000)
[425] K Kowalski J Rembielinski The Bargmann representation for the quantum mechanicson a sphere J Math Phys 42 4138ndash4147 (2001)
[426] C Kristjansen J Plefka GW Semenoff M Staudacher A new double-scaling limit ofN = 4 super-Yang-Mills theory and pp-wave strings Nuclear Phys B 643 3ndash30 (2002)
[427] M Kulesh M Holschneider MS Diallo Geophysical wavelet library Applications ofthe continuous wavelet transform to the polarization and dispersion analysis of signalsComput Geosci 34 1732ndash1752 (2008)
[428] R Kunze On the Frobenius reciprocity theorem for square integrable representationsPacific J Math 53 465ndash471 (1974)
[429] Y Kuroda A Wada T Yamazaki K Nagayama Postacquisition data processing methodfor suppression of the solvent signal I J Magn Reson 84 604ndash610 (1989)
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[431] G Kutyniok D Labate Resolution of the wavefront set using continuous shearlets TransAmer Math Soc 361 2719ndash2754 (2009)
[432] G Kutyniok W-Q Lim Compactly supported shearlets are optimally sparse J ApproxTheory 163 1564ndash1589 (2011)
[433] D Labate W-Q Lim G Kutyniok G Weiss Sparse multidimensional representationusing shearlets in Wavelets XI (San Diego CA 2005) ed by M Papadakis A Laine MUnser SPIE Proceedings vol 5914 (SPIE Bellingham WA 2005) pp 254ndash262
[434] P Lahti J-P Pellonpaumlauml Continuous variable tomographic measurements Phys Lett A373 3435ndash3438 (2009)
[435] Lambertrsquos projection see WikipediahttpenwikipediaorgwikiLambert_azimuthal_equal-area_projection
[436] J-P Leduc F Mujica R Murenzi MJT Smith Missile-tracking algorithm using target-adapted spatio-temporal wavelets in Automatic Object Recognition VII SPIE Proceedingsvol 5914 (SPIE Bellingham WA 1997) pp 400ndash411
[437] J-P Leduc F Mujica R Murenzi MJT Smith Spatio-temporal wavelet transforms formotion tracking in IEEE ICASSP 1997 vol 4 (1997) pp 3013ndash3016
[438] J-P Leduc F Mujica R Murenzi MJT Smith Spatio-temporal continuous waveletsapplied to missile warhead detection and tracking in SPIE VCIP rsquo97 vol 3024 ed byJ Biemond EJ Delp (1997) pp 787ndash798
[439] B Leistedt JD McEwen Exact wavelets on the ball IEEE Trans Signal Proc 60 1564ndash1589 (2012)
[440] PG Lemarieacute Y Meyer Ondelettes et bases hilbertiennes Rev Math Iberoamer 2 1ndash18(1986)
[441] C Lemke A Schuck Jr J-P Antoine D Sima Metabolite-sensitive analysis of magneticresonance spectroscopic signals using the continuous wavelet transform Meas SciTechnol 22 (2011) Art 114013
[442] J-M Leacutevy-Leblond Galilei group and non-relativistic quantum mechanics J Math Phys4 776-788 (1963)
[443] J-M Leacutevy-Leblond Galilei group and Galilean invariance in Group Theory and ItsApplications vol II ed by EM Loebl (Academic New York 1971) pp 221ndash299
[444] J-M Leacutevy-Leblond On the conceptual nature of the physical constants Riv Nuovo Cim7 187ndash214 (1977)
[445] EH Lieb The classical limit of quantum spin systems Commun Math Phys 31 327ndash340(1973)
[446] G Lindblad B Nagel Continuous bases for unitary irreducible representations of SU(11)Ann Inst H Poincareacute 13 27ndash56 (1970)
[447] W Lisiecki Kaumlhler coherent states orbits for representations of semisimple Lie groupsAnn Inst H Poincareacute 53 857ndash890 (1990)
[448] A Lisowska Moment-based fast wedgelet transform J Math Imaging Vis 39 180ndash192(2011)
[449] H Liu L Peng Admissible wavelets associated with the Heisenberg group Pacific JMath 180 101ndash123 (1997)
[450] E Livine S Speziale Physical boundary state for the quantum tetrahedron Class QuantGrav 25 085003 (2008)
[451] F Low Complete sets of wave packets in A Passion for Physics ndash Essay in Honor ofGeoffrey Chew ed by C DeTar (World Scientific Singapore 1985) pp 17ndash22
[452] G Mack All unitary ray representations of the conformal group SU(22) with positiveenergy Commun Math Phys 55 1ndash28 (1977)
[453] GW Mackey Imprimitivity for representations of locally compact groups I Proc NatAcad Sci 35 537ndash545 (1949)
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[456] SG Mallat Multifrequency channel decompositions of images and wavelet models IEEETrans Acoust Speech Signal Proc 37 2091ndash2110 (1989)
[457] SG Mallat A theory for multiresolution signal decomposition The wavelet representa-tion IEEE Trans Pattern Anal Machine Intell 11 674ndash693 (1989)
[458] S Mallat W-L Hwang Singularity detection and processing with wavelets IEEE TransInform Theory 38 617ndash643 (1992)
[459] S Mallat Z Zhang Matching pursuits with time frequency dictionaries IEEE TransSignal Proc 41 3397ndash3415 (1993)
[460] S Mallat S Zhong Wavelet maxima representation in Wavelets and Applications (ProcMarseille 1989) ed by Y Meyer (Masson and Springer Paris and Berlin 1991) pp 207ndash284
[461] VI Manrsquoko G Marmo ECG Sudarshan F Zaccaria f -oscillators and non-linearcoherent states Phys Scr 55 528ndash541 (1997)
[462] D Marinucci D Pietrobon A Baldi P Baldi P Cabella G Kerkyacharian P Natoli DPicard N Vittorio Spherical needlets for CMB data analysis Mon Not R Astron Soc383 539ndash545 (2008)
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[464] Y Meyer Principe drsquoincertitude bases hilbertiennes et algegravebres drsquoopeacuterateurs SeacuteminaireBourbaki 662 (1985ndash1986)
[465] Y Meyer Principe drsquoincertitude bases hilbertiennes et algegravebres drsquoopeacuterateurs Asteacuterisque145ndash146 209ndash223 (1987)
[466] Y Meyer H Xu Wavelet analysis and chirps Appl Comput Harmon Anal 4 366ndash379(1997)
[467] L Michel Invariance in quantum mechanics and group extensions in Group TheoreticalConcepts and Methods in Elementary Particle Physics ed by F Guumlrsey (Gordon andBreach New York and London 1964) pp 135ndash200
[468] J Mickelsson J Niederle Contractions of representations of the de Sitter groupsCommun Math Phys 27 167ndash180 (1972)
[469] MM Miller Convergence of the Sudarshan expansion for the diagonal coherent-stateweight functional J Math Phys 9 1270ndash1274 (1968)
[470] V F Molchanov Harmonic analysis on homogeneous spaces in Representation Theoryand Noncommutative Harmonic Analysis II ed by AA Kirillov (Springer Berlin 1995)
[471] MI Monastyrsky AM Perelomov Coherent states and symmetric spaces II Ann InstH Poincareacute 23 23ndash48 (1975)
[472] B Moran S Howard D Cochran Positive-operator-valued measures A general settingfor frames in Excursions in Harmonic Analysis vol 1 2 ed by TD Andrews R BalanJJ Benedetto W Czaja KA Okoudjou (Birkhaumluser Boston 2013) pp 49ndash64
[473] H Moscovici Coherent states representations of nilpotent Lie groups Commun MathPhys 54 63ndash68 (1977)
[474] H Moscovici A Verona Coherent states and square integrable representations Ann InstH Poincareacute 29 139ndash156 (1978)
[475] F Mujica R Murenzi MJT Smith J-P Leduc Robust tracking in compressed imagesequences J Electr Imaging 7 746ndash754 (1998)
[476] R Murenzi Wavelet transforms associated to the n-dimensional Euclidean group withdilations Signals in more than one dimension in Wavelets Time-Frequency Methodsand Phase Space (Proc Marseille 1987) ed by J-M Combes A Grossmann PTchamitchian 2nd edn (Springer Berlin 1990) pp 239ndash246
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[479] MA Naımark Dokl Akad Nauk SSSR 41 359ndash361 (1943) see also B Sz-NagyExtensions of linear transformations in Hilbert space which extend beyond this spaceAppendix to F Riesz B Sz-Nagy Functional Analysis (Frederick Ungar New York 1960)
[480] FJ Narcowich P Petrushev JD Ward Localized tight frames on spheres SIAM J MathAnal 38 574ndash594 (2006)
[481] M Nauenberg Quantum wave packets on Kepler elliptic orbits Phys Rev A 40 1133ndash1136 (1989)
[482] M Nauenberg C Stroud J Yeazell The classical limit of an atom Scient Amer 27024ndash29 (1994)
[483] H Neumann Transformation properties of observables Helv Phys Acta 45 811ndash819(1972)
[484] U Niederer The maximal kinematical invariance group of the free Schroumldinger equationHelv Phys Acta 45 802ndash881 (1972)
[485] MM Nieto LM Simmons Jr Coherent states for general potentials I Formalism IIConfining one-dimensional examples III Nonconfining one-dimensional examples PhysRev D 20 1321ndash1331 1332ndash1341 1342ndash1350 (1979)
[486] MM Nieto LM Simmons Jr Coherent states for general potentials Phys Rev Lett 41207ndash210 (1987)
[487] A Odzijewicz On reproducing kernels and quantization of states Commun Math Phys114 577ndash597 (1988)
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[490] A Odzijewicz M Horowski A Tereszkiewicz Integrable multi-boson systems andorthogonal polynomials J Phys A Math Gen 34 4353ndash4376 (2001)
[491] G Oacutelafsson B Oslashrsted The holomorphic discrete series for affine symmetric spaces JFunct Anal 81 126ndash159 (1988)
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[494] E Onofri Dynamical quantization of the Kepler manifold J Math Phys 17 401ndash408(1976)
[495] D Oriti R Pereira L Sindoni Coherent states in quantum gravity A construction basedon the flux representation of loop quantum gravity J Phys A Math Theor 45 244004(2012)
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[498] Z Pasternak-Winiarski On reproducing kernels for holomorphic vector bundles inQuantization and Infinite Dimensional Systems (Proc Białowieza Poland 1993) ed by J-P Antoine ST Ali W Lisiecki IM Mladenov A Odzijewicz (Plenum Press New Yorkand London 1994) pp 109ndash112
[499] T Paul Affine coherent states and the radial Schroumldinger equation I preprint CPT-84P1710 (1984) (unpublished)
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[501] AM Perelomov On the completeness of a system of coherent states Theor Math Phys6 156ndash164 (1971)
[502] AM Perelomov Coherent states for arbitrary Lie group Commun Math Phys 26 222ndash236 (1972)
[503] AM Perelomov Coherent states and symmetric spaces Commun Math Phys 44 197ndash210 (1975)
[504] M Perroud Projective representations of the Schroumldinger group Helv Phys Acta 50 233ndash252 (1977)
[505] J Phillips A note on square-integrable representations J Funct Anal 20 83ndash92 (1975)[506] D Pietrobon P Baldi D Marinucci Integrated Sachs-Wolfe effect from the cross
correlation of WMAP3 year and the NRAO VLA sky survey data New results andconstraints on dark energy Phys Rev D 74 043524 (2006)
[507] WWF Pijnappel A van den Boogaart R de Beer D van Ormondt SVD-basedquantification of magnetic resonance signals J Magn Reson 97 122ndash134 (1992)
[508] V Pop D Rosca Generalized piecewise constant orthogonal wavelet bases on 2D-domains Appl Anal 90 715ndash723 (2011)
[509] G Poumlschl E Teller Bemerkungen zur Quantenmechanik des anharmonischen OszillatorsZ Physik 83 143ndash151 (1933)
[510] D Potts G Steidl M Tasche Kernels of spherical harmonics and spherical frames inAdvanced Topics in Multivariate Approximation ed by F Fontanella K Jetter PJ Laurent(World Scientific Singapore 1996) pp 287ndash301
[511] E Prugovecki Consistent formulation of relativistic dynamics for massive spin-zeroparticles in external fields Phys Rev D 18 3655ndash3673 (1978) (Appendix C)
[512] E Prugovecki Relativistic quantum kinematics on stochastic phase space for massiveparticles J MathPhys 19 2261ndash2270 (1978)
[513] C Quesne Coherent states of the real symplectic group in a complex analytic parametriza-tion I II J Math Phys 27 428ndash441 869ndash878 (1986)
[514] C Quesne Generalized vector coherent states of sp(2NR) vector operators and ofsp(2NR) sup u(N) reduced Wigner coefficients J Phys A Math Gen 24 2697ndash2714(1991)
[515] JM Radcliffe Some properties of spin coherent states J Phys A Math Gen 4 313ndash323(1971)
[516] A Rahimi A Najati YN Dehghan Continuous frames in Hilbert spaces Methods FunctAnal Topol 12 170ndash182 (2006)
[517] H Rauhut M Roumlsler Radial multiresolution in dimension three Constr Approx 22 193ndash218 (2005)
[518] JH Rawnsley Coherent states and Kaumlhler manifolds Quart J Math Oxford 28(2) 403ndash415 (1977)
[519] J Renaud The contraction of the SU(11) discrete series of representations by means ofcoherent states J Math Phys 37 3168ndash3179 (1996)
[520] A Reacutenyi Representations for real numbers and their ergodic properties Acta Math AcadSci Hungary 8(3ndash4) 477ndash493 (1957)
[521] D Robert La coheacuterence dans tous ses eacutetats SMF Gazette 132 (2012)[522] JE Roberts The Dirac bra and ket formalism J Math Phys 7 1097ndash1104 (1966)[523] JE Roberts Rigged Hilbert spaces in quantum mechanics Commun Math Phys 3 98ndash
119 (1966)[524] S Roques F Bourzeix K Bouyoucef Soft-thresholding technique and restoration of
3C273 jet Astrophys Space Sci Nr 239 297ndash304 (1996)[525] D Rosca Haar wavelets on spherical triangulations in Advances in Multiresolution for
Geometric Modelling ed by NA Dogson MS Floater MA Sabin (Springer Berlin2005) pp 407ndash419
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501ndash511 (2007)[529] D Rosca Wavelet bases on the sphere obtained by radial projection J Fourier Anal Appl
13 421ndash434 (2007)[530] D Rosca Piecewise constant wavelets on triangulations obtained by 1ndash3 splitting Int J
Wavelets Multiresolut Inf Process 6 209ndash222 (2008)[531] D Rosca On a norm equivalence on L2(S2) Results Math 53 399ndash405 (2009)[532] D Rosca New uniform grids on the sphere Astron Astrophys 520 (2010) Art A63[533] D Rosca Uniform and refinable grids on elliptic domains and on some surfaces of
revolution Appl Math Comput 217 7812ndash7817 (2011)[534] D Rosca Wavelet analysis on some surfaces of revolution via area preserving projection
Appl Comput Harmon Anal 30 262ndash272 (2011)[535] D Rosca J-P Antoine Locally supported orthogonal wavelet bases on the sphere via
stereographic projection Math Probl Eng 2009 124904 (2009)[536] D Rosca J-P Antoine Constructing wavelet frames and orthogonal wavelet bases on the
sphere in Recent Advances in Signal Processing ed by S Miron (IN-TECH ViennaAustria and Rijeka Croatia 2010) pp 59ndash76
[537] D Rosca G Plonka Uniform spherical grids via area preserving projection from the cubeto the sphere J Comput Appl Math 236 1033ndash1041 (2011)
[538] D Rosca G Plonka An area preserving projection from the regular octahedron to thesphere Results Math 63 429ndash444 (2012)
[539] H Rossi M Vergne Analytic continuation of the holomorphic discrete series for a semi-simple Lie group Acta Math 136 1ndash59 (1976)
[540] DJ Rotenberg Application of Sturmian functions to the Schroedinger three-body prob-lem Elastic e+ndashH scattering Ann Phys (NY) 19 262ndash278 (1962)
[541] C Rovelli Zakopane lectures on loop gravity in Proceedings of 3rd Quantum Gravityand Quantum Geometry School 28 Febndash13 March 2011 (Zakopane Poland 2011)arXiv11023660v5
[542] C Rovelli S Speziale A semiclassical tetrahedron Class Quant Grav 23 5861ndash5870(2006)
[543] DJ Rowe Coherent state theory of the noncompact symplectic group J Math Phys 252662ndash2271 (1984)
[544] DJ Rowe Microscopic theory of the nuclear collective model Rep Prog Phys 48 1419ndash1480 (1985)
[545] DJ Rowe Vector coherent state representations and their inner products J Phys A MathGen 45 244003 (2012) (This paper belongs to the special issue [38])
[546] DJ Rowe J Repka Vector-coherent-state theory as a theory of induced representationsJ Math Phys 32 2614ndash2634 (1991)
[547] DJ Rowe G Rosensteel R Gilmore Vector coherent state representation theory J MathPhys 26 2787ndash2791 (1985)
[548] A Royer Phase states and phase operators for the quantum harmonic oscillator Phys RevA 53 70ndash108 (1996)
[549] J Saletan Contraction of Lie groups J Math Phys 2 1ndash21 (1961)[550] G Saracco A Grossmann P Tchamitchian Use of wavelet transforms in the study of
propagation of transient acoustic signals across a plane interface between two homoge-neous media in Wavelets Time-Frequency Methods and Phase Space (Proc Marseille1987) ed by J-M Combes A Grossmann P Tchamitchian 2nd edn (Springer Berlin1990) pp 139ndash146
[551] P Schroumlder W Sweldens Spherical wavelets Efficiently representing functions on thesphere in Computer Graphics Proceedings (SIGGRAPH95) (ACM Siggraph Los Angeles1995) pp 161ndash175
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[552] E Schroumldinger Der stetige Uumlbergang von der Mikro- zur Makromechanik Naturwiss 14664ndash666 (1926)
[553] S Scodeller Oslash Rudjord FK Hansen D Marinucci D Geller A Mayeli IntroducingMexican needlets for CMB analysis Issues for practical applications and comparison withstandard needlets Astrophys J 733 (2011) Art 121
[554] H Scutaru Coherent states and induced representations Lett Math Phys 2 101ndash107(1977)
[555] B Simon Distributions and their Hermite expansions J Math Phys 12 140ndash148 (1971)[556] B Simon The classical moment problem as a self-adjoint finite difference operator Adv
Math 137 82ndash203 (1998)[557] R Simon ECG Sudarshan N Mukunda Gaussian pure states in quantum mechanics
and the symplectic group Phys Rev A37 3028ndash3038 (1988)[558] S Sivakumar Studies on nonlinear coherent states J Opt B Quant Semiclass Opt 2
R61ndashR75 (2000)[559] E Slezak A Bijaoui G Mars Identification of structures from galaxy counts Use of the
wavelet transform Astron Astroph 227 301ndash316 (1990)[560] A Solomon A characteristic functional for deformed photon phenomenology Phys Lett
A 196 29ndash34 (1994)[561] SB Sontz Paragrassmann algebras as quantum spaces Part I Reproducing kernels in
Geometric Methods in Physics XXXI Workshop 2012 (Trends in Mathematics ed byP Kielanowski et al Birkhaumluser Verlag Basel 2013) pp 47ndash63
[562] SB Sontz Paragrassmann algebras as quantum spaces Part II Toeplitz operators J OperTh (2013 to appear) arXiv12055493
[563] SB Sontz A reproducing kernel and Toeplitz operators in the quantum plane Preprint(2013) arXiv13056986 [math-ph]
[564] SB Sontz Toeplitz quantization of an algebra with conjugation Preprint (2013)arXiv13085454 [math-ph]
[565] M Spera On a generalized Uncertainty Principle coherent states and the moment mapJ Geom Phys 12 165ndash182 (1993)
[566] J-L Starck EJ Candegraves DL Donoho The curvelet transform for image denoising IEEETrans Image Proc 11 670ndash684 (2002)
[567] J-L Starck DL Donoho E J Candegraves Astronomical image representation by the curvelettransform Astron Astroph 398 785ndash800 (2003)
[568] J-L Starck Y Moudden P Abrial M Nguyen Wavelets ridgelets and curvelets on thesphere Astron Astroph 446 1191ndash1204 (2006)
[569] MB Stenzel The Segal-Bargmann transform on a symmetric space of compact type JFunct Analysis 165 44ndash58 (1994)
[570] ECG Sudarshan Equivalence of semiclassical and quantum mechanical descriptions ofstatistical light beams Phys Rev Lett 10 277ndash279 (1963)
[571] A Suvichakorn H Ratiney A Bucur S Cavassila J-P Antoine Toward a quantitativeanalysis of in vivo magnetic resonance proton spectroscopic signals using the continuousMorlet wavelet transform Meas Sci Technol 20 (2009) Art 104029
[572] W Sweldens The lifting scheme A custom-design construction of biorthogonal waveletsApplied Comput Harmon Anal 3 1186ndash1200 (1996)
[573] W Sweldens The lifting scheme A construction of second generation wavelets SIAM JMath Anal 29 511ndash546 (1998)
[574] FH Szafraniec The reproducing kernel Hilbert space and its multiplication operatorsin Complex Analysis and Related Topics ed by E Ramirez de Arellano et al OperatorTheory Advances and Applications vol 114 (Birkhaumluser Basel 2000) pp 254ndash263
[575] FH Szafraniec Multipliers in the reproducing kernel Hilbert space subnormality andnoncommutative complex analysis in Reproducing Kernel Spaces and Applications edby D Alpay Operator Theory Advances and Applications vol 143 (Birkhaumluser Basel2003) pp 313ndash331
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[577] MC Teich BEA Saleh Squeezed states of light Quantum Opt 1 152ndash191 (1989)[578] R Terrier L Demanet IA Grenier J-P Antoine Wavelet analysis of EGRET data in
Proceedings of the 27th International Cosmic Ray Conference (ICRC 2001) (CopernicusGesellschaft DE 2001) pp 2923ndash2926
[579] T Thiemann Gauge field theory coherent states (GCS) 1 General properties Class QuantGrav 18 2025ndash2064 (2001)
[580] T Thiemann O Winkler Gauge field theory coherent states (GCS) 2 Peakednessproperties Class Quant Grav 18 2561ndash2636 (2001)
[581] T Thiemann O Winkler Gauge field theory coherent states (GCS) 3 Ehrenfest theoremsClass Quant Grav 18 4629ndash4682 (2001)
[582] T Thiemann O Winkler Gauge field theory coherent states (GCS) 4 Infinite tensorproduct and thermodynamical limit Class Quant Grav 18 4997ndash5054 (2001)
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[584] K Thirulogasanthar G Honnouvo A Krzyzak Coherent states and Hermite polynomialson quaternionic Hilbert spaces J Phys A Math Theor 43 385205 (2010)
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simulation of an impact test using wavelets analytical and finite element models Int JSolids Struct 38 5481ndash5508 (2001)
[594] L Vanhamme RD Fierro S Van Huffel R de Beer Fast removal of residual water inproton spectra J Magn Reson 132 197ndash203 (1998)
[595] J Ville Theacuteorie et applications de la notion de signal analytique Cacircbles et Trans 2 61ndash74(1948)
[596] J Voisin On some unitary representations of the Galilei group I Irreducible representa-tions J Math Phys 6 1519ndash1529 (1965)
[597] A Vourdas Analytic representations in quantum mechanics J Phys A Math Gen 39R65ndashR141 (2006)
[598] DF Walls Squeezed states of light Nature 306 141ndash146 (1983)[599] YK Wang FT Hioe Phase transition in the Dicke maser model Phys Rev A 7 831ndash836
(1973)[600] PSP Wang J Yang A review of wavelet-based edge detection methods Int J Patt
Recogn Artif Intell 26 1255011 (2012)[601] I Weinreich A construction of C1-wavelets on the two-dimensional sphere Appl Comput
Harmon Anal 10 1ndash26 (2001)[602] H Weyl Quantenmechanik und Gruppentheorie Z Phys 46 1ndash46 (1927)
References 571
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[605] Y Wiaux JD McEwen P Vandergheynst O Blanc Exact reconstruction with directionalwavelets on the sphere Mon Not R Astron Soc 388 770ndash788 (2008)
[606] WM Wieland Complex Ashtekar variables and reality conditions for Holstrsquos action AnnHenri Poincareacute 13 425ndash448 (2012)
[607] EP Wigner On the quantum correction for thermodynamic equilibrium Phys Rev 40749ndash759 (1932)
[608] RM Willette RD Nowak Platelets A multiscale approach for recovering edges andsurfaces in photon-limited medical imaging IEEE Trans Med Imaging 22 332ndash350(2003)
[609] W Wisnoe P Gajan A Strzelecki C Lempereur J-M Matheacute The use of the two-dimensional wavelet transform in flow visualization processing in Progress in WaveletAnalysis and Applications (Proc Toulouse 1992) ed by Y Meyer S Roques (EdFrontiegraveres Gif-sur-Yvette 1993) pp 455ndash458
[610] K Woacutedkiewicz On the quantum mechanics of squeezed states J Modern Optics 34 941ndash948(1987)
[611] JA Yeazell M Mallalieu CR Stroud Jr Observation of the collapse and revival of aRydberg electronic wave packet Phys Rev Lett 64 2007ndash2010 (1990)
[612] JA Yeazell CR Stroud Jr Observation of fractional revivals in the evolution of aRydberg atomic wave packet Phys Rev A 43 5153ndash5156 (1991)
[613] HP Yuen Two-photon coherent states of the radiation field Phys Rev A 13 2226ndash2243(1976)
[614] J Zak Balian-Low theorem for Landau levels Phys Rev Lett 79 533ndash536 (1997)[615] J Zak Orthonormal sets of localized functions for a Landau level J Math Phys 39 4195ndash
4200 (1998) and references quoted there[616] AA Zakharova On the properties of generalized frames Math Notes 83 190ndash200 (2008)[617] W-M Zhang DH Feng R Gilmore Coherent states Theory and some applications Rev
Mod Phys 26 867ndash927 (1990)[618] I Zlatev W-M Zhang DH Feng Possibility that Schroumldingerrsquos conjecture for the
hydrogen atom coherent states is not attainable Phys Rev A 50 R1973ndashR1975 (1994)[619] WH Zurek Decoherence einselection and the quantum origins of the classical Rev Mod
Phys 75 715ndash775 (2003)[620] WH Zurek S Habib JP Paz Coherent states via decoherence Phys Rev Lett 70 1187ndash
1190 (1993)[621] K Zyczkowski Squeezed states in a quantum chaotic system J Phys A Math Theor 22
of SU(11) 81 296 297HilbertClowast-modules 164holomorphic 140nonholomorphic 151nonlinear 146of affine Galilei group 505of affine Poincareacute group 509of affine Weyl-Heisenberg group GaWH
497of compact semisimple Lie groups 174of Euclidean group E(n) 266of Galilei group G (11) 290of isochronous Galilei group 237of non-semisimple Lie groups 179of noncompact semisimple Lie groups 177of Poincareacute group Puarr
+(11) 283massless case 288
of Poincareacute group Puarr+(13) 279
of Schroumldinger group 508quasi-coherent states 186quaternionic 164
ST Ali et al Coherent States Wavelets and Their Generalizations Theoreticaland Mathematical Physics DOI 101007978-1-4614-8535-3copy Springer Science+Business Media New York 2014
573
574 Index
coherent states (CS) (cont)spin or SU(2) 175square integrable covariant 166 180 264vector (VCS) 73 108 112 170weighted 184 523
of affine Weyl-Heisenberg group GaWH497
of Poincareacute group Puarr+(11) 284
cohomology group 393 403coboundaries 403cochains 402cocycle 403
algebraic 387Cauchy 418Cauchy-Paul 354 419 425conical 418difference 417 462directional 416 440kinematical 499local 488metabolite-based 355 374minimal uncertainty 425multiselective 440on a graph 493on the sphere S
2 458on the sphere S
n 479on the torus T2 481steerable 439von Mises 440
wedgelet transform 455Wigner function 322Wigner-Ville transform 349Windowed Fourier or Gabor transform 349
ZZak transform 518
References
A Books and Theses
B Articles
Index
548 References
[42] P Aniello G Cassinelli E De Vito A Levrero Wavelet transforms and discrete framesassociated to semidirect products J Math Phys 39 3965ndash3973 (1998)
[43] J-P Antoine Remarques sur le vecteur de Runge-Lenz Ann Soc Scient Bruxelles 80160ndash168 (1966)
[44] J-P Antoine Etude de la deacutegeacuteneacuterescence orbitale du potentiel coulombien en theacuteorie desgroupes I II Ann Soc Scient Bruxelles 80 169ndash184 (1966)
[45] J-P Antoine Etude de la deacutegeacuteneacuterescence orbitale du potentiel coulombien en theacuteorie desgroupes I II Ann Soc Scient Bruxelles 81 49ndash68 (1967)
[46] J-P Antoine Dirac formalism and symmetry problems in quantum mechanics I Generaldirac formalism J Math Phys 10 53ndash69 (1969)
[47] J-P Antoine Dirac formalism and symmetry problems in quantum mechanics II Symme-try problems J Math Phys 10 2276ndash2290 (1969)
[48] J-P Antoine Quantum mechanics beyond Hilbert space in Irreversibility and Causality mdashSemigroups and Rigged Hilbert Spaces ed by A Boumlhm H-D Doebner P KielanowskiLecture Notes in Physics vol 504 (Springer Berlin 1998) pp 3ndash33
[49] J-P Antoine Discrete wavelets on abelian locally compact groups Rev Cien Math(Habana) 19 3ndash21 (2003)
[50] J-P Antoine Introduction to precursors in physics Affine coherent states in FundamentalPapers in Wavelet Theory ed by C Heil D Walnut (Princeton University Press PrincetonNJ 2006) pp 113ndash116
[51] J-P Antoine F Bagarello Wavelet-like orthonormal bases for the lowest Landau levelJ Phys A Math Gen 27 2471ndash2481 (1994)
[52] J-P Antoine P Balazs Frames and semi-frames J Phys A Math Theor 44 205201(2011) (25 pages) Corrigendum J-P Antoine P Balazs Frames and semi-frames J PhysA Math Theor 44 479501 (2011) (2 pages)
[53] J-P Antoine P Balazs Frames semi-frames and Hilbert scales Numer Funct AnalOptim 33 736ndash769 (2012)
[54] J-P Antoine A Coron Time-frequency and time-scale approach to magnetic resonancespectroscopy J Comput Methods Sci Eng (JCMSE) 1 327ndash352 (2001)
[55] J-P Antoine AL Hohoueacuteto Discrete frames of Poincareacute coherent states in 1+3 dimen-sions J Fourier Anal Appl 9 141ndash173 (2003)
[56] J-P Antoine I Mahara Galilean wavelets Coherent states for the affine Galilei groupJ Math Phys 40 5956ndash5971 (1999)
[57] J-P Antoine U Moschella Poincareacute coherent states The two-dimensional massless caseJ Phys A Math Gen 26 591ndash607 (1993)
[58] J-P Antoine R Murenzi Two-dimensional directional wavelets and the scale-anglerepresentation Signal Process 52 259ndash281 (1996)
[59] J-P Antoine R Murenzi Two-dimensional continuous wavelet transform as linear phasespace representation of two-dimensional signals in Wavelet Applications IV SPIE Pro-ceedings vol 3078 (SPIE Bellingham WA 1997) pp 206ndash217
[60] J-P Antoine D Rosca The wavelet transform on the two-sphere and related manifolds mdashA review in Optical and Digital Image Processing SPIE Proceedings vol 7000 (2008)pp 70000B-1ndash15
[61] J-P Antoine D Speiser Characters of irreducible representations of simple Lie groupsJ Math Phys 5 1226ndash1234 (1964)
[62] J-P Antoine P Vandergheynst Wavelets on the n-sphere and related manifolds J MathPhys 39 3987ndash4008 (1998)
[63] J-P Antoine P Vandergheynst Wavelets on the 2-sphere A group-theoretical approachAppl Comput Harmon Anal 7 262ndash291 (1999)
[64] J-P Antoine P Vandergheynst Wavelets on the two-sphere and other conic sections JFourier Anal Appl 13 369ndash386 (2007)
[65] J-P Antoine M Duval-Destin R Murenzi B Piette Image analysis with 2D wavelettransform Detection of position orientation and visual contrast of simple objects inWavelets and Applications (Proc Marseille 1989) ed by Y Meyer (Masson and SpringerParis and Berlin 1991) pp144ndash159
References 549
[66] J-P Antoine P Carrette R Murenzi B Piette Image analysis with 2D continuous wavelettransform Signal Process 31 241ndash272 (1993)
[67] J-P Antoine P Vandergheynst K Bouyoucef R Murenzi Alternative representations ofan image via the 2D wavelet transform Application to character recognition in VisualInformation Processing IV SPIE Proceedings vol 2488 (SPIE Bellingham WA 1995)pp 486ndash497
[68] J-P Antoine R Murenzi P Vandergheynst Two-dimensional directional wavelets inimage processing Int J Imaging Syst Tech 7 152ndash165 (1996)
[69] J-P Antoine D Barache RM Cesar Jr LF Costa Shape characterization with thewavelet transform Signal Process 62 265ndash290 (1997)
[70] J-P Antoine P Antoine B Piraux Wavelets in atomic physics in Spline Functions andthe Theory of Wavelets ed by S Dubuc G Deslauriers CRM Proceedings and LectureNotes vol 18 (AMS Providence RI 1999) pp261ndash276
[71] J-P Antoine P Antoine B Piraux Wavelets in atomic physics and in solid state physicsin Wavelets in Physics Chap 8 ed by JC van den Berg (Cambridge University PressCambridge 1999)
[72] J-P Antoine R Murenzi P Vandergheynst Directional wavelets revisited Cauchywavelets and symmetry detection in patterns Appl Comput Harmon Anal 6 314ndash345(1999)
[73] J-P Antoine L Jacques R Twarock Wavelet analysis of a quasiperiodic tiling withfivefold symmetry Phys Lett A 261 265ndash274 (1999)
[74] J-P Antoine L Jacques P Vandergheynst Penrose tilings quasicrystals and wavelets inWavelet Applications in Signal and Image Processing VII SPIE Proceedings vol 3813(SPIE Bellingham WA 1999) pp 28ndash39
[75] J-P Antoine YB Kouagou D Lambert B Torreacutesani An algebraic approach to discretedilations Application to discrete wavelet transforms J Fourier Anal Appl 6 113ndash141(2000)
[76] J-P Antoine A Coron J-M Dereppe Water peak suppression Time-frequency vs time-scale approach J Magn Reson 144 189ndash194 (2000)
[77] J-P Antoine J-P Gazeau P Monceau J R Klauder K Penson Temporally stablecoherent states for infinite well and Poumlschl-Teller potentials J Math Phys 42 2349ndash2387(2001)
[78] J-P Antoine A Coron C Chauvin Wavelets and related time-frequency techniques inmagnetic resonance spectroscopy NMR Biomed 14 265ndash270 (2001)
[79] J-P Antoine L Demanet J-F Hochedez L Jacques R Terrier E Verwichte Applicationof the 2-D wavelet transform to astrophysical images Phys Mag 24 93ndash116 (2002)
[80] J-P Antoine L Demanet L Jacques P Vandergheynst Wavelets on the sphere Imple-mentation and approximations Appl Comput Harmon Anal 13 177ndash200 (2002)
[81] J-P Antoine I Bogdanova P Vandergheynst The continuous wavelet transform on conicsections Int J Wavelets Multires Inform Proc 6 137ndash156 (2007)
[82] J-P Antoine D Rosca P Vandergheynst Wavelet transform on manifolds Old and newapproaches Appl Comput Harmon Anal 28 189ndash202 (2010)
[83] P Antoine B Piraux A Maquet Time profile of harmonics generated by a single atom ina strong electromagnetic field Phys Rev A 51 R1750ndashR1753 (1995)
[84] P Antoine B Piraux DB Miloševic M Gajda Generation of ultrashort pulses ofharmonics Phys Rev A 54 R1761ndashR1764 (1996)
[85] P Antoine B Piraux DB Miloševic M Gajda Temporal profile and time control ofharmonic generation Laser Phys 7 594ndash601 (1997)
[86] Apollonius see Wikipedia httpenwikipediaorgwikiApollonius_of_Perga[87] FT Arecchi E Courtens R Gilmore H Thomas Atomic coherent states in quantum
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systems with cylindric phase space J Phys A Math Theor 45 335302 (2012)
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[96] A Arneacuteodo Y drsquoAubenton E Bacry PV Graves JF Muzy C Thermes Wavelet basedfractal analysis of DNA sequences Physica D 96 291ndash320 (1996)
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J Math Phys 10 2267ndash2275 (1969)[104] D Astruc L Plantieacute R Murenzi Y Lebret D Vandromme On the use of the 3D
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[105] PW Atkins JC Dobson Angular momentum coherent states Proc Roy Soc London A321 321ndash340 (1971)
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[121] D Barache S De Biegravevre J-P Gazeau Affine symmetry semigroups for quasicrystalsEurophys Lett 25 435ndash440 (1994)
[122] D Barache J-P Antoine J-M Dereppe The continuous wavelet transform a tool for NMRspectroscopy J Magn Reson 128 1ndash11 (1997)
[123] V Bargmann On a Hilbert space of analytic functions and an associated integral transformPart I Commun Pure Appl Math 14 187ndash214 (1961)
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[125] V Bargmann P Butera L Girardello JR Klauder On the completeness of coherentstates Reports Math Phys 2 221ndash228 (1971)
[126] AO Barut L Girardello New ldquocoherentrdquo states associated with non compact groupsCommun Math Phys 21 41ndash55 (1971)
[127] AO Barut H Kleinert Transition probabilities of the hydrogen atom from noncompactdynamical groups Phys Rev 156 1541ndash1545 (1967)
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[134] JJ Benedetto A Teolis A wavelet auditory model and data compression Appl ComputHarmon Anal 1 3ndash28 (1993)
[135] FA Berezin Quantization Math USSR Izvestija 8 1109ndash1165 (1974)[136] FA Berezin General concept of quantization Commun Math Phys 40 153ndash174 (1975)[137] H Bergeron From classical to quantum mechanics How to translate physical ideas into
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[145] S Bergman Uumlber die Kernfunktion eines Bereiches und ihr Verhalten am Rande I ReineAngw Math 169 1ndash42 (1933)
[146] D Bernier KF Taylor Wavelets from square-integrable representations SIAM J MathAnal 27 594ndash608 (1996)
[147] G Bernuau Wavelet bases associated to a self-similar quasicrystal J Math Phys 394213ndash4225 (1998)
[148] A Bertrand Deacuteveloppements en base de Pisot et reacutepartition modulo 1 C R Acad SciParis 285 419ndash421 (1977)
[149] J Bertrand P Bertrand Classification of affine Wigner functions via an extendedcovariance principle in Group Theoretical Methods in Physics (Proc Sainte-Adegravele 1988)ed by Y Saint-Aubin L Vinet (World Scientific Singapore 1989) pp 1380ndash1383
[150] Z Białynicka-Birula I Białynicki-Birula Space-time description of squeezing J OptSoc Am B4 1621ndash1626 (1987)
[151] E Bianchi E Magliaro C Perini Coherent spin-networks Phys Rev D 82 024012(2010)
[152] S Biskri J-P Antoine B Inhester F Mekideche Extraction of Solar coronal magneticloops with the 2-D Morlet wavelet transform Solar Phys 262 373ndash385 (2010)
[153] R Bluhm VA Kostelecky JA Porter The evolution and revival structure of localizedquantum wave packets Am J Phys 64 944ndash953 (1996)
[154] I Bogdanova P Vandergheynst J-P Antoine L Jacques M Morvidone Stereographicwavelet frames on the sphere Appl Comput Harmon Anal 19 223ndash252 (2005)
[155] I Bogdanova X Bresson J-P Thiran P Vandergheynst Scale space analysis and activecontours for omnidirectional images IEEE Trans Image Process 16 1888ndash1901 (2007)
[156] I Bogdanova P Vandergheynst J-P Gazeau Continuous wavelet transform on thehyperboloid Appl Comput Harmon Anal 23 (2007) 286ndash306 (2007)
[157] P Boggiatto E Cordero Anti-Wick quantization of tempered distributions in Progress inAnalysis Berlin (2001) vol I II (World Sci Publ River Edge NJ 2003) pp 655ndash662
[158] P Boggiatto E Cordero K Groumlchenig Generalized Anti-Wick operators with symbols indistributional Sobolev spaces Int Equ Oper Theory 48 427ndash442 (2004)
[159] A Boumlhm The Rigged Hilbert Space in quantum mechanics in Lectures in TheoreticalPhysics vol IX A ed by WA Brittin et al (Gordon amp Breach New York 1967) pp255ndash315
[160] G Bohnkeacute Treillis drsquoondelettes associeacutes aux groupes de Lorentz Ann Inst H Poincareacute54 245ndash259 (1991)
[161] WR Bomstad JR Klauder Linearized quantum gravity using the projection operatorformalism Class Quantum Grav 23 5961ndash5981 (2006)
[162] VV Borzov Orthogonal polynomials and generalized oscillator algebras Int TransformSpec Funct 12 115ndash138 (2001)
[163] VV Borzov EV Damaskinsky Generalized coherent states for classical orthogonalpolynomials Day on Diffraction (2002) arXivmathQA0209181v1 (SPb 2002)
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[165] A Bouzouina S De Biegravevre Equipartition of the eigenfunctions of quantized ergodic mapson the torus Commun Math Phys 178 83ndash105 (1996)
[166] P Brault J-P Antoine A spatio-temporal Gaussian-Conical wavelet with high apertureselectivity for motion and speed analysis Appl Comput Harmon Anal 34 148ndash161(2012)
[167] A Briguet S Cavassila D Graveron-Demilly Suppression of huge signals using theCadzow enhancement procedure The NMR Newslett 440 26 (1995)
[168] CM Brislawn Fingerprints go digital Notices Amer Math Soc 42 1278ndash1283 (1995)[169] CM Brislawn On the group-theoretic structure of lifted filter banks in Excursions in
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[170] F Bruhat Sur les repreacutesentations induites des groupes de Lie Bull Soc Math France 8497ndash205 (1956)
[171] T Buumllow Multiscale image processing on the sphere in DAGM-Symposium (2002) pp609ndash617
[172] C Burdik C Frougny J-P Gazeau R Krejcar Beta-integers as natural counting systemsfor quasicrystals J Phys A Math Gen 31 6449ndash6472 (1998)
[173] KE Cahill Coherent-state representations for the photon density Phys Rev 138 B1566ndash1576 (1965)
[174] KE Cahill R Glauber Density operators and quasiprobability distributions Phys Rev177 1882ndash1902 (1969)
[175] KE Cahill R Glauber Ordered expansions in boson amplitude operators Phys Rev 1771857ndash1881 (1969)
[176] AR Calderbank I Daubechies W Sweldens BL Yeo Wavelets that map integers tointegers Appl Comput Harmon Anal 5 332ndash369 (1998)
[177] M Calixto J Guerrero Wavelet transform on the circle and the real line A unified group-theoretical treatment Appl Comput Harmon Anal 21 204ndash229 (2006)
[178] M Calixto E Peacuterez-Romero Extended MacMahon-Schwingerrsquos master theorem andconformal wavelets in complex Minkowski space Appl Comput Harmon Anal 31 143ndash168 (2011)
[179] M Calixto J Guerrero D Rosca Wavelet transform on the torus A group-theoreticalapproach preprint (2013)
[180] EJ Candegraves Harmonic analysis of neural networks Appl Comput Harmon Anal 6 197ndash218 (1999)
[181] EJ Candegraves Ridgelets and the representation of mutilated Sobolev functions SIAM JMath Anal 33 347ndash368 (2001)
[182] EJ Candegraves L Demanet Curvelets and Fourier integral operators CR Acad Sci ParisSeacuter I Math 336 395ndash398 (2003)
[183] EJ Candegraves L Demanet The curvelet representation of wave propagators is optimallysparse Commun Pure Appl Math 58 1472ndash1528 (2004)
[184] EJ Candegraves L Demanet The curvelet representation of wave propagators is optimallysparse Commun Pure Appl Math 58 1472ndash1528 (2005)
[185] EJ Candegraves DL Donoho Curvelets ndash A surprisingly effective nonadaptive representationfor objects with edges in Curves and Surfaces ed by LL Schumaker et al (VanderbiltUniversity Press Nashville TN 1999)
[186] EJ Candegraves DL Donoho Ridgelets A key to higher-dimensional intermittency PhilTrans R Soc Lond A 357 2495ndash2509 (1999)
[187] EJ Candegraves DL Donoho Curvelets multiresolution representation and scaling laws inWavelet Applications in Signal and Image Processing VIII ed by A Aldroubi A LaineM Unser SPIE Proceedings vol 4119 (SPIE Bellingham WA 2000) pp 1ndash12
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[189] EJ Candegraves DL Donoho New tight frames of curvelets and optimal representations ofobjects with piecewise C2 singularities Commun Pure Appl Math 57 219ndash266 (2004)
[190] EJ Candegraves DL Donoho Continuous curvelet transform I Resolution of the wavefrontset II Discretization and frames Appl Comput Harmon Anal 19 162ndash197 198ndash222(2005)
[191] EJ Candegraves F Guo New multiscale transforms minimum total variationsynthesisApplications to edge-preserving image reconstruction Signal Proc 82 1519ndash1543 (2002)
[192] EJ Candegraves L Demanet D Donoho L Ying Fast discrete curvelet transforms MultiscaleModel Simul 5 861ndash899 (2006)
[193] AL Carey Square integrable representations of non-unimodular groups Bull AustrMath Soc 15 1ndash12 (1976)
[194] AL Carey Group representations in reproducing kernel Hilbert spaces Rep Math Phys14 247ndash259 (1978)
[195] P Carruthers MM Nieto Phase and angle variables in quantum mechanics Rev ModPhys 40 411ndash440 (1968)
[196] PG Casazza G Kutyniok Frames of subspaces in Wavelets Frames and Operator The-ory Contemporary Mathematics vol 345 (American Mathematical Society ProvidenceRI 2004) pp 87ndash113
[197] PG Casazza D Han DR Larson Frames for Banach spaces Contemp Math 247 149ndash182 (1999)
[198] P Casazza O Christensen S Li A Lindner Riesz-Fischer sequences and lower framebounds Z Anal Anwend 21 305ndash314 (2002)
[199] PG Casazza G Kutyniok S Li Fusion frames and distributed processing ApplComputHarmon Anal 25 114ndash132 (2008)
[200] DPL Castrigiano RW Henrichs Systems of covariance and subrepresentations ofinduced representations Lett Math Phys 4 169ndash175 (1980)
[201] U Cattaneo Densities of covariant observables J Math Phys 23 659ndash664 (1982)[202] A Cerioni L Genovese I Duchemin Th Deutsch Accurate complex scaling of three
dimensional numerical potentials Preprint (2013) arXiv13036439v2[203] S-J Chang K-J Shi Evolution and exact eigenstates of a resonant quantum system Phys
Rev A 34 7ndash22 (1986)[204] SHH Chowdhury ST Ali All the groups of signal analysis from the (1+1) affine Galilei
group J Math Phys 52 103504 (2011)[205] SL Chown Antarctic marine biodiversity and deep-sea hydrothermal vents PLoS Biol
10 1ndash4 (2012)[206] C Cishahayo S De Biegravevre On the contraction of the discrete series of SU(11) Ann Inst
Fourier (Grenoble) 43 551ndash567 (1993)[207] M Clerc and S Mallat Shape from texture and shading with wavelets in Dynamical
Systems Control Coding Computer Vision Progress in Systems and Control Theory 25393ndash417 (1999)
[208] L Cohen General phase-space distribution functions J Math Phys 7 781ndash786 (1966)[209] A Cohen I Daubechies J-C Feauveau Biorthogonal bases of compactly supported
wavelets Commun Pure Appl Math 45 485ndash560 (1992)[210] R Coifman Y Meyer MV Wickerhauser Wavelet analysis and signal processing
in Wavelets and Their Applications ed by MB Ruskai G Beylkin R CoifmanI Daubechies S Mallat Y Meyer L Raphael (Jones and Bartlett Boston 1992)pp 153ndash178
[211] R Coifman Y Meyer MV Wickerhauser Entropy-based algorithms for best basisselection IEEE Trans Inform Theory 38 713ndash718 (1992)
[212] R Coquereaux A Jadczyk Conformal theories curved spaces relativistic wavelets andthe geometry of complex domains Rev Math Phys 2 1ndash44 (1990)
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[214] N Cotfas J-P Gazeau Finite tight frames and some applications (topical review) J PhysA Math Theor 43 193001 (2010)
[215] N Cotfas J-P Gazeau K Goacuterska Complex and real Hermite polynomials and relatedquantizations J Phys A Math Theor 43 305304 (2010)
[216] N Cotfas J-P Gazeau A Vourdas Finite-dimensional Hilbert space and frame quantiza-tion J Phys A Math Gen 44 175303 (2011)
[217] EMF Curado MA Rego-Monteiro LMCS Rodrigues Y Hassouni Coherent statesfor a degenerate system The hydrogen atom Physica A 371 16ndash19 (2006)
[218] S Dahlke P Maass The affine uncertainty principle in one and two dimensions CompMath Appl 30 293ndash305 (1995)
[219] S Dahlke W Dahmen E Schmidt I Weinreich Multiresolution analysis and wavelets onS
2 and S3 Numer Funct Anal Optim 16 19ndash41 (1995)
[220] S Dahlke V Lehmann G Teschke Applications of wavelet methods to the analysis ofmeteorological radar data - An overview Arabian J Sci Eng 28 3ndash44 (2003)
[221] S Dahlke G Kutyniok P Maass C Sagiv H-G Stark G Teschke The uncertaintyprinciple associated with the continuous shearlet transform Int J Wavelets MultiresolutInf Process 6 157ndash181 (2008)
[222] S Dahlke G Kutyniok G Steidl G Teschke Shearlet coorbit spaces and associatedBanach frames Appl Comput Harmon Anal 27 195ndash214 (2009)
[223] S Dahlke G Steidl G Teschke The continuous shearlet transform in arbitrary spacedimensions J Fourier Anal Appl 16 340ndash364 (2010)
[224] S Dahlke G Steidl G Teschke Shearlet coorbit spaces Compactly supported analyzingshearlets traces and embeddings J Fourier Anal Appl 17 1232ndash1355 (2011)
[225] T Dallard GR Spedding 2-D wavelet transforms Generalisation of the Hardy space andapplication to experimental studies Eur J Mech BFluids 12 107ndash134 (1993)
[226] C Daskaloyannis Generalized deformed oscillator and nonlinear algebras J Phys AMath Gen 24 L789ndashL794 (1991)
[227] C Daskaloyannis K Ypsilantis A deformed oscillator with Coulomb energy spectrumJ Phys A Math Gen 25 4157ndash4166 (1992)
[228] I Daubechies On the distributions corresponding to bounded operators in the Weylquantization Commun Math Phys 75 229ndash238 (1980)
[229] I Daubechies and A Grossmann An integral transform related to quantization I J MathPhys 21 2080ndash2090 (1980)
[230] I Daubechies A Grossmann J Reignier An integral transform related to quantization IIJ Math Phys 24 239ndash254 (1983)
[231] I Daubechies Orthonormal bases of compactly supported wavelets Commun Pure ApplMath 41 909ndash996 (1988)
[232] I Daubechies The wavelet transform time-frequency localisation and signal analysisIEEE Trans Inform Theory 36 961ndash1005 (1990)
[233] I Daubechies S Maes A nonlinear squeezing of the continuous wavelet transform basedon auditory nerve models in Wavelets in Medicine and Biology ed by A Aldroubi MUnser (CRC Press Boca Raton 1996) pp 527ndash546
[234] I Daubechies A Grossmann Y Meyer Painless nonorthogonal expansions J Math Phys27 1271ndash1283 (1986)
[235] ER Davies Introduction to texture analysis in Handbook of texture analysis ed by MMirmehdi X Xie J Suri (World Scientific Singapore 2008) pp 1ndash31
[236] R De Beer D van Ormondt FTAW Wajer S Cavassila D Graveron-Demilly S VanHuffel SVD-based modelling of medical NMR signals in SVD and Signal ProcessingIII Algorithms Architectures and Applications ed by M Moonen B De Moor (Elsevier(North-Holland) Amsterdam 1995) pp 467ndash474
[237] S De Biegravevre Coherent states over symplectic homogeneous spaces J Math Phys 301401ndash1407 (1989)
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[239] S De Biegravevre JA Gonzaacutelez Semiclassical behaviour of coherent states on the circle inQuantization and Coherent States Methods in Physics ed by A Odzijewicz et al (WorldScientific Singapore 1993)
[240] S De Biegravevre AE Gradechi Quantum mechanics and coherent states on the anti-de Sitterspace-time and their Poincareacute contraction Ann Inst H Poincareacute 57 403ndash428 (1992)
[241] J Deenen C Quesne Dynamical group of collective states I II III J Math Phys 23878ndash889 2004ndash2015 (1982)
[242] J Deenen C Quesne Dynamical group of collective states I II III J Math Phys 251638ndash1650 (1984)
[243] J Deenen C Quesne Partially coherent states of the real symplectic group J Math Phys25 2354ndash2366 (1984)
[244] J Deenen C Quesne Boson representations of the real symplectic group and theirapplication to the nuclear collective model J Math Phys 26 2705ndash2716 (1985)
[245] R Delbourgo Minimal uncertainty states for the rotation and allied groups J Phys AMath Gen 10 1837ndash1846 (1977)
[246] R Delbourgo J R Fox Maximum weight vectors possess minimal uncertainty J PhysA Math Gen 10 L233ndashL235 (1977)
[247] V Delouille J de Patoul J-F Hochedez L Jacques J-P Antoine Wavelet spectrumanalysis of EITSoHO images Solar Phys 228 301ndash321 (2005)
[248] N Delprat B Escudieacute P Guillemain R Kronland-Martinet P Tchamitchian B Tor-reacutesani Asymptotic wavelet and Gabor analysis Extraction of instantaneous frequenciesIEEE Trans Inform Theory 38 644ndash664 (1992)
[249] Th Deutsch L Genovese Wavelets for electronic structure calculations Collection SocFr Neut 12 33ndash76 (2011)
[250] B Dewitt Quantum theory of gravity I The canonical theory Phys Rev 160 1113ndash1148(1967)
[251] RH Dicke Coherence in spontaneous radiation processes Phys Rev 93 99ndash110 (1954)[252] AN Dinkelaker AL MacKinnon Wavelets intermittency and solar flare hard X-rays 1
Local intermittency measure in cascade and avalanche scenarios Solar Phys 282 471ndash481(2013)
[253] AN Dinkelaker AL MacKinnon Wavelets intermittency and solar flare hard X-rays 2LIM analysis of high time resolution BATSE data Solar Phys 282 483ndash501 (2013)
[254] MN Do M Vetterli Contourlets in Beyond Wavelets ed by GV Welland (AcademicSan Diego 2003) pp 83ndash105
[255] MN Do M Vetterli The contourlet transform An efficient directional multiresolutionimage representation IEEE Trans Image Process 14 2091ndash2106 (2005)
[256] VV Dodonov Nonclassical states in quantum optics A ldquosqueezedrdquo review of the first 75years J Opt B Quant Semiclass Opot 4 R1ndashR33 (2002)
[257] DL Donoho Nonlinear wavelet methods for recovery of signals densities and spectrafrom indirect and noisy data in Different Perspectives on Wavelets Proceedings ofSymposia in Applied Mathematics vol 38 ed by I Daubechies (American MathematicalSociety Providence RI 1993) pp 173ndash205
[258] DL Donoho Wedgelets Nearly minimax estimation of edges Ann Stat 27 859ndash897(1999)
[259] DL Donoho X Huo Beamlet pyramids A new form of multiresolution analysis suitedfor extracting lines curves and objects from very noisy image data in SPIE Proceedingsvol 5914 (SPIE Bellingham WA 2005) pp 1ndash12
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[261] AH Dooley JW Rice Contractions of rotation groups and their representations MathProc Camb Phil Soc 94 509ndash517 (1983)
[262] AH Dooley JW Rice On contractions of semisimple Lie groups Trans Amer MathSoc 289 185ndash202 (1985)
[263] JR Driscoll DM Healy Computing Fourier transforms and convolutions on the 2-sphereAdv Appl Math 15 202ndash250 (1994)
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[265] RJ Duffin AC Schaeffer A class of nonharmonic Fourier series Trans Amer MathSoc 72 341ndash366 (1952)
[266] M Duflo CC Moore On the regular representation of a nonunimodular locally compactgroup J Funct Anal 21 209ndash243 (1976)
[267] M Duval-Destin R Murenzi Spatio-temporal wavelets Application to the analysis ofmoving patterns in Progress in Wavelet Analysis and Applications (Proc Toulouse 1992)ed by Y Meyer S Roques (Ed Frontiegraveres Gif-sur-Yvette 1993) pp 399ndash408
[268] M Duval-Destin M-A Muschietti B Torreacutesani Continuous wavelet decompositionsmultiresolution and contrast analysis SIAM J Math Anal 24 739ndash755 (1993)
[269] SJL van Eindhoven JLH Meyers New orthogonality relations for the Hermitepolynomials and related Hilbert spaces J Math Anal Appl 146 89ndash98 (1990)
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[273] M Fanuel S Zonetti Affine quantization and the initial cosmological singularity Euro-phys Lett 101 10001 (2013)
[274] M Farge Wavelet transforms and their applications to turbulence Annu Rev Fluid Mech24 395ndash457 (1992)
[275] M Farge N Kevlahan V Perrier E Goirand Wavelets and turbulence Proc IEEE 84639ndash669 (1996)
[276] M Farge NK-R Kevlahan V Perrier K Schneider Turbulence analysis modellingand computing using wavelets in Wavelets in Physics Chap 4 ed by JC van den Berg(Cambridge University Press Cambridge 1999)
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[280] M Flensted-Jensen Discrete series for semisimple symmetric spaces Ann of Math 111253ndash311 (1980)
[281] K Flornes A Grossmann M Holschneider B Torreacutesani Wavelets on discrete fieldsAppl Comput Harmon Anal 1 137ndash146 (1994)
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[286] W Freeden T Maier S Zimmermann A survey on wavelet methods for (geo)applicationsRevista Mathematica Complutense 16 (2003) 277ndash310
[287] W Freeden M Schreiner Biorthogonal locally supported wavelets on the sphere based onzonal kernel functions J Fourier Anal Appl 13 693ndash709 (2007)
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[289] L Freidel ER Livine U(N) coherent states for loop quantum gravity J Math Phys 52052502 (2011)
[290] J Froment S Mallat Arbitrary low bit rate image compression using wavelets in Progressin Wavelet Analysis and Applications (Proc Toulouse 1992) ed by Y Meyer S Roques(Ed Frontiegraveres Gif-sur-Yvette 1993) pp 413ndash418 and references therein
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[292] H Fuumlhr Wavelet frames and admissibility in higher dimensions J Math Phys 37 6353ndash6366 (1996)
[293] H Fuumlhr M Mayer Continuous wavelet transforms from semidirect products Cyclicrepresentations and Plancherel measure J Fourier Anal Appl 8 375ndash396 (2002)
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127ndash147 (2003)[296] E Galapon Paulirsquos theorem and quantum canonical pairs The consistency of a bounded
self-adjoint time operator canonically conjugate to a Hamiltonian with non-empty pointspectrum Proc R Soc Lond A 458 451ndash472 (2002)
[297] PL Garciacutea de Leacuteon J-P Gazeau Coherent state quantization and phase operator PhysLett A 361 301ndash304 (2007)
[298] L Garciacutea de Leoacuten J-P Gazeau J Queacuteva The infinite well revisited Coherent states andquantization Phys Lett A 372 3597ndash3607 (2008)
[299] T Garidi J-P Gazeau E Huguet M Lachiegraveze Rey J Renaud Fuzzy spheres frominequivalent coherent states quantization J Phys A Math Theor 40 10225ndash10249 (2007)
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[301] J-P Gazeau On the four Euclidean conformal group structure of the sturmian operatorLett Math Phys 3 285ndash292 (1979)
[302] J-P Gazeau Technique Sturmienne pour le spectre discret de lrsquoeacutequation de SchroumldingerJ Phys A Math Gen 13 3605ndash3617 (1980)
[303] J-P Gazeau Four Euclidean conformal group approach to the multiphoton processes in theH atom J Math Phys 23 156ndash164 (1982)
[304] J-P Gazeau A remarkable duality in one particle quantum mechanics between someconfining potentials and (R+Linfin
ε ) potentials Phys Lett 75A 159ndash163 (1980)[305] J-P Gazeau SL(2R)-coherent states and integrable systems in classical and quantum
physics in Quantization Coherent States and Complex Structures ed by J-P AntoineST Ali W Lisiecki IM Mladenov A Odzijewicz (Plenum Press New York and London1995) pp 147ndash158
[306] J-P Gazeau S Graffi Quantum harmonic oscillator A relativistic and statistical point ofview Boll Unione Mat Ital 11-A 815ndash839 (1997)
[307] J-P Gazeau V Hussin Poincareacute contraction of SU(11) Fock-Bargmann structure J PhysA Math Gen 25 1549ndash1573 (1992)
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[310] J-P Gazeau P Monceau Generalized coherent states for arbitrary quantum systems inColloquium M Flato (Dijon Sept 99) vol II (Kluumlwer Dordrecht 2000) pp 131ndash144
[311] J-P Gazeau M Novello The question of mass in (Anti-) de Sitter space-times J Phys AMath Theor 41 304008 (2008)
[312] J-P Gazeau M del Olmo q-coherent states quantization of the harmonic oscillator AnnPhys (NY) 330 220ndash245 (2013) arXiv12071200 [quant-ph]
[313] J-P Gazeau J Patera Tau-wavelets of Haar J Phys A Math Gen 29 4549ndash4559 (1996)[314] J-P Gazeau W Piechocki Coherent states quantization of a particle in de Sitter space
J Phys A Math Gen 37 6977ndash6986 (2004)[315] J-P Gazeau J Renaud Lie algorithm for an interacting SU(11) elementary system and its
contraction Ann Phys (NY) 222 89ndash121 (1993)[316] J-P Gazeau J Renaud Relativistic harmonic oscillator and space curvature Phys Lett A
179 67ndash71 (1993)[317] J-P Gazeau V Spiridonov Toward discrete wavelets with irrational scaling factor J Math
plane J Phys A Math Theor 44 495201 (2011)[319] J-P Gazeau J Patera E Pelantovaacute Tau-wavelets in the plane J Math Phys 39 4201ndash
4212 (1998)[320] J-P Gazeau M Andrle C Burdiacutek R Krejcar Wavelet multiresolutions for the Fibonacci
chain J Phys A Math Gen 33 L47ndashL51 (2000)[321] J-P Gazeau M Andrle C Burdiacutek Bernuau spline wavelets and sturmian sequences
J Fourier Anal Appl 10 269ndash300 (2004)[322] J-P Gazeau F-X Josse-Michaux P Monceau Finite dimensional quantizations of the
(q p) plane new space and momentum inequalities Int J Modern Phys B 20 1778ndash1791 (2006)
[323] J-P Gazeau J Mourad J Queacuteva Fuzzy de Sitter space-times via coherent statesquantization in Proceedings of the XXVIth Colloquium on Group Theoretical Methodsin Physics New York 2006 ed by J Birman S Catto B Nicolescu (Canopus PublishingLimited London 2009)
[324] D Geller A Mayeli Continuous wavelets on compact manifolds Math Z 262 895ndash927(2009)
[325] D Geller A Mayeli Nearly tight frames and space-frequency analysis on compactmanifolds Math Z 263 235ndash264 (2009)
[326] L Genovese B Videau M Ospici Th Deutsch S Goedecker J-F Mhaut Daubechieswavelets for high performance electronic structure calculations The BigDFT project CR Mecanique 339 149ndash164 (2011)
[327] G Gentili C Stoppato Power series and analyticity over the quaternions Math Ann 352113ndash131 (2012)
[328] G Gentili DC Struppa A new theory of regular functions of a quaternionic variable AdvMath 216 279ndash301 (2007)
[329] C Geyer K Daniilidis Catadioptric projective geometry Int J Comput Vision 45 223ndash243 (2001)
[330] R Gilmore Geometry of symmetrized states Ann Phys (NY) 74 391ndash463 (1972)[331] R Gilmore On properties of coherent states Rev Mex Fis 23 143ndash187 (1974)[332] J Ginibre Statistical ensembles of complex quaternion and real matrices J Math Phys
6 440ndash449 (1965)[333] RJ Glauber The quantum theory of optical coherence Phys Rev 130 2529ndash2539 (1963)
560 References
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[335] J Glimm Locally compact transformation groups Trans Amer Math Soc 101 124ndash138(1961)
[336] R Godement Sur les relations drsquoorthogonaliteacute de V Bargmann C R Acad Sci Paris 255521ndash523 657ndash659 (1947)
[337] C Gonnet B Torreacutesani Local frequency analysis with two-dimensional wavelet trans-form Signal Proc 37 389ndash404 (1994)
[338] JA Gonzalez MA del Olmo Coherent states on the circle J Phys A Math Gen 318841ndash8857 (1998)
[339] XGonze B Amadon et al ABINIT First-principles approach to material and nanosystemproperties Computer Physics Comm 180 2582ndash2615 (2009)
[340] KM Gograverski E Hivon AJ Banday BD Wandelt FK Hansen M Reinecke MBartelmann HEALPix A framework for high-resolution discretization and fast analysisof data distributed on the sphere Astrophys J 622 759ndash771 (2005)
[341] P Goupillaud A Grossmann J Morlet Cycle-octave and related transforms in seismicsignal analysis Geoexploration 23 85ndash102 (1984)
[342] KH Groumlchenig A new approach to irregular sampling of band-limited functions in RecentAdvances in Fourier Analysis and Its applications ed by JS Byrnes JL Byrnes (KluwerDordrecht 1990) pp 251ndash260
[343] KH Groumlchenig Gabor analysis over LCA groups in Gabor Analysis and Algorithms ndashTheory and Applications ed by HG Feichtinger T Strohmer (Birkhaumluser Boston-Basel-Berlin 1998) pp 211ndash231
[344] HJ Groenewold On the principles of elementary quantum mechanics Physica 12 405ndash460 (1946)
[345] P Grohs Continuous shearlet tight frames J Fourier Anal Appl 17 506ndash518 (2011)[346] P Grohs G Kutyniok Parabolic molecules preprint TU Berlin (2012)[347] M Grosser A note on distribution spaces on manifolds Novi Sad J Math 38 121ndash128
(2008)[348] A Grossmann Parity operator and quantization of δ -functions Commun Math Phys 48
191ndash194 (1976)[349] A Grossmann J Morlet Decomposition of Hardy functions into square integrable
wavelets of constant shape SIAM J Math Anal 15 723ndash736 (1984)[350] A Grossmann J Morlet Decomposition of functions into wavelets of constant shape and
related transforms in Mathematics + Physics Lectures on recent results I ed by L Streit(World Scientific Singapore 1985) pp 135ndash166
[351] A Grossmann J Morlet T Paul Integral transforms associated to square integrablerepresentations I General results J Math Phys 26 2473ndash2479 (1985)
[352] A Grossmann J Morlet T Paul Integral transforms associated to square integrablerepresentations II Examples Ann Inst H Poincareacute 45 293ndash309 (1986)
[353] A Grossmann R Kronland-Martinet J Morlet Reading and understanding the contin-uous wavelet transform in Wavelets Time-Frequency Methods and Phase Space (ProcMarseille 1987) ed by J-M Combes A Grossmann P Tchamitchian 2nd edn (SpringerBerlin 1990) pp 2ndash20
[354] P Guillemain R Kronland-Martinet B Martens Estimation of spectral lines with helpof the wavelet transform Application in NMR spectroscopy in Wavelets and Applications(Proc Marseille 1989) ed by Y Meyer (Masson and Springer Paris and Berlin 1991) pp38ndash60
[355] H de Guise M Bertola Coherent state realizations of su(n+ 1) on the n-torus J MathPhys 43 3425ndash3444 (2002)
[356] K Guo D Labate Representation of Fourier Integral Operators using shearlets J FourierAnal Appl 14 327ndash371 (2008)
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[358] K Guo D Labate W-Q Lim G Weiss E Wilson Wavelets with composite dilationsand their MRA properties Appl Comput Harmon Anal 20 202ndash236 (2006)
[359] EA Gutkin Overcomplete subspace systems and operator symbols Funct Anal Appl 9260ndash261 (1975)
[360] G Gyoumlrgyi Integration of the dynamical symmetry groups for the 1r potential Acta PhysAcad Sci Hung 27 435ndash439 (1969)
[361] BC Hall The Segal-Bargmann ldquoCoherent Staterdquo transform for compact Lie groups JFunct Analysis 122 103ndash151 (1994)
[362] B Hall JJ Mitchell Coherent states on spheres J Math Phys 43 1211ndash1236 (2002)[363] DK Hammond P Vandergheynst R Gribonval Wavelets on graphs via spectral theory
Appl Comput Harmon Anal 30 129ndash150 (2011)[364] Y Hassouni EMF Curado MA Rego-Monteiro Construction of coherent states for
physical algebraic system Phys Rev A 71 022104 (2005)[365] J He H Liu Admissible wavelets associated with the affine automorphism group of the
Siegel upper half-plane J Math Anal Appl 208 58ndash70 (1997)[366] J He H Liu Admissible wavelets associated with the classical domain of type one
Approx Appl 14 (1998) 89ndash105[367] J He L Peng Wavelet transform on the symmetric matrix space preprint Beijing (1997)
(unpublished)[368] J He L Peng Admissible wavelets on the unit disk Complex Variables 35 109ndash119
(1998)[369] DM Healy Jr FE Schroeck Jr On informational completeness of covariant localization
observables and Wigner coefficients J Math Phys 36 453ndash507 (1995)[370] C Heil D Walnut Continuous and discrete wavelet transforms SIAM Review 31 628ndash
666 (1989)[371] K Hepp EH Lieb On the superradiant phase transition for molecules in a quantized
radiation field The Dicke maser model Ann Phys (NY) 76 360ndash404 (1973)[372] K Hepp EH Lieb Equilibrium statistical mechanics of matter interacting with the
quantized radiation field Phys Rev A 8 2517ndash2525 (1973)[373] JA Hogan JD Lakey Extensions of the Heisenberg group by dilations and frames Appl
Comput Harmon Anal 2 174ndash199 (1995)[374] AL Hohoueacuteto K Thirulogasanthar ST Ali J-P Antoine Coherent states lattices and
square integrability of representations J Phys A Math Gen36 11817ndash11835 (2003)[375] M Holschneider On the wavelet transformation of fractal objects J Stat Phys 50 963ndash
993 (1988)[376] M Holschneider Wavelet analysis on the circle J Math Phys 31 39ndash44 (1990)[377] M Holschneider Inverse Radon transforms through inverse wavelet transforms Inv Probl
7 853ndash861 (1991)[378] M Holschneider Localization properties of wavelet transforms J Math Phys 34 3227ndash
3244 (1993)[379] M Holschneider General inversion formulas for wavelet transforms J Math Phys 34
4190ndash4198 (1993)[380] M Holschneider Wavelet analysis over abelian groups Applied Comput Harmon Anal
2 52ndash60 (1995)[381] M Holschneider Continuous wavelet transforms on the sphere J Math Phys 37 4156ndash
4165 (1996)[382] M Holschneider I Iglewska-Nowak Poisson wavelets on the sphere J Fourier Anal
Appl 13 405ndash419 (2007)
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[383] M Holschneider R Kronland-Martinet J Morlet P Tchamitchian A real-time algorithmfor signal analysis with the help of wavelet transform in Wavelets Time-FrequencyMethods and Phase Space (Proc Marseille 1987) ed by J-M Combes A Grossmann PTchamitchian 2nd edn (Springer Berlin 1990) pp 286ndash297
[384] M Holschneider P Tchamitchian Pointwise analysis of Riemannrsquos ldquonondifferentiablerdquofunction Invent Math 105 157ndash175 (1991)
[385] GR Honarasa MK Tavassoly M Hatami R Roknizadeh Nonclassical properties ofcoherent states and excited coherent states for continuous spectra J Phys A Math Theor44 085303 (2011)
[386] M Hongoh Coherent states associated with the continuous spectrum of noncompactgroups J Math Phys 18 2081ndash2085 (1977)
[387] A Horzela FH Szafraniec A measure free approach to coherent states J Phys A MathGen 45 244018 (2012)
[388] W-L Hwang S Mallat Characterization of self-similar multifractals with waveletmaxima Appl Comput Harmon Anal 1 316ndash328 (1994)
[389] W-L Hwang C-S Lu P-C Chung Shape from texture Estimation of planar surfaceorientation through the ridge surfaces of continuous wavelet transform IEEE Trans ImageProc 7 773ndash780 (1998)
[390] I Iglewska-Nowak M Holschneider Frames of Poisson wavelets on the sphere ApplComput Harmon Anal 28 227ndash248 (2010)
[391] E Inoumlnuuml EP Wigner On the contraction of groups and their representations Proc NatAcad Sci U S 39 510ndash524 (1953)
[392] S Iqbal F Saif Generalized coherent states and their statistical characteristics in power-law potentials J Math Phys 52 082105 (2011)
[393] CJ Isham JR Klauder Coherent states for n-dimensional Euclidean groups E(n) andtheir application J MathPhys 32 607ndash620 (1991)
[394] L Jacques J-P Antoine Multiselective pyramidal decomposition of images Wavelets withadaptive angular selectivity Int J Wavelets Multires Inform Proc 5 785ndash814 (2007)
[395] L Jacques L Duval C Chaux G Peyreacute A panorama on multiscale geometric rep-resentations intertwining spatial directional and frequency selectivity Signal Proc 912699ndash2730 (2011)
[396] HR Jalali M K Tavassoly On the ladder operators and nonclassicality of generalizedcoherent state associated with a particle in an infinite square well preprint (2013)arXiv13034100v1 [quant-ph]
[397] C Johnston On the pseudo-dilation representations of Flornes Grossmann Holschneiderand Torreacutesani Appl Comput Harmon Anal 3 377ndash385 (1997)
[398] G Kaiser Phase-space approach to relativistic quantum mechanics I Coherent staterepresentation for massive scalar particles J MathPhys 18 952ndash959 (1977)
[399] G Kaiser Phase-space approach to relativistic quantum mechanics II Geometrical aspectsJ MathPhys 19 502ndash507 (1978)
[400] C Kalisa B Torreacutesani N-dimensional affine Weyl-Heisenberg wavelets Ann Inst HPoincareacute 59 201ndash236 (1993)
[401] W Kaminski J Lewandowski T Pawłowski Quantum constraints Dirac observables andevolution group averaging versus the Schroumldinger picture in LQC Class Quant Grav 26245016 (2009)
[402] MR Karim ST Ali A relativistic windowed Fourier transform preprint ConcordiaUniversity Montreacuteal (1997) (unpublished)
[403] M R Karim ST Ali M Bodruzzaman A relativistic windowed Fourier transform inProceedings of IEEE SoutheastCon 2000 Nashville Tennessee pp 253ndash260 (2000)
[404] T Kawazoe Wavelet transforms associated to a principal series representation of semisim-ple Lie groups I II Proc Japan Acad Ser A ndash Math Sci 71 154ndash157 158ndash160 (1995)
[405] T Kawazoe Wavelet transform associated to an induced representation of SL(n+ 2R)Ann Inst H Poincareacute 65 1ndash13 (1996)
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[407] P Kittipoom G Kutyniok W-Q Lim Construction of compactly supported shearletframes Constr Approx 35 21ndash72 (2012)
[408] J Kiukas P Lahti K Ylinenc Phase space quantization and the operator moment problemJ Math Phys 47 072104 (2006)
[409] JR Klauder Continuous-representation theory I Postulates of continuous-representationtheory J Math Phys 4 1055ndash1058 (1963)
[410] JR Klauder Continuous-representation theory II Generalized relation between quantumand classical dynamics J Math Phys 4 1058ndash1073 (1963)
[411] JR Klauder Path integrals for affine variables in Functional Integration Theory andApplications ed by J-P Antoine E Tirapegui (Plenum Press New York and London1980) pp 101ndash119
[412] JR Klauder Are coherent states the natural language of quantum mechanics inFundamental Aspects of Quantum Theory ed by V Gorini A Frigerio NATO ASI Seriesvol B 144 (Plenum Press New York 1986) pp 1ndash12
[413] JR Klauder Quantization without quantization Ann Phys (NY) 237 147ndash160 (1995)[414] JR Klauder Coherent states for the hydrogen atom J Phys A Math Gen 29 L293ndash
L296 (1996)[415] JR Klauder An affinity for affine quantum gravity Proc Steklov Inst Math 272 169ndash176
(2011) and references therein[416] JR Klauder RF Streater A wavelet transform for the Poincareacute group J Math Phys 32
1609ndash1611 (1991)[417] JR Klauder RF Streater Wavelets and the Poincareacute half-plane J Math Phys 35 471ndash
478 (1994)[418] JR Klauder K Penson J-M Sixdeniers Constructing coherent states through solutions
of Stieltjes and Hausdorff moment problems Phys Rev A 64 013817 (2001)[419] A Kleppner RL Lipsman The Plancherel formula for group extensions Ann Ec Norm
Sup 5 459ndash516 (1972)[420] AB Klimov C Muntildeoz Coherent isotropic and squeezed states in a N-qubit system Phys
Scr 87 038110 (2013)[421] A Klyashko Dynamical symmetry approach to entanglement in Physics and Theoretical
Computer Science From Numbers and Languages to (Quantum) Cryptography - NATOSecurity through Science Series D - Information and Communication Security vol 7 edby J-P Gazeau J Nesetril B Rovan (IOS Press Washington DC 2007) pp 25ndash54
[422] S Kobayashi Irreducibility of certain unitary representations J Math Soc Japan 20 638ndash642 (1968)
[423] K Kowalski J Rembielinski LC Papaloucas Coherent states for a quantum particle ona circle J Phys A Math Gen 29 4149ndash4167 (1996)
[424] K Kowalski J Rembielinski Quantum mechanics on a sphere and coherent states J PhysA Math Gen 33 6035ndash6048 (2000)
[425] K Kowalski J Rembielinski The Bargmann representation for the quantum mechanicson a sphere J Math Phys 42 4138ndash4147 (2001)
[426] C Kristjansen J Plefka GW Semenoff M Staudacher A new double-scaling limit ofN = 4 super-Yang-Mills theory and pp-wave strings Nuclear Phys B 643 3ndash30 (2002)
[427] M Kulesh M Holschneider MS Diallo Geophysical wavelet library Applications ofthe continuous wavelet transform to the polarization and dispersion analysis of signalsComput Geosci 34 1732ndash1752 (2008)
[428] R Kunze On the Frobenius reciprocity theorem for square integrable representationsPacific J Math 53 465ndash471 (1974)
[429] Y Kuroda A Wada T Yamazaki K Nagayama Postacquisition data processing methodfor suppression of the solvent signal I J Magn Reson 84 604ndash610 (1989)
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[431] G Kutyniok D Labate Resolution of the wavefront set using continuous shearlets TransAmer Math Soc 361 2719ndash2754 (2009)
[432] G Kutyniok W-Q Lim Compactly supported shearlets are optimally sparse J ApproxTheory 163 1564ndash1589 (2011)
[433] D Labate W-Q Lim G Kutyniok G Weiss Sparse multidimensional representationusing shearlets in Wavelets XI (San Diego CA 2005) ed by M Papadakis A Laine MUnser SPIE Proceedings vol 5914 (SPIE Bellingham WA 2005) pp 254ndash262
[434] P Lahti J-P Pellonpaumlauml Continuous variable tomographic measurements Phys Lett A373 3435ndash3438 (2009)
[435] Lambertrsquos projection see WikipediahttpenwikipediaorgwikiLambert_azimuthal_equal-area_projection
[436] J-P Leduc F Mujica R Murenzi MJT Smith Missile-tracking algorithm using target-adapted spatio-temporal wavelets in Automatic Object Recognition VII SPIE Proceedingsvol 5914 (SPIE Bellingham WA 1997) pp 400ndash411
[437] J-P Leduc F Mujica R Murenzi MJT Smith Spatio-temporal wavelet transforms formotion tracking in IEEE ICASSP 1997 vol 4 (1997) pp 3013ndash3016
[438] J-P Leduc F Mujica R Murenzi MJT Smith Spatio-temporal continuous waveletsapplied to missile warhead detection and tracking in SPIE VCIP rsquo97 vol 3024 ed byJ Biemond EJ Delp (1997) pp 787ndash798
[439] B Leistedt JD McEwen Exact wavelets on the ball IEEE Trans Signal Proc 60 1564ndash1589 (2012)
[440] PG Lemarieacute Y Meyer Ondelettes et bases hilbertiennes Rev Math Iberoamer 2 1ndash18(1986)
[441] C Lemke A Schuck Jr J-P Antoine D Sima Metabolite-sensitive analysis of magneticresonance spectroscopic signals using the continuous wavelet transform Meas SciTechnol 22 (2011) Art 114013
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[443] J-M Leacutevy-Leblond Galilei group and Galilean invariance in Group Theory and ItsApplications vol II ed by EM Loebl (Academic New York 1971) pp 221ndash299
[444] J-M Leacutevy-Leblond On the conceptual nature of the physical constants Riv Nuovo Cim7 187ndash214 (1977)
[445] EH Lieb The classical limit of quantum spin systems Commun Math Phys 31 327ndash340(1973)
[446] G Lindblad B Nagel Continuous bases for unitary irreducible representations of SU(11)Ann Inst H Poincareacute 13 27ndash56 (1970)
[447] W Lisiecki Kaumlhler coherent states orbits for representations of semisimple Lie groupsAnn Inst H Poincareacute 53 857ndash890 (1990)
[448] A Lisowska Moment-based fast wedgelet transform J Math Imaging Vis 39 180ndash192(2011)
[449] H Liu L Peng Admissible wavelets associated with the Heisenberg group Pacific JMath 180 101ndash123 (1997)
[450] E Livine S Speziale Physical boundary state for the quantum tetrahedron Class QuantGrav 25 085003 (2008)
[451] F Low Complete sets of wave packets in A Passion for Physics ndash Essay in Honor ofGeoffrey Chew ed by C DeTar (World Scientific Singapore 1985) pp 17ndash22
[452] G Mack All unitary ray representations of the conformal group SU(22) with positiveenergy Commun Math Phys 55 1ndash28 (1977)
[453] GW Mackey Imprimitivity for representations of locally compact groups I Proc NatAcad Sci 35 537ndash545 (1949)
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[456] SG Mallat Multifrequency channel decompositions of images and wavelet models IEEETrans Acoust Speech Signal Proc 37 2091ndash2110 (1989)
[457] SG Mallat A theory for multiresolution signal decomposition The wavelet representa-tion IEEE Trans Pattern Anal Machine Intell 11 674ndash693 (1989)
[458] S Mallat W-L Hwang Singularity detection and processing with wavelets IEEE TransInform Theory 38 617ndash643 (1992)
[459] S Mallat Z Zhang Matching pursuits with time frequency dictionaries IEEE TransSignal Proc 41 3397ndash3415 (1993)
[460] S Mallat S Zhong Wavelet maxima representation in Wavelets and Applications (ProcMarseille 1989) ed by Y Meyer (Masson and Springer Paris and Berlin 1991) pp 207ndash284
[461] VI Manrsquoko G Marmo ECG Sudarshan F Zaccaria f -oscillators and non-linearcoherent states Phys Scr 55 528ndash541 (1997)
[462] D Marinucci D Pietrobon A Baldi P Baldi P Cabella G Kerkyacharian P Natoli DPicard N Vittorio Spherical needlets for CMB data analysis Mon Not R Astron Soc383 539ndash545 (2008)
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[464] Y Meyer Principe drsquoincertitude bases hilbertiennes et algegravebres drsquoopeacuterateurs SeacuteminaireBourbaki 662 (1985ndash1986)
[465] Y Meyer Principe drsquoincertitude bases hilbertiennes et algegravebres drsquoopeacuterateurs Asteacuterisque145ndash146 209ndash223 (1987)
[466] Y Meyer H Xu Wavelet analysis and chirps Appl Comput Harmon Anal 4 366ndash379(1997)
[467] L Michel Invariance in quantum mechanics and group extensions in Group TheoreticalConcepts and Methods in Elementary Particle Physics ed by F Guumlrsey (Gordon andBreach New York and London 1964) pp 135ndash200
[468] J Mickelsson J Niederle Contractions of representations of the de Sitter groupsCommun Math Phys 27 167ndash180 (1972)
[469] MM Miller Convergence of the Sudarshan expansion for the diagonal coherent-stateweight functional J Math Phys 9 1270ndash1274 (1968)
[470] V F Molchanov Harmonic analysis on homogeneous spaces in Representation Theoryand Noncommutative Harmonic Analysis II ed by AA Kirillov (Springer Berlin 1995)
[471] MI Monastyrsky AM Perelomov Coherent states and symmetric spaces II Ann InstH Poincareacute 23 23ndash48 (1975)
[472] B Moran S Howard D Cochran Positive-operator-valued measures A general settingfor frames in Excursions in Harmonic Analysis vol 1 2 ed by TD Andrews R BalanJJ Benedetto W Czaja KA Okoudjou (Birkhaumluser Boston 2013) pp 49ndash64
[473] H Moscovici Coherent states representations of nilpotent Lie groups Commun MathPhys 54 63ndash68 (1977)
[474] H Moscovici A Verona Coherent states and square integrable representations Ann InstH Poincareacute 29 139ndash156 (1978)
[475] F Mujica R Murenzi MJT Smith J-P Leduc Robust tracking in compressed imagesequences J Electr Imaging 7 746ndash754 (1998)
[476] R Murenzi Wavelet transforms associated to the n-dimensional Euclidean group withdilations Signals in more than one dimension in Wavelets Time-Frequency Methodsand Phase Space (Proc Marseille 1987) ed by J-M Combes A Grossmann PTchamitchian 2nd edn (Springer Berlin 1990) pp 239ndash246
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[479] MA Naımark Dokl Akad Nauk SSSR 41 359ndash361 (1943) see also B Sz-NagyExtensions of linear transformations in Hilbert space which extend beyond this spaceAppendix to F Riesz B Sz-Nagy Functional Analysis (Frederick Ungar New York 1960)
[480] FJ Narcowich P Petrushev JD Ward Localized tight frames on spheres SIAM J MathAnal 38 574ndash594 (2006)
[481] M Nauenberg Quantum wave packets on Kepler elliptic orbits Phys Rev A 40 1133ndash1136 (1989)
[482] M Nauenberg C Stroud J Yeazell The classical limit of an atom Scient Amer 27024ndash29 (1994)
[483] H Neumann Transformation properties of observables Helv Phys Acta 45 811ndash819(1972)
[484] U Niederer The maximal kinematical invariance group of the free Schroumldinger equationHelv Phys Acta 45 802ndash881 (1972)
[485] MM Nieto LM Simmons Jr Coherent states for general potentials I Formalism IIConfining one-dimensional examples III Nonconfining one-dimensional examples PhysRev D 20 1321ndash1331 1332ndash1341 1342ndash1350 (1979)
[486] MM Nieto LM Simmons Jr Coherent states for general potentials Phys Rev Lett 41207ndash210 (1987)
[487] A Odzijewicz On reproducing kernels and quantization of states Commun Math Phys114 577ndash597 (1988)
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[491] G Oacutelafsson B Oslashrsted The holomorphic discrete series for affine symmetric spaces JFunct Anal 81 126ndash159 (1988)
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[493] E Onofri A note on coherent state representations of Lie groups J Math Phys 16 1087ndash1089 (1975)
[494] E Onofri Dynamical quantization of the Kepler manifold J Math Phys 17 401ndash408(1976)
[495] D Oriti R Pereira L Sindoni Coherent states in quantum gravity A construction basedon the flux representation of loop quantum gravity J Phys A Math Theor 45 244004(2012)
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[498] Z Pasternak-Winiarski On reproducing kernels for holomorphic vector bundles inQuantization and Infinite Dimensional Systems (Proc Białowieza Poland 1993) ed by J-P Antoine ST Ali W Lisiecki IM Mladenov A Odzijewicz (Plenum Press New Yorkand London 1994) pp 109ndash112
[499] T Paul Affine coherent states and the radial Schroumldinger equation I preprint CPT-84P1710 (1984) (unpublished)
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[501] AM Perelomov On the completeness of a system of coherent states Theor Math Phys6 156ndash164 (1971)
[502] AM Perelomov Coherent states for arbitrary Lie group Commun Math Phys 26 222ndash236 (1972)
[503] AM Perelomov Coherent states and symmetric spaces Commun Math Phys 44 197ndash210 (1975)
[504] M Perroud Projective representations of the Schroumldinger group Helv Phys Acta 50 233ndash252 (1977)
[505] J Phillips A note on square-integrable representations J Funct Anal 20 83ndash92 (1975)[506] D Pietrobon P Baldi D Marinucci Integrated Sachs-Wolfe effect from the cross
correlation of WMAP3 year and the NRAO VLA sky survey data New results andconstraints on dark energy Phys Rev D 74 043524 (2006)
[507] WWF Pijnappel A van den Boogaart R de Beer D van Ormondt SVD-basedquantification of magnetic resonance signals J Magn Reson 97 122ndash134 (1992)
[508] V Pop D Rosca Generalized piecewise constant orthogonal wavelet bases on 2D-domains Appl Anal 90 715ndash723 (2011)
[509] G Poumlschl E Teller Bemerkungen zur Quantenmechanik des anharmonischen OszillatorsZ Physik 83 143ndash151 (1933)
[510] D Potts G Steidl M Tasche Kernels of spherical harmonics and spherical frames inAdvanced Topics in Multivariate Approximation ed by F Fontanella K Jetter PJ Laurent(World Scientific Singapore 1996) pp 287ndash301
[511] E Prugovecki Consistent formulation of relativistic dynamics for massive spin-zeroparticles in external fields Phys Rev D 18 3655ndash3673 (1978) (Appendix C)
[512] E Prugovecki Relativistic quantum kinematics on stochastic phase space for massiveparticles J MathPhys 19 2261ndash2270 (1978)
[513] C Quesne Coherent states of the real symplectic group in a complex analytic parametriza-tion I II J Math Phys 27 428ndash441 869ndash878 (1986)
[514] C Quesne Generalized vector coherent states of sp(2NR) vector operators and ofsp(2NR) sup u(N) reduced Wigner coefficients J Phys A Math Gen 24 2697ndash2714(1991)
[515] JM Radcliffe Some properties of spin coherent states J Phys A Math Gen 4 313ndash323(1971)
[516] A Rahimi A Najati YN Dehghan Continuous frames in Hilbert spaces Methods FunctAnal Topol 12 170ndash182 (2006)
[517] H Rauhut M Roumlsler Radial multiresolution in dimension three Constr Approx 22 193ndash218 (2005)
[518] JH Rawnsley Coherent states and Kaumlhler manifolds Quart J Math Oxford 28(2) 403ndash415 (1977)
[519] J Renaud The contraction of the SU(11) discrete series of representations by means ofcoherent states J Math Phys 37 3168ndash3179 (1996)
[520] A Reacutenyi Representations for real numbers and their ergodic properties Acta Math AcadSci Hungary 8(3ndash4) 477ndash493 (1957)
[521] D Robert La coheacuterence dans tous ses eacutetats SMF Gazette 132 (2012)[522] JE Roberts The Dirac bra and ket formalism J Math Phys 7 1097ndash1104 (1966)[523] JE Roberts Rigged Hilbert spaces in quantum mechanics Commun Math Phys 3 98ndash
119 (1966)[524] S Roques F Bourzeix K Bouyoucef Soft-thresholding technique and restoration of
3C273 jet Astrophys Space Sci Nr 239 297ndash304 (1996)[525] D Rosca Haar wavelets on spherical triangulations in Advances in Multiresolution for
Geometric Modelling ed by NA Dogson MS Floater MA Sabin (Springer Berlin2005) pp 407ndash419
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[527] D Rosca Wavelets defined on closed surfaces J Comput Anal Appl 8 121ndash132 (2006)[528] D Rosca Weighted Haar wavelets on the sphere Int J Wavelets Multiresol Inf Proc 5
501ndash511 (2007)[529] D Rosca Wavelet bases on the sphere obtained by radial projection J Fourier Anal Appl
13 421ndash434 (2007)[530] D Rosca Piecewise constant wavelets on triangulations obtained by 1ndash3 splitting Int J
Wavelets Multiresolut Inf Process 6 209ndash222 (2008)[531] D Rosca On a norm equivalence on L2(S2) Results Math 53 399ndash405 (2009)[532] D Rosca New uniform grids on the sphere Astron Astrophys 520 (2010) Art A63[533] D Rosca Uniform and refinable grids on elliptic domains and on some surfaces of
revolution Appl Math Comput 217 7812ndash7817 (2011)[534] D Rosca Wavelet analysis on some surfaces of revolution via area preserving projection
Appl Comput Harmon Anal 30 262ndash272 (2011)[535] D Rosca J-P Antoine Locally supported orthogonal wavelet bases on the sphere via
stereographic projection Math Probl Eng 2009 124904 (2009)[536] D Rosca J-P Antoine Constructing wavelet frames and orthogonal wavelet bases on the
sphere in Recent Advances in Signal Processing ed by S Miron (IN-TECH ViennaAustria and Rijeka Croatia 2010) pp 59ndash76
[537] D Rosca G Plonka Uniform spherical grids via area preserving projection from the cubeto the sphere J Comput Appl Math 236 1033ndash1041 (2011)
[538] D Rosca G Plonka An area preserving projection from the regular octahedron to thesphere Results Math 63 429ndash444 (2012)
[539] H Rossi M Vergne Analytic continuation of the holomorphic discrete series for a semi-simple Lie group Acta Math 136 1ndash59 (1976)
[540] DJ Rotenberg Application of Sturmian functions to the Schroedinger three-body prob-lem Elastic e+ndashH scattering Ann Phys (NY) 19 262ndash278 (1962)
[541] C Rovelli Zakopane lectures on loop gravity in Proceedings of 3rd Quantum Gravityand Quantum Geometry School 28 Febndash13 March 2011 (Zakopane Poland 2011)arXiv11023660v5
[542] C Rovelli S Speziale A semiclassical tetrahedron Class Quant Grav 23 5861ndash5870(2006)
[543] DJ Rowe Coherent state theory of the noncompact symplectic group J Math Phys 252662ndash2271 (1984)
[544] DJ Rowe Microscopic theory of the nuclear collective model Rep Prog Phys 48 1419ndash1480 (1985)
[545] DJ Rowe Vector coherent state representations and their inner products J Phys A MathGen 45 244003 (2012) (This paper belongs to the special issue [38])
[546] DJ Rowe J Repka Vector-coherent-state theory as a theory of induced representationsJ Math Phys 32 2614ndash2634 (1991)
[547] DJ Rowe G Rosensteel R Gilmore Vector coherent state representation theory J MathPhys 26 2787ndash2791 (1985)
[548] A Royer Phase states and phase operators for the quantum harmonic oscillator Phys RevA 53 70ndash108 (1996)
[549] J Saletan Contraction of Lie groups J Math Phys 2 1ndash21 (1961)[550] G Saracco A Grossmann P Tchamitchian Use of wavelet transforms in the study of
propagation of transient acoustic signals across a plane interface between two homoge-neous media in Wavelets Time-Frequency Methods and Phase Space (Proc Marseille1987) ed by J-M Combes A Grossmann P Tchamitchian 2nd edn (Springer Berlin1990) pp 139ndash146
[551] P Schroumlder W Sweldens Spherical wavelets Efficiently representing functions on thesphere in Computer Graphics Proceedings (SIGGRAPH95) (ACM Siggraph Los Angeles1995) pp 161ndash175
References 569
[552] E Schroumldinger Der stetige Uumlbergang von der Mikro- zur Makromechanik Naturwiss 14664ndash666 (1926)
[553] S Scodeller Oslash Rudjord FK Hansen D Marinucci D Geller A Mayeli IntroducingMexican needlets for CMB analysis Issues for practical applications and comparison withstandard needlets Astrophys J 733 (2011) Art 121
[554] H Scutaru Coherent states and induced representations Lett Math Phys 2 101ndash107(1977)
[555] B Simon Distributions and their Hermite expansions J Math Phys 12 140ndash148 (1971)[556] B Simon The classical moment problem as a self-adjoint finite difference operator Adv
Math 137 82ndash203 (1998)[557] R Simon ECG Sudarshan N Mukunda Gaussian pure states in quantum mechanics
and the symplectic group Phys Rev A37 3028ndash3038 (1988)[558] S Sivakumar Studies on nonlinear coherent states J Opt B Quant Semiclass Opt 2
R61ndashR75 (2000)[559] E Slezak A Bijaoui G Mars Identification of structures from galaxy counts Use of the
wavelet transform Astron Astroph 227 301ndash316 (1990)[560] A Solomon A characteristic functional for deformed photon phenomenology Phys Lett
A 196 29ndash34 (1994)[561] SB Sontz Paragrassmann algebras as quantum spaces Part I Reproducing kernels in
Geometric Methods in Physics XXXI Workshop 2012 (Trends in Mathematics ed byP Kielanowski et al Birkhaumluser Verlag Basel 2013) pp 47ndash63
[562] SB Sontz Paragrassmann algebras as quantum spaces Part II Toeplitz operators J OperTh (2013 to appear) arXiv12055493
[563] SB Sontz A reproducing kernel and Toeplitz operators in the quantum plane Preprint(2013) arXiv13056986 [math-ph]
[564] SB Sontz Toeplitz quantization of an algebra with conjugation Preprint (2013)arXiv13085454 [math-ph]
[565] M Spera On a generalized Uncertainty Principle coherent states and the moment mapJ Geom Phys 12 165ndash182 (1993)
[566] J-L Starck EJ Candegraves DL Donoho The curvelet transform for image denoising IEEETrans Image Proc 11 670ndash684 (2002)
[567] J-L Starck DL Donoho E J Candegraves Astronomical image representation by the curvelettransform Astron Astroph 398 785ndash800 (2003)
[568] J-L Starck Y Moudden P Abrial M Nguyen Wavelets ridgelets and curvelets on thesphere Astron Astroph 446 1191ndash1204 (2006)
[569] MB Stenzel The Segal-Bargmann transform on a symmetric space of compact type JFunct Analysis 165 44ndash58 (1994)
[570] ECG Sudarshan Equivalence of semiclassical and quantum mechanical descriptions ofstatistical light beams Phys Rev Lett 10 277ndash279 (1963)
[571] A Suvichakorn H Ratiney A Bucur S Cavassila J-P Antoine Toward a quantitativeanalysis of in vivo magnetic resonance proton spectroscopic signals using the continuousMorlet wavelet transform Meas Sci Technol 20 (2009) Art 104029
[572] W Sweldens The lifting scheme A custom-design construction of biorthogonal waveletsApplied Comput Harmon Anal 3 1186ndash1200 (1996)
[573] W Sweldens The lifting scheme A construction of second generation wavelets SIAM JMath Anal 29 511ndash546 (1998)
[574] FH Szafraniec The reproducing kernel Hilbert space and its multiplication operatorsin Complex Analysis and Related Topics ed by E Ramirez de Arellano et al OperatorTheory Advances and Applications vol 114 (Birkhaumluser Basel 2000) pp 254ndash263
[575] FH Szafraniec Multipliers in the reproducing kernel Hilbert space subnormality andnoncommutative complex analysis in Reproducing Kernel Spaces and Applications edby D Alpay Operator Theory Advances and Applications vol 143 (Birkhaumluser Basel2003) pp 313ndash331
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Proceedings of the 27th International Cosmic Ray Conference (ICRC 2001) (CopernicusGesellschaft DE 2001) pp 2923ndash2926
[579] T Thiemann Gauge field theory coherent states (GCS) 1 General properties Class QuantGrav 18 2025ndash2064 (2001)
[580] T Thiemann O Winkler Gauge field theory coherent states (GCS) 2 Peakednessproperties Class Quant Grav 18 2561ndash2636 (2001)
[581] T Thiemann O Winkler Gauge field theory coherent states (GCS) 3 Ehrenfest theoremsClass Quant Grav 18 4629ndash4682 (2001)
[582] T Thiemann O Winkler Gauge field theory coherent states (GCS) 4 Infinite tensorproduct and thermodynamical limit Class Quant Grav 18 4997ndash5054 (2001)
[583] K Thirulagasanthar ST Ali Regular subspaces of a quaternionic Hilbert space fromquaternionic Hermite polynomials and associated coherent states J Math Phys 54013506 (2013)
[584] K Thirulogasanthar G Honnouvo A Krzyzak Coherent states and Hermite polynomialson quaternionic Hilbert spaces J Phys A Math Theor 43 385205 (2010)
[585] Tokamak see Wikipedia httpenwikipediaorgwikiTokamak[586] B Torreacutesani Wavelets associated with representations of the affine Weyl-Heisenberg
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simulation of an impact test using wavelets analytical and finite element models Int JSolids Struct 38 5481ndash5508 (2001)
[594] L Vanhamme RD Fierro S Van Huffel R de Beer Fast removal of residual water inproton spectra J Magn Reson 132 197ndash203 (1998)
[595] J Ville Theacuteorie et applications de la notion de signal analytique Cacircbles et Trans 2 61ndash74(1948)
[596] J Voisin On some unitary representations of the Galilei group I Irreducible representa-tions J Math Phys 6 1519ndash1529 (1965)
[597] A Vourdas Analytic representations in quantum mechanics J Phys A Math Gen 39R65ndashR141 (2006)
[598] DF Walls Squeezed states of light Nature 306 141ndash146 (1983)[599] YK Wang FT Hioe Phase transition in the Dicke maser model Phys Rev A 7 831ndash836
(1973)[600] PSP Wang J Yang A review of wavelet-based edge detection methods Int J Patt
Recogn Artif Intell 26 1255011 (2012)[601] I Weinreich A construction of C1-wavelets on the two-dimensional sphere Appl Comput
Harmon Anal 10 1ndash26 (2001)[602] H Weyl Quantenmechanik und Gruppentheorie Z Phys 46 1ndash46 (1927)
References 571
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[605] Y Wiaux JD McEwen P Vandergheynst O Blanc Exact reconstruction with directionalwavelets on the sphere Mon Not R Astron Soc 388 770ndash788 (2008)
[606] WM Wieland Complex Ashtekar variables and reality conditions for Holstrsquos action AnnHenri Poincareacute 13 425ndash448 (2012)
[607] EP Wigner On the quantum correction for thermodynamic equilibrium Phys Rev 40749ndash759 (1932)
[608] RM Willette RD Nowak Platelets A multiscale approach for recovering edges andsurfaces in photon-limited medical imaging IEEE Trans Med Imaging 22 332ndash350(2003)
[609] W Wisnoe P Gajan A Strzelecki C Lempereur J-M Matheacute The use of the two-dimensional wavelet transform in flow visualization processing in Progress in WaveletAnalysis and Applications (Proc Toulouse 1992) ed by Y Meyer S Roques (EdFrontiegraveres Gif-sur-Yvette 1993) pp 455ndash458
[610] K Woacutedkiewicz On the quantum mechanics of squeezed states J Modern Optics 34 941ndash948(1987)
[611] JA Yeazell M Mallalieu CR Stroud Jr Observation of the collapse and revival of aRydberg electronic wave packet Phys Rev Lett 64 2007ndash2010 (1990)
[612] JA Yeazell CR Stroud Jr Observation of fractional revivals in the evolution of aRydberg atomic wave packet Phys Rev A 43 5153ndash5156 (1991)
[613] HP Yuen Two-photon coherent states of the radiation field Phys Rev A 13 2226ndash2243(1976)
[614] J Zak Balian-Low theorem for Landau levels Phys Rev Lett 79 533ndash536 (1997)[615] J Zak Orthonormal sets of localized functions for a Landau level J Math Phys 39 4195ndash
4200 (1998) and references quoted there[616] AA Zakharova On the properties of generalized frames Math Notes 83 190ndash200 (2008)[617] W-M Zhang DH Feng R Gilmore Coherent states Theory and some applications Rev
Mod Phys 26 867ndash927 (1990)[618] I Zlatev W-M Zhang DH Feng Possibility that Schroumldingerrsquos conjecture for the
hydrogen atom coherent states is not attainable Phys Rev A 50 R1973ndashR1975 (1994)[619] WH Zurek Decoherence einselection and the quantum origins of the classical Rev Mod
Phys 75 715ndash775 (2003)[620] WH Zurek S Habib JP Paz Coherent states via decoherence Phys Rev Lett 70 1187ndash
1190 (1993)[621] K Zyczkowski Squeezed states in a quantum chaotic system J Phys A Math Theor 22
of SU(11) 81 296 297HilbertClowast-modules 164holomorphic 140nonholomorphic 151nonlinear 146of affine Galilei group 505of affine Poincareacute group 509of affine Weyl-Heisenberg group GaWH
497of compact semisimple Lie groups 174of Euclidean group E(n) 266of Galilei group G (11) 290of isochronous Galilei group 237of non-semisimple Lie groups 179of noncompact semisimple Lie groups 177of Poincareacute group Puarr
+(11) 283massless case 288
of Poincareacute group Puarr+(13) 279
of Schroumldinger group 508quasi-coherent states 186quaternionic 164
ST Ali et al Coherent States Wavelets and Their Generalizations Theoreticaland Mathematical Physics DOI 101007978-1-4614-8535-3copy Springer Science+Business Media New York 2014
573
574 Index
coherent states (CS) (cont)spin or SU(2) 175square integrable covariant 166 180 264vector (VCS) 73 108 112 170weighted 184 523
of affine Weyl-Heisenberg group GaWH497
of Poincareacute group Puarr+(11) 284
cohomology group 393 403coboundaries 403cochains 402cocycle 403
algebraic 387Cauchy 418Cauchy-Paul 354 419 425conical 418difference 417 462directional 416 440kinematical 499local 488metabolite-based 355 374minimal uncertainty 425multiselective 440on a graph 493on the sphere S
2 458on the sphere S
n 479on the torus T2 481steerable 439von Mises 440
wedgelet transform 455Wigner function 322Wigner-Ville transform 349Windowed Fourier or Gabor transform 349
ZZak transform 518
References
A Books and Theses
B Articles
Index
References 549
[66] J-P Antoine P Carrette R Murenzi B Piette Image analysis with 2D continuous wavelettransform Signal Process 31 241ndash272 (1993)
[67] J-P Antoine P Vandergheynst K Bouyoucef R Murenzi Alternative representations ofan image via the 2D wavelet transform Application to character recognition in VisualInformation Processing IV SPIE Proceedings vol 2488 (SPIE Bellingham WA 1995)pp 486ndash497
[68] J-P Antoine R Murenzi P Vandergheynst Two-dimensional directional wavelets inimage processing Int J Imaging Syst Tech 7 152ndash165 (1996)
[69] J-P Antoine D Barache RM Cesar Jr LF Costa Shape characterization with thewavelet transform Signal Process 62 265ndash290 (1997)
[70] J-P Antoine P Antoine B Piraux Wavelets in atomic physics in Spline Functions andthe Theory of Wavelets ed by S Dubuc G Deslauriers CRM Proceedings and LectureNotes vol 18 (AMS Providence RI 1999) pp261ndash276
[71] J-P Antoine P Antoine B Piraux Wavelets in atomic physics and in solid state physicsin Wavelets in Physics Chap 8 ed by JC van den Berg (Cambridge University PressCambridge 1999)
[72] J-P Antoine R Murenzi P Vandergheynst Directional wavelets revisited Cauchywavelets and symmetry detection in patterns Appl Comput Harmon Anal 6 314ndash345(1999)
[73] J-P Antoine L Jacques R Twarock Wavelet analysis of a quasiperiodic tiling withfivefold symmetry Phys Lett A 261 265ndash274 (1999)
[74] J-P Antoine L Jacques P Vandergheynst Penrose tilings quasicrystals and wavelets inWavelet Applications in Signal and Image Processing VII SPIE Proceedings vol 3813(SPIE Bellingham WA 1999) pp 28ndash39
[75] J-P Antoine YB Kouagou D Lambert B Torreacutesani An algebraic approach to discretedilations Application to discrete wavelet transforms J Fourier Anal Appl 6 113ndash141(2000)
[76] J-P Antoine A Coron J-M Dereppe Water peak suppression Time-frequency vs time-scale approach J Magn Reson 144 189ndash194 (2000)
[77] J-P Antoine J-P Gazeau P Monceau J R Klauder K Penson Temporally stablecoherent states for infinite well and Poumlschl-Teller potentials J Math Phys 42 2349ndash2387(2001)
[78] J-P Antoine A Coron C Chauvin Wavelets and related time-frequency techniques inmagnetic resonance spectroscopy NMR Biomed 14 265ndash270 (2001)
[79] J-P Antoine L Demanet J-F Hochedez L Jacques R Terrier E Verwichte Applicationof the 2-D wavelet transform to astrophysical images Phys Mag 24 93ndash116 (2002)
[80] J-P Antoine L Demanet L Jacques P Vandergheynst Wavelets on the sphere Imple-mentation and approximations Appl Comput Harmon Anal 13 177ndash200 (2002)
[81] J-P Antoine I Bogdanova P Vandergheynst The continuous wavelet transform on conicsections Int J Wavelets Multires Inform Proc 6 137ndash156 (2007)
[82] J-P Antoine D Rosca P Vandergheynst Wavelet transform on manifolds Old and newapproaches Appl Comput Harmon Anal 28 189ndash202 (2010)
[83] P Antoine B Piraux A Maquet Time profile of harmonics generated by a single atom ina strong electromagnetic field Phys Rev A 51 R1750ndashR1753 (1995)
[84] P Antoine B Piraux DB Miloševic M Gajda Generation of ultrashort pulses ofharmonics Phys Rev A 54 R1761ndashR1764 (1996)
[85] P Antoine B Piraux DB Miloševic M Gajda Temporal profile and time control ofharmonic generation Laser Phys 7 594ndash601 (1997)
[86] Apollonius see Wikipedia httpenwikipediaorgwikiApollonius_of_Perga[87] FT Arecchi E Courtens R Gilmore H Thomas Atomic coherent states in quantum
optics Phys Rev A 6 2211ndash2237 (1972)[88] I Aremua J-P Gazeau MN Hounkonnou Action-angle coherent states for quantum
systems with cylindric phase space J Phys A Math Theor 45 335302 (2012)
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[91] TA Arias Multiresolution analysis of electronic structure Semicardinal and waveletbases Rev Mod Phys 71 267ndash312 (1999)
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[123] V Bargmann On a Hilbert space of analytic functions and an associated integral transformPart I Commun Pure Appl Math 14 187ndash214 (1961)
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[125] V Bargmann P Butera L Girardello JR Klauder On the completeness of coherentstates Reports Math Phys 2 221ndash228 (1971)
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[131] J Ben Geloun J R Klauder Ladder operators and coherent states for continuous spectraJ Phys A Math Theor 42 375209 (2009)
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[134] JJ Benedetto A Teolis A wavelet auditory model and data compression Appl ComputHarmon Anal 1 3ndash28 (1993)
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[141] H Bergeron J-P Gazeau P Siegl A Youssef Semi-classical behavior of Poumlschl-Tellercoherent states Eur Phys Lett 92 60003 (2010)
[142] H Bergeron P Siegl A Youssef New SUSYQM coherent states for Poumlschl-Tellerpotentials A detailed mathematical analysis J Phys A Math Theor 45 244028 (2012)
[143] H Bergeron J-P Gazeau A Youssef Are the Weyl and coherent state descriptionsphysically equivalent Phys Lett A 377 598ndash605 (2013)
[144] H Bergeron A Dapor J-P Gazeau P Małkiewicz Wavelet quantum cosmology preprint(2013) arXiv13050653 [gr-qc]
[145] S Bergman Uumlber die Kernfunktion eines Bereiches und ihr Verhalten am Rande I ReineAngw Math 169 1ndash42 (1933)
[146] D Bernier KF Taylor Wavelets from square-integrable representations SIAM J MathAnal 27 594ndash608 (1996)
[147] G Bernuau Wavelet bases associated to a self-similar quasicrystal J Math Phys 394213ndash4225 (1998)
[148] A Bertrand Deacuteveloppements en base de Pisot et reacutepartition modulo 1 C R Acad SciParis 285 419ndash421 (1977)
[149] J Bertrand P Bertrand Classification of affine Wigner functions via an extendedcovariance principle in Group Theoretical Methods in Physics (Proc Sainte-Adegravele 1988)ed by Y Saint-Aubin L Vinet (World Scientific Singapore 1989) pp 1380ndash1383
[150] Z Białynicka-Birula I Białynicki-Birula Space-time description of squeezing J OptSoc Am B4 1621ndash1626 (1987)
[151] E Bianchi E Magliaro C Perini Coherent spin-networks Phys Rev D 82 024012(2010)
[152] S Biskri J-P Antoine B Inhester F Mekideche Extraction of Solar coronal magneticloops with the 2-D Morlet wavelet transform Solar Phys 262 373ndash385 (2010)
[153] R Bluhm VA Kostelecky JA Porter The evolution and revival structure of localizedquantum wave packets Am J Phys 64 944ndash953 (1996)
[154] I Bogdanova P Vandergheynst J-P Antoine L Jacques M Morvidone Stereographicwavelet frames on the sphere Appl Comput Harmon Anal 19 223ndash252 (2005)
[155] I Bogdanova X Bresson J-P Thiran P Vandergheynst Scale space analysis and activecontours for omnidirectional images IEEE Trans Image Process 16 1888ndash1901 (2007)
[156] I Bogdanova P Vandergheynst J-P Gazeau Continuous wavelet transform on thehyperboloid Appl Comput Harmon Anal 23 (2007) 286ndash306 (2007)
[157] P Boggiatto E Cordero Anti-Wick quantization of tempered distributions in Progress inAnalysis Berlin (2001) vol I II (World Sci Publ River Edge NJ 2003) pp 655ndash662
[158] P Boggiatto E Cordero K Groumlchenig Generalized Anti-Wick operators with symbols indistributional Sobolev spaces Int Equ Oper Theory 48 427ndash442 (2004)
[159] A Boumlhm The Rigged Hilbert Space in quantum mechanics in Lectures in TheoreticalPhysics vol IX A ed by WA Brittin et al (Gordon amp Breach New York 1967) pp255ndash315
[160] G Bohnkeacute Treillis drsquoondelettes associeacutes aux groupes de Lorentz Ann Inst H Poincareacute54 245ndash259 (1991)
[161] WR Bomstad JR Klauder Linearized quantum gravity using the projection operatorformalism Class Quantum Grav 23 5961ndash5981 (2006)
[162] VV Borzov Orthogonal polynomials and generalized oscillator algebras Int TransformSpec Funct 12 115ndash138 (2001)
[163] VV Borzov EV Damaskinsky Generalized coherent states for classical orthogonalpolynomials Day on Diffraction (2002) arXivmathQA0209181v1 (SPb 2002)
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Harmonic Analysis vol 1 2 ed by TD Andrews R Balan JJ Benedetto W CzajaKA Okoudjou (Birkhaumluser Boston 2013) pp 113ndash135
[170] F Bruhat Sur les repreacutesentations induites des groupes de Lie Bull Soc Math France 8497ndash205 (1956)
[171] T Buumllow Multiscale image processing on the sphere in DAGM-Symposium (2002) pp609ndash617
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[173] KE Cahill Coherent-state representations for the photon density Phys Rev 138 B1566ndash1576 (1965)
[174] KE Cahill R Glauber Density operators and quasiprobability distributions Phys Rev177 1882ndash1902 (1969)
[175] KE Cahill R Glauber Ordered expansions in boson amplitude operators Phys Rev 1771857ndash1881 (1969)
[176] AR Calderbank I Daubechies W Sweldens BL Yeo Wavelets that map integers tointegers Appl Comput Harmon Anal 5 332ndash369 (1998)
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[179] M Calixto J Guerrero D Rosca Wavelet transform on the torus A group-theoreticalapproach preprint (2013)
[180] EJ Candegraves Harmonic analysis of neural networks Appl Comput Harmon Anal 6 197ndash218 (1999)
[181] EJ Candegraves Ridgelets and the representation of mutilated Sobolev functions SIAM JMath Anal 33 347ndash368 (2001)
[182] EJ Candegraves L Demanet Curvelets and Fourier integral operators CR Acad Sci ParisSeacuter I Math 336 395ndash398 (2003)
[183] EJ Candegraves L Demanet The curvelet representation of wave propagators is optimallysparse Commun Pure Appl Math 58 1472ndash1528 (2004)
[184] EJ Candegraves L Demanet The curvelet representation of wave propagators is optimallysparse Commun Pure Appl Math 58 1472ndash1528 (2005)
[185] EJ Candegraves DL Donoho Curvelets ndash A surprisingly effective nonadaptive representationfor objects with edges in Curves and Surfaces ed by LL Schumaker et al (VanderbiltUniversity Press Nashville TN 1999)
[186] EJ Candegraves DL Donoho Ridgelets A key to higher-dimensional intermittency PhilTrans R Soc Lond A 357 2495ndash2509 (1999)
[187] EJ Candegraves DL Donoho Curvelets multiresolution representation and scaling laws inWavelet Applications in Signal and Image Processing VIII ed by A Aldroubi A LaineM Unser SPIE Proceedings vol 4119 (SPIE Bellingham WA 2000) pp 1ndash12
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[188] EJ Candegraves DL Donoho Recovering edges in ill-posed inverse problems Optimality ofcurvelet frames Ann Statist 30 784ndash842 (2002)
[189] EJ Candegraves DL Donoho New tight frames of curvelets and optimal representations ofobjects with piecewise C2 singularities Commun Pure Appl Math 57 219ndash266 (2004)
[190] EJ Candegraves DL Donoho Continuous curvelet transform I Resolution of the wavefrontset II Discretization and frames Appl Comput Harmon Anal 19 162ndash197 198ndash222(2005)
[191] EJ Candegraves F Guo New multiscale transforms minimum total variationsynthesisApplications to edge-preserving image reconstruction Signal Proc 82 1519ndash1543 (2002)
[192] EJ Candegraves L Demanet D Donoho L Ying Fast discrete curvelet transforms MultiscaleModel Simul 5 861ndash899 (2006)
[193] AL Carey Square integrable representations of non-unimodular groups Bull AustrMath Soc 15 1ndash12 (1976)
[194] AL Carey Group representations in reproducing kernel Hilbert spaces Rep Math Phys14 247ndash259 (1978)
[195] P Carruthers MM Nieto Phase and angle variables in quantum mechanics Rev ModPhys 40 411ndash440 (1968)
[196] PG Casazza G Kutyniok Frames of subspaces in Wavelets Frames and Operator The-ory Contemporary Mathematics vol 345 (American Mathematical Society ProvidenceRI 2004) pp 87ndash113
[197] PG Casazza D Han DR Larson Frames for Banach spaces Contemp Math 247 149ndash182 (1999)
[198] P Casazza O Christensen S Li A Lindner Riesz-Fischer sequences and lower framebounds Z Anal Anwend 21 305ndash314 (2002)
[199] PG Casazza G Kutyniok S Li Fusion frames and distributed processing ApplComputHarmon Anal 25 114ndash132 (2008)
[200] DPL Castrigiano RW Henrichs Systems of covariance and subrepresentations ofinduced representations Lett Math Phys 4 169ndash175 (1980)
[201] U Cattaneo Densities of covariant observables J Math Phys 23 659ndash664 (1982)[202] A Cerioni L Genovese I Duchemin Th Deutsch Accurate complex scaling of three
dimensional numerical potentials Preprint (2013) arXiv13036439v2[203] S-J Chang K-J Shi Evolution and exact eigenstates of a resonant quantum system Phys
Rev A 34 7ndash22 (1986)[204] SHH Chowdhury ST Ali All the groups of signal analysis from the (1+1) affine Galilei
group J Math Phys 52 103504 (2011)[205] SL Chown Antarctic marine biodiversity and deep-sea hydrothermal vents PLoS Biol
10 1ndash4 (2012)[206] C Cishahayo S De Biegravevre On the contraction of the discrete series of SU(11) Ann Inst
Fourier (Grenoble) 43 551ndash567 (1993)[207] M Clerc and S Mallat Shape from texture and shading with wavelets in Dynamical
Systems Control Coding Computer Vision Progress in Systems and Control Theory 25393ndash417 (1999)
[208] L Cohen General phase-space distribution functions J Math Phys 7 781ndash786 (1966)[209] A Cohen I Daubechies J-C Feauveau Biorthogonal bases of compactly supported
wavelets Commun Pure Appl Math 45 485ndash560 (1992)[210] R Coifman Y Meyer MV Wickerhauser Wavelet analysis and signal processing
in Wavelets and Their Applications ed by MB Ruskai G Beylkin R CoifmanI Daubechies S Mallat Y Meyer L Raphael (Jones and Bartlett Boston 1992)pp 153ndash178
[211] R Coifman Y Meyer MV Wickerhauser Entropy-based algorithms for best basisselection IEEE Trans Inform Theory 38 713ndash718 (1992)
[212] R Coquereaux A Jadczyk Conformal theories curved spaces relativistic wavelets andthe geometry of complex domains Rev Math Phys 2 1ndash44 (1990)
References 555
[213] A Coron L Vanhamme J-P Antoine P Van Hecke S Van Huffel The filtering approachto solvent peak suppression in MRS A critical review J Magn Reson 152 26ndash40 (2001)
[214] N Cotfas J-P Gazeau Finite tight frames and some applications (topical review) J PhysA Math Theor 43 193001 (2010)
[215] N Cotfas J-P Gazeau K Goacuterska Complex and real Hermite polynomials and relatedquantizations J Phys A Math Theor 43 305304 (2010)
[216] N Cotfas J-P Gazeau A Vourdas Finite-dimensional Hilbert space and frame quantiza-tion J Phys A Math Gen 44 175303 (2011)
[217] EMF Curado MA Rego-Monteiro LMCS Rodrigues Y Hassouni Coherent statesfor a degenerate system The hydrogen atom Physica A 371 16ndash19 (2006)
[218] S Dahlke P Maass The affine uncertainty principle in one and two dimensions CompMath Appl 30 293ndash305 (1995)
[219] S Dahlke W Dahmen E Schmidt I Weinreich Multiresolution analysis and wavelets onS
2 and S3 Numer Funct Anal Optim 16 19ndash41 (1995)
[220] S Dahlke V Lehmann G Teschke Applications of wavelet methods to the analysis ofmeteorological radar data - An overview Arabian J Sci Eng 28 3ndash44 (2003)
[221] S Dahlke G Kutyniok P Maass C Sagiv H-G Stark G Teschke The uncertaintyprinciple associated with the continuous shearlet transform Int J Wavelets MultiresolutInf Process 6 157ndash181 (2008)
[222] S Dahlke G Kutyniok G Steidl G Teschke Shearlet coorbit spaces and associatedBanach frames Appl Comput Harmon Anal 27 195ndash214 (2009)
[223] S Dahlke G Steidl G Teschke The continuous shearlet transform in arbitrary spacedimensions J Fourier Anal Appl 16 340ndash364 (2010)
[224] S Dahlke G Steidl G Teschke Shearlet coorbit spaces Compactly supported analyzingshearlets traces and embeddings J Fourier Anal Appl 17 1232ndash1355 (2011)
[225] T Dallard GR Spedding 2-D wavelet transforms Generalisation of the Hardy space andapplication to experimental studies Eur J Mech BFluids 12 107ndash134 (1993)
[226] C Daskaloyannis Generalized deformed oscillator and nonlinear algebras J Phys AMath Gen 24 L789ndashL794 (1991)
[227] C Daskaloyannis K Ypsilantis A deformed oscillator with Coulomb energy spectrumJ Phys A Math Gen 25 4157ndash4166 (1992)
[228] I Daubechies On the distributions corresponding to bounded operators in the Weylquantization Commun Math Phys 75 229ndash238 (1980)
[229] I Daubechies and A Grossmann An integral transform related to quantization I J MathPhys 21 2080ndash2090 (1980)
[230] I Daubechies A Grossmann J Reignier An integral transform related to quantization IIJ Math Phys 24 239ndash254 (1983)
[231] I Daubechies Orthonormal bases of compactly supported wavelets Commun Pure ApplMath 41 909ndash996 (1988)
[232] I Daubechies The wavelet transform time-frequency localisation and signal analysisIEEE Trans Inform Theory 36 961ndash1005 (1990)
[233] I Daubechies S Maes A nonlinear squeezing of the continuous wavelet transform basedon auditory nerve models in Wavelets in Medicine and Biology ed by A Aldroubi MUnser (CRC Press Boca Raton 1996) pp 527ndash546
[234] I Daubechies A Grossmann Y Meyer Painless nonorthogonal expansions J Math Phys27 1271ndash1283 (1986)
[235] ER Davies Introduction to texture analysis in Handbook of texture analysis ed by MMirmehdi X Xie J Suri (World Scientific Singapore 2008) pp 1ndash31
[236] R De Beer D van Ormondt FTAW Wajer S Cavassila D Graveron-Demilly S VanHuffel SVD-based modelling of medical NMR signals in SVD and Signal ProcessingIII Algorithms Architectures and Applications ed by M Moonen B De Moor (Elsevier(North-Holland) Amsterdam 1995) pp 467ndash474
[237] S De Biegravevre Coherent states over symplectic homogeneous spaces J Math Phys 301401ndash1407 (1989)
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[238] S De Biegravevre JA Gonzalez Semi-classical behaviour of the Weyl correspondence on thecircle in Group-Theoretical Methods in Physics (Proc Salamanca 1992) ed by M delOlmo M Santander J Mateos Guilarte (CIEMAT Madrid 1993) pp 343ndash346
[239] S De Biegravevre JA Gonzaacutelez Semiclassical behaviour of coherent states on the circle inQuantization and Coherent States Methods in Physics ed by A Odzijewicz et al (WorldScientific Singapore 1993)
[240] S De Biegravevre AE Gradechi Quantum mechanics and coherent states on the anti-de Sitterspace-time and their Poincareacute contraction Ann Inst H Poincareacute 57 403ndash428 (1992)
[241] J Deenen C Quesne Dynamical group of collective states I II III J Math Phys 23878ndash889 2004ndash2015 (1982)
[242] J Deenen C Quesne Dynamical group of collective states I II III J Math Phys 251638ndash1650 (1984)
[243] J Deenen C Quesne Partially coherent states of the real symplectic group J Math Phys25 2354ndash2366 (1984)
[244] J Deenen C Quesne Boson representations of the real symplectic group and theirapplication to the nuclear collective model J Math Phys 26 2705ndash2716 (1985)
[245] R Delbourgo Minimal uncertainty states for the rotation and allied groups J Phys AMath Gen 10 1837ndash1846 (1977)
[246] R Delbourgo J R Fox Maximum weight vectors possess minimal uncertainty J PhysA Math Gen 10 L233ndashL235 (1977)
[247] V Delouille J de Patoul J-F Hochedez L Jacques J-P Antoine Wavelet spectrumanalysis of EITSoHO images Solar Phys 228 301ndash321 (2005)
[248] N Delprat B Escudieacute P Guillemain R Kronland-Martinet P Tchamitchian B Tor-reacutesani Asymptotic wavelet and Gabor analysis Extraction of instantaneous frequenciesIEEE Trans Inform Theory 38 644ndash664 (1992)
[249] Th Deutsch L Genovese Wavelets for electronic structure calculations Collection SocFr Neut 12 33ndash76 (2011)
[250] B Dewitt Quantum theory of gravity I The canonical theory Phys Rev 160 1113ndash1148(1967)
[251] RH Dicke Coherence in spontaneous radiation processes Phys Rev 93 99ndash110 (1954)[252] AN Dinkelaker AL MacKinnon Wavelets intermittency and solar flare hard X-rays 1
Local intermittency measure in cascade and avalanche scenarios Solar Phys 282 471ndash481(2013)
[253] AN Dinkelaker AL MacKinnon Wavelets intermittency and solar flare hard X-rays 2LIM analysis of high time resolution BATSE data Solar Phys 282 483ndash501 (2013)
[254] MN Do M Vetterli Contourlets in Beyond Wavelets ed by GV Welland (AcademicSan Diego 2003) pp 83ndash105
[255] MN Do M Vetterli The contourlet transform An efficient directional multiresolutionimage representation IEEE Trans Image Process 14 2091ndash2106 (2005)
[256] VV Dodonov Nonclassical states in quantum optics A ldquosqueezedrdquo review of the first 75years J Opt B Quant Semiclass Opot 4 R1ndashR33 (2002)
[257] DL Donoho Nonlinear wavelet methods for recovery of signals densities and spectrafrom indirect and noisy data in Different Perspectives on Wavelets Proceedings ofSymposia in Applied Mathematics vol 38 ed by I Daubechies (American MathematicalSociety Providence RI 1993) pp 173ndash205
[258] DL Donoho Wedgelets Nearly minimax estimation of edges Ann Stat 27 859ndash897(1999)
[259] DL Donoho X Huo Beamlet pyramids A new form of multiresolution analysis suitedfor extracting lines curves and objects from very noisy image data in SPIE Proceedingsvol 5914 (SPIE Bellingham WA 2005) pp 1ndash12
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[260] AH Dooley Contractions of Lie groups and applications to analysis in Topics in ModernHarmonic Analysis vol I (Istituto Nazionale di Alta Matematica Francesco Severi Roma1983) pp 483ndash515
[261] AH Dooley JW Rice Contractions of rotation groups and their representations MathProc Camb Phil Soc 94 509ndash517 (1983)
[262] AH Dooley JW Rice On contractions of semisimple Lie groups Trans Amer MathSoc 289 185ndash202 (1985)
[263] JR Driscoll DM Healy Computing Fourier transforms and convolutions on the 2-sphereAdv Appl Math 15 202ndash250 (1994)
[264] H Drissi F Regragui J-P Antoine M Bennouna Wavelet transform analysis of visualevoked potentials Some preliminary results ITBM-RBM 21 84ndash91 (2000)
[265] RJ Duffin AC Schaeffer A class of nonharmonic Fourier series Trans Amer MathSoc 72 341ndash366 (1952)
[266] M Duflo CC Moore On the regular representation of a nonunimodular locally compactgroup J Funct Anal 21 209ndash243 (1976)
[267] M Duval-Destin R Murenzi Spatio-temporal wavelets Application to the analysis ofmoving patterns in Progress in Wavelet Analysis and Applications (Proc Toulouse 1992)ed by Y Meyer S Roques (Ed Frontiegraveres Gif-sur-Yvette 1993) pp 399ndash408
[268] M Duval-Destin M-A Muschietti B Torreacutesani Continuous wavelet decompositionsmultiresolution and contrast analysis SIAM J Math Anal 24 739ndash755 (1993)
[269] SJL van Eindhoven JLH Meyers New orthogonality relations for the Hermitepolynomials and related Hilbert spaces J Math Anal Appl 146 89ndash98 (1990)
[270] M ElBaz R Fresneda J-P Gazeau Y Hassouni Coherent state quantization of para-grassmann algebras J Phys A Math Theor 43 385202 (2010) Corrigendum J PhysA Math Theor 45 (2012)
[271] A Elkharrat J-P Gazeau F Deacutenoyer Multiresolution of quasicrystal diffraction spectraActa Cryst A65 466ndash489 (2009)
[272] Q Fan Phase space analysis of the identity decompositions J Math Phys 34 3471ndash3477(1993)
[273] M Fanuel S Zonetti Affine quantization and the initial cosmological singularity Euro-phys Lett 101 10001 (2013)
[274] M Farge Wavelet transforms and their applications to turbulence Annu Rev Fluid Mech24 395ndash457 (1992)
[275] M Farge N Kevlahan V Perrier E Goirand Wavelets and turbulence Proc IEEE 84639ndash669 (1996)
[276] M Farge NK-R Kevlahan V Perrier K Schneider Turbulence analysis modellingand computing using wavelets in Wavelets in Physics Chap 4 ed by JC van den Berg(Cambridge University Press Cambridge 1999)
[277] HG Feichtinger Coherent frames and irregular sampling in Recent Advances in FourierAnalysis and Its applications ed by JS Byrnes JL Byrnes (Kluwer Dordrecht 1990)pp 427ndash440
[278] HG Feichtinger KH Groumlchenig Banach spaces related to integrable group representa-tions and their atomic decompositions I J Funct Anal 86 307ndash340 (1989)
[279] HG Feichtinger KH Groumlchenig Banach spaces related to integrable group representa-tions and their atomic decompositions II Mh Math 108 129ndash148 (1989)
[280] M Flensted-Jensen Discrete series for semisimple symmetric spaces Ann of Math 111253ndash311 (1980)
[281] K Flornes A Grossmann M Holschneider B Torreacutesani Wavelets on discrete fieldsAppl Comput Harmon Anal 1 137ndash146 (1994)
[282] V Fock Zur Theorie der Wasserstoffatoms Zs f Physik 98 145ndash54 (1936)[283] M Fornasier H Rauhut Continuous frames function spaces and the discretization
problem J Fourier Anal Appl 11 245ndash287 (2005)
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[285] W Freeden U Windheuser Combined spherical harmonic and wavelet expansion mdash Afuture concept in Earthrsquos gravitational determination Appl Comput Harmon Anal 4 1ndash37 (1997)
[286] W Freeden T Maier S Zimmermann A survey on wavelet methods for (geo)applicationsRevista Mathematica Complutense 16 (2003) 277ndash310
[287] W Freeden M Schreiner Biorthogonal locally supported wavelets on the sphere based onzonal kernel functions J Fourier Anal Appl 13 693ndash709 (2007)
[288] WT Freeman EH Adelson The design and use of steerable filters IEEE Trans PatternAnal Machine Intell 13 891ndash906 (1991)
[289] L Freidel ER Livine U(N) coherent states for loop quantum gravity J Math Phys 52052502 (2011)
[290] J Froment S Mallat Arbitrary low bit rate image compression using wavelets in Progressin Wavelet Analysis and Applications (Proc Toulouse 1992) ed by Y Meyer S Roques(Ed Frontiegraveres Gif-sur-Yvette 1993) pp 413ndash418 and references therein
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[292] H Fuumlhr Wavelet frames and admissibility in higher dimensions J Math Phys 37 6353ndash6366 (1996)
[293] H Fuumlhr M Mayer Continuous wavelet transforms from semidirect products Cyclicrepresentations and Plancherel measure J Fourier Anal Appl 8 375ndash396 (2002)
[294] D Gabor Theory of communication J Inst Electr Engrg(London) 93 429ndash457 (1946)[295] J-P Gabardo D Han Frames associated with measurable spaces Adv Comput Math 18
127ndash147 (2003)[296] E Galapon Paulirsquos theorem and quantum canonical pairs The consistency of a bounded
self-adjoint time operator canonically conjugate to a Hamiltonian with non-empty pointspectrum Proc R Soc Lond A 458 451ndash472 (2002)
[297] PL Garciacutea de Leacuteon J-P Gazeau Coherent state quantization and phase operator PhysLett A 361 301ndash304 (2007)
[298] L Garciacutea de Leoacuten J-P Gazeau J Queacuteva The infinite well revisited Coherent states andquantization Phys Lett A 372 3597ndash3607 (2008)
[299] T Garidi J-P Gazeau E Huguet M Lachiegraveze Rey J Renaud Fuzzy spheres frominequivalent coherent states quantization J Phys A Math Theor 40 10225ndash10249 (2007)
[300] J-P Gazeau Four Euclidean conformal group in atomic calculations Exact analyticalexpressions for the bound-bound two-photon transition matrix elements in the H atomJ Math Phys 19 1041ndash1048 (1978)
[301] J-P Gazeau On the four Euclidean conformal group structure of the sturmian operatorLett Math Phys 3 285ndash292 (1979)
[302] J-P Gazeau Technique Sturmienne pour le spectre discret de lrsquoeacutequation de SchroumldingerJ Phys A Math Gen 13 3605ndash3617 (1980)
[303] J-P Gazeau Four Euclidean conformal group approach to the multiphoton processes in theH atom J Math Phys 23 156ndash164 (1982)
[304] J-P Gazeau A remarkable duality in one particle quantum mechanics between someconfining potentials and (R+Linfin
ε ) potentials Phys Lett 75A 159ndash163 (1980)[305] J-P Gazeau SL(2R)-coherent states and integrable systems in classical and quantum
physics in Quantization Coherent States and Complex Structures ed by J-P AntoineST Ali W Lisiecki IM Mladenov A Odzijewicz (Plenum Press New York and London1995) pp 147ndash158
[306] J-P Gazeau S Graffi Quantum harmonic oscillator A relativistic and statistical point ofview Boll Unione Mat Ital 11-A 815ndash839 (1997)
[307] J-P Gazeau V Hussin Poincareacute contraction of SU(11) Fock-Bargmann structure J PhysA Math Gen 25 1549ndash1573 (1992)
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[310] J-P Gazeau P Monceau Generalized coherent states for arbitrary quantum systems inColloquium M Flato (Dijon Sept 99) vol II (Kluumlwer Dordrecht 2000) pp 131ndash144
[311] J-P Gazeau M Novello The question of mass in (Anti-) de Sitter space-times J Phys AMath Theor 41 304008 (2008)
[312] J-P Gazeau M del Olmo q-coherent states quantization of the harmonic oscillator AnnPhys (NY) 330 220ndash245 (2013) arXiv12071200 [quant-ph]
[313] J-P Gazeau J Patera Tau-wavelets of Haar J Phys A Math Gen 29 4549ndash4559 (1996)[314] J-P Gazeau W Piechocki Coherent states quantization of a particle in de Sitter space
J Phys A Math Gen 37 6977ndash6986 (2004)[315] J-P Gazeau J Renaud Lie algorithm for an interacting SU(11) elementary system and its
contraction Ann Phys (NY) 222 89ndash121 (1993)[316] J-P Gazeau J Renaud Relativistic harmonic oscillator and space curvature Phys Lett A
179 67ndash71 (1993)[317] J-P Gazeau V Spiridonov Toward discrete wavelets with irrational scaling factor J Math
plane J Phys A Math Theor 44 495201 (2011)[319] J-P Gazeau J Patera E Pelantovaacute Tau-wavelets in the plane J Math Phys 39 4201ndash
4212 (1998)[320] J-P Gazeau M Andrle C Burdiacutek R Krejcar Wavelet multiresolutions for the Fibonacci
chain J Phys A Math Gen 33 L47ndashL51 (2000)[321] J-P Gazeau M Andrle C Burdiacutek Bernuau spline wavelets and sturmian sequences
J Fourier Anal Appl 10 269ndash300 (2004)[322] J-P Gazeau F-X Josse-Michaux P Monceau Finite dimensional quantizations of the
(q p) plane new space and momentum inequalities Int J Modern Phys B 20 1778ndash1791 (2006)
[323] J-P Gazeau J Mourad J Queacuteva Fuzzy de Sitter space-times via coherent statesquantization in Proceedings of the XXVIth Colloquium on Group Theoretical Methodsin Physics New York 2006 ed by J Birman S Catto B Nicolescu (Canopus PublishingLimited London 2009)
[324] D Geller A Mayeli Continuous wavelets on compact manifolds Math Z 262 895ndash927(2009)
[325] D Geller A Mayeli Nearly tight frames and space-frequency analysis on compactmanifolds Math Z 263 235ndash264 (2009)
[326] L Genovese B Videau M Ospici Th Deutsch S Goedecker J-F Mhaut Daubechieswavelets for high performance electronic structure calculations The BigDFT project CR Mecanique 339 149ndash164 (2011)
[327] G Gentili C Stoppato Power series and analyticity over the quaternions Math Ann 352113ndash131 (2012)
[328] G Gentili DC Struppa A new theory of regular functions of a quaternionic variable AdvMath 216 279ndash301 (2007)
[329] C Geyer K Daniilidis Catadioptric projective geometry Int J Comput Vision 45 223ndash243 (2001)
[330] R Gilmore Geometry of symmetrized states Ann Phys (NY) 74 391ndash463 (1972)[331] R Gilmore On properties of coherent states Rev Mex Fis 23 143ndash187 (1974)[332] J Ginibre Statistical ensembles of complex quaternion and real matrices J Math Phys
6 440ndash449 (1965)[333] RJ Glauber The quantum theory of optical coherence Phys Rev 130 2529ndash2539 (1963)
560 References
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[335] J Glimm Locally compact transformation groups Trans Amer Math Soc 101 124ndash138(1961)
[336] R Godement Sur les relations drsquoorthogonaliteacute de V Bargmann C R Acad Sci Paris 255521ndash523 657ndash659 (1947)
[337] C Gonnet B Torreacutesani Local frequency analysis with two-dimensional wavelet trans-form Signal Proc 37 389ndash404 (1994)
[338] JA Gonzalez MA del Olmo Coherent states on the circle J Phys A Math Gen 318841ndash8857 (1998)
[339] XGonze B Amadon et al ABINIT First-principles approach to material and nanosystemproperties Computer Physics Comm 180 2582ndash2615 (2009)
[340] KM Gograverski E Hivon AJ Banday BD Wandelt FK Hansen M Reinecke MBartelmann HEALPix A framework for high-resolution discretization and fast analysisof data distributed on the sphere Astrophys J 622 759ndash771 (2005)
[341] P Goupillaud A Grossmann J Morlet Cycle-octave and related transforms in seismicsignal analysis Geoexploration 23 85ndash102 (1984)
[342] KH Groumlchenig A new approach to irregular sampling of band-limited functions in RecentAdvances in Fourier Analysis and Its applications ed by JS Byrnes JL Byrnes (KluwerDordrecht 1990) pp 251ndash260
[343] KH Groumlchenig Gabor analysis over LCA groups in Gabor Analysis and Algorithms ndashTheory and Applications ed by HG Feichtinger T Strohmer (Birkhaumluser Boston-Basel-Berlin 1998) pp 211ndash231
[344] HJ Groenewold On the principles of elementary quantum mechanics Physica 12 405ndash460 (1946)
[345] P Grohs Continuous shearlet tight frames J Fourier Anal Appl 17 506ndash518 (2011)[346] P Grohs G Kutyniok Parabolic molecules preprint TU Berlin (2012)[347] M Grosser A note on distribution spaces on manifolds Novi Sad J Math 38 121ndash128
(2008)[348] A Grossmann Parity operator and quantization of δ -functions Commun Math Phys 48
191ndash194 (1976)[349] A Grossmann J Morlet Decomposition of Hardy functions into square integrable
wavelets of constant shape SIAM J Math Anal 15 723ndash736 (1984)[350] A Grossmann J Morlet Decomposition of functions into wavelets of constant shape and
related transforms in Mathematics + Physics Lectures on recent results I ed by L Streit(World Scientific Singapore 1985) pp 135ndash166
[351] A Grossmann J Morlet T Paul Integral transforms associated to square integrablerepresentations I General results J Math Phys 26 2473ndash2479 (1985)
[352] A Grossmann J Morlet T Paul Integral transforms associated to square integrablerepresentations II Examples Ann Inst H Poincareacute 45 293ndash309 (1986)
[353] A Grossmann R Kronland-Martinet J Morlet Reading and understanding the contin-uous wavelet transform in Wavelets Time-Frequency Methods and Phase Space (ProcMarseille 1987) ed by J-M Combes A Grossmann P Tchamitchian 2nd edn (SpringerBerlin 1990) pp 2ndash20
[354] P Guillemain R Kronland-Martinet B Martens Estimation of spectral lines with helpof the wavelet transform Application in NMR spectroscopy in Wavelets and Applications(Proc Marseille 1989) ed by Y Meyer (Masson and Springer Paris and Berlin 1991) pp38ndash60
[355] H de Guise M Bertola Coherent state realizations of su(n+ 1) on the n-torus J MathPhys 43 3425ndash3444 (2002)
[356] K Guo D Labate Representation of Fourier Integral Operators using shearlets J FourierAnal Appl 14 327ndash371 (2008)
References 561
[357] K Guo G Kutyniok D Labate Sparse multidimensional representations usinganisotropic dilation and shear operators in Wavelets and Spines (Athens GA 2005)(Nashboro Press Nashville TN 2006) pp 189ndash201
[358] K Guo D Labate W-Q Lim G Weiss E Wilson Wavelets with composite dilationsand their MRA properties Appl Comput Harmon Anal 20 202ndash236 (2006)
[359] EA Gutkin Overcomplete subspace systems and operator symbols Funct Anal Appl 9260ndash261 (1975)
[360] G Gyoumlrgyi Integration of the dynamical symmetry groups for the 1r potential Acta PhysAcad Sci Hung 27 435ndash439 (1969)
[361] BC Hall The Segal-Bargmann ldquoCoherent Staterdquo transform for compact Lie groups JFunct Analysis 122 103ndash151 (1994)
[362] B Hall JJ Mitchell Coherent states on spheres J Math Phys 43 1211ndash1236 (2002)[363] DK Hammond P Vandergheynst R Gribonval Wavelets on graphs via spectral theory
Appl Comput Harmon Anal 30 129ndash150 (2011)[364] Y Hassouni EMF Curado MA Rego-Monteiro Construction of coherent states for
physical algebraic system Phys Rev A 71 022104 (2005)[365] J He H Liu Admissible wavelets associated with the affine automorphism group of the
Siegel upper half-plane J Math Anal Appl 208 58ndash70 (1997)[366] J He H Liu Admissible wavelets associated with the classical domain of type one
Approx Appl 14 (1998) 89ndash105[367] J He L Peng Wavelet transform on the symmetric matrix space preprint Beijing (1997)
(unpublished)[368] J He L Peng Admissible wavelets on the unit disk Complex Variables 35 109ndash119
(1998)[369] DM Healy Jr FE Schroeck Jr On informational completeness of covariant localization
observables and Wigner coefficients J Math Phys 36 453ndash507 (1995)[370] C Heil D Walnut Continuous and discrete wavelet transforms SIAM Review 31 628ndash
666 (1989)[371] K Hepp EH Lieb On the superradiant phase transition for molecules in a quantized
radiation field The Dicke maser model Ann Phys (NY) 76 360ndash404 (1973)[372] K Hepp EH Lieb Equilibrium statistical mechanics of matter interacting with the
quantized radiation field Phys Rev A 8 2517ndash2525 (1973)[373] JA Hogan JD Lakey Extensions of the Heisenberg group by dilations and frames Appl
Comput Harmon Anal 2 174ndash199 (1995)[374] AL Hohoueacuteto K Thirulogasanthar ST Ali J-P Antoine Coherent states lattices and
square integrability of representations J Phys A Math Gen36 11817ndash11835 (2003)[375] M Holschneider On the wavelet transformation of fractal objects J Stat Phys 50 963ndash
993 (1988)[376] M Holschneider Wavelet analysis on the circle J Math Phys 31 39ndash44 (1990)[377] M Holschneider Inverse Radon transforms through inverse wavelet transforms Inv Probl
7 853ndash861 (1991)[378] M Holschneider Localization properties of wavelet transforms J Math Phys 34 3227ndash
3244 (1993)[379] M Holschneider General inversion formulas for wavelet transforms J Math Phys 34
4190ndash4198 (1993)[380] M Holschneider Wavelet analysis over abelian groups Applied Comput Harmon Anal
2 52ndash60 (1995)[381] M Holschneider Continuous wavelet transforms on the sphere J Math Phys 37 4156ndash
4165 (1996)[382] M Holschneider I Iglewska-Nowak Poisson wavelets on the sphere J Fourier Anal
Appl 13 405ndash419 (2007)
562 References
[383] M Holschneider R Kronland-Martinet J Morlet P Tchamitchian A real-time algorithmfor signal analysis with the help of wavelet transform in Wavelets Time-FrequencyMethods and Phase Space (Proc Marseille 1987) ed by J-M Combes A Grossmann PTchamitchian 2nd edn (Springer Berlin 1990) pp 286ndash297
[384] M Holschneider P Tchamitchian Pointwise analysis of Riemannrsquos ldquonondifferentiablerdquofunction Invent Math 105 157ndash175 (1991)
[385] GR Honarasa MK Tavassoly M Hatami R Roknizadeh Nonclassical properties ofcoherent states and excited coherent states for continuous spectra J Phys A Math Theor44 085303 (2011)
[386] M Hongoh Coherent states associated with the continuous spectrum of noncompactgroups J Math Phys 18 2081ndash2085 (1977)
[387] A Horzela FH Szafraniec A measure free approach to coherent states J Phys A MathGen 45 244018 (2012)
[388] W-L Hwang S Mallat Characterization of self-similar multifractals with waveletmaxima Appl Comput Harmon Anal 1 316ndash328 (1994)
[389] W-L Hwang C-S Lu P-C Chung Shape from texture Estimation of planar surfaceorientation through the ridge surfaces of continuous wavelet transform IEEE Trans ImageProc 7 773ndash780 (1998)
[390] I Iglewska-Nowak M Holschneider Frames of Poisson wavelets on the sphere ApplComput Harmon Anal 28 227ndash248 (2010)
[391] E Inoumlnuuml EP Wigner On the contraction of groups and their representations Proc NatAcad Sci U S 39 510ndash524 (1953)
[392] S Iqbal F Saif Generalized coherent states and their statistical characteristics in power-law potentials J Math Phys 52 082105 (2011)
[393] CJ Isham JR Klauder Coherent states for n-dimensional Euclidean groups E(n) andtheir application J MathPhys 32 607ndash620 (1991)
[394] L Jacques J-P Antoine Multiselective pyramidal decomposition of images Wavelets withadaptive angular selectivity Int J Wavelets Multires Inform Proc 5 785ndash814 (2007)
[395] L Jacques L Duval C Chaux G Peyreacute A panorama on multiscale geometric rep-resentations intertwining spatial directional and frequency selectivity Signal Proc 912699ndash2730 (2011)
[396] HR Jalali M K Tavassoly On the ladder operators and nonclassicality of generalizedcoherent state associated with a particle in an infinite square well preprint (2013)arXiv13034100v1 [quant-ph]
[397] C Johnston On the pseudo-dilation representations of Flornes Grossmann Holschneiderand Torreacutesani Appl Comput Harmon Anal 3 377ndash385 (1997)
[398] G Kaiser Phase-space approach to relativistic quantum mechanics I Coherent staterepresentation for massive scalar particles J MathPhys 18 952ndash959 (1977)
[399] G Kaiser Phase-space approach to relativistic quantum mechanics II Geometrical aspectsJ MathPhys 19 502ndash507 (1978)
[400] C Kalisa B Torreacutesani N-dimensional affine Weyl-Heisenberg wavelets Ann Inst HPoincareacute 59 201ndash236 (1993)
[401] W Kaminski J Lewandowski T Pawłowski Quantum constraints Dirac observables andevolution group averaging versus the Schroumldinger picture in LQC Class Quant Grav 26245016 (2009)
[402] MR Karim ST Ali A relativistic windowed Fourier transform preprint ConcordiaUniversity Montreacuteal (1997) (unpublished)
[403] M R Karim ST Ali M Bodruzzaman A relativistic windowed Fourier transform inProceedings of IEEE SoutheastCon 2000 Nashville Tennessee pp 253ndash260 (2000)
[404] T Kawazoe Wavelet transforms associated to a principal series representation of semisim-ple Lie groups I II Proc Japan Acad Ser A ndash Math Sci 71 154ndash157 158ndash160 (1995)
[405] T Kawazoe Wavelet transform associated to an induced representation of SL(n+ 2R)Ann Inst H Poincareacute 65 1ndash13 (1996)
References 563
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[407] P Kittipoom G Kutyniok W-Q Lim Construction of compactly supported shearletframes Constr Approx 35 21ndash72 (2012)
[408] J Kiukas P Lahti K Ylinenc Phase space quantization and the operator moment problemJ Math Phys 47 072104 (2006)
[409] JR Klauder Continuous-representation theory I Postulates of continuous-representationtheory J Math Phys 4 1055ndash1058 (1963)
[410] JR Klauder Continuous-representation theory II Generalized relation between quantumand classical dynamics J Math Phys 4 1058ndash1073 (1963)
[411] JR Klauder Path integrals for affine variables in Functional Integration Theory andApplications ed by J-P Antoine E Tirapegui (Plenum Press New York and London1980) pp 101ndash119
[412] JR Klauder Are coherent states the natural language of quantum mechanics inFundamental Aspects of Quantum Theory ed by V Gorini A Frigerio NATO ASI Seriesvol B 144 (Plenum Press New York 1986) pp 1ndash12
[413] JR Klauder Quantization without quantization Ann Phys (NY) 237 147ndash160 (1995)[414] JR Klauder Coherent states for the hydrogen atom J Phys A Math Gen 29 L293ndash
L296 (1996)[415] JR Klauder An affinity for affine quantum gravity Proc Steklov Inst Math 272 169ndash176
(2011) and references therein[416] JR Klauder RF Streater A wavelet transform for the Poincareacute group J Math Phys 32
1609ndash1611 (1991)[417] JR Klauder RF Streater Wavelets and the Poincareacute half-plane J Math Phys 35 471ndash
478 (1994)[418] JR Klauder K Penson J-M Sixdeniers Constructing coherent states through solutions
of Stieltjes and Hausdorff moment problems Phys Rev A 64 013817 (2001)[419] A Kleppner RL Lipsman The Plancherel formula for group extensions Ann Ec Norm
Sup 5 459ndash516 (1972)[420] AB Klimov C Muntildeoz Coherent isotropic and squeezed states in a N-qubit system Phys
Scr 87 038110 (2013)[421] A Klyashko Dynamical symmetry approach to entanglement in Physics and Theoretical
Computer Science From Numbers and Languages to (Quantum) Cryptography - NATOSecurity through Science Series D - Information and Communication Security vol 7 edby J-P Gazeau J Nesetril B Rovan (IOS Press Washington DC 2007) pp 25ndash54
[422] S Kobayashi Irreducibility of certain unitary representations J Math Soc Japan 20 638ndash642 (1968)
[423] K Kowalski J Rembielinski LC Papaloucas Coherent states for a quantum particle ona circle J Phys A Math Gen 29 4149ndash4167 (1996)
[424] K Kowalski J Rembielinski Quantum mechanics on a sphere and coherent states J PhysA Math Gen 33 6035ndash6048 (2000)
[425] K Kowalski J Rembielinski The Bargmann representation for the quantum mechanicson a sphere J Math Phys 42 4138ndash4147 (2001)
[426] C Kristjansen J Plefka GW Semenoff M Staudacher A new double-scaling limit ofN = 4 super-Yang-Mills theory and pp-wave strings Nuclear Phys B 643 3ndash30 (2002)
[427] M Kulesh M Holschneider MS Diallo Geophysical wavelet library Applications ofthe continuous wavelet transform to the polarization and dispersion analysis of signalsComput Geosci 34 1732ndash1752 (2008)
[428] R Kunze On the Frobenius reciprocity theorem for square integrable representationsPacific J Math 53 465ndash471 (1974)
[429] Y Kuroda A Wada T Yamazaki K Nagayama Postacquisition data processing methodfor suppression of the solvent signal I J Magn Reson 84 604ndash610 (1989)
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[431] G Kutyniok D Labate Resolution of the wavefront set using continuous shearlets TransAmer Math Soc 361 2719ndash2754 (2009)
[432] G Kutyniok W-Q Lim Compactly supported shearlets are optimally sparse J ApproxTheory 163 1564ndash1589 (2011)
[433] D Labate W-Q Lim G Kutyniok G Weiss Sparse multidimensional representationusing shearlets in Wavelets XI (San Diego CA 2005) ed by M Papadakis A Laine MUnser SPIE Proceedings vol 5914 (SPIE Bellingham WA 2005) pp 254ndash262
[434] P Lahti J-P Pellonpaumlauml Continuous variable tomographic measurements Phys Lett A373 3435ndash3438 (2009)
[435] Lambertrsquos projection see WikipediahttpenwikipediaorgwikiLambert_azimuthal_equal-area_projection
[436] J-P Leduc F Mujica R Murenzi MJT Smith Missile-tracking algorithm using target-adapted spatio-temporal wavelets in Automatic Object Recognition VII SPIE Proceedingsvol 5914 (SPIE Bellingham WA 1997) pp 400ndash411
[437] J-P Leduc F Mujica R Murenzi MJT Smith Spatio-temporal wavelet transforms formotion tracking in IEEE ICASSP 1997 vol 4 (1997) pp 3013ndash3016
[438] J-P Leduc F Mujica R Murenzi MJT Smith Spatio-temporal continuous waveletsapplied to missile warhead detection and tracking in SPIE VCIP rsquo97 vol 3024 ed byJ Biemond EJ Delp (1997) pp 787ndash798
[439] B Leistedt JD McEwen Exact wavelets on the ball IEEE Trans Signal Proc 60 1564ndash1589 (2012)
[440] PG Lemarieacute Y Meyer Ondelettes et bases hilbertiennes Rev Math Iberoamer 2 1ndash18(1986)
[441] C Lemke A Schuck Jr J-P Antoine D Sima Metabolite-sensitive analysis of magneticresonance spectroscopic signals using the continuous wavelet transform Meas SciTechnol 22 (2011) Art 114013
[442] J-M Leacutevy-Leblond Galilei group and non-relativistic quantum mechanics J Math Phys4 776-788 (1963)
[443] J-M Leacutevy-Leblond Galilei group and Galilean invariance in Group Theory and ItsApplications vol II ed by EM Loebl (Academic New York 1971) pp 221ndash299
[444] J-M Leacutevy-Leblond On the conceptual nature of the physical constants Riv Nuovo Cim7 187ndash214 (1977)
[445] EH Lieb The classical limit of quantum spin systems Commun Math Phys 31 327ndash340(1973)
[446] G Lindblad B Nagel Continuous bases for unitary irreducible representations of SU(11)Ann Inst H Poincareacute 13 27ndash56 (1970)
[447] W Lisiecki Kaumlhler coherent states orbits for representations of semisimple Lie groupsAnn Inst H Poincareacute 53 857ndash890 (1990)
[448] A Lisowska Moment-based fast wedgelet transform J Math Imaging Vis 39 180ndash192(2011)
[449] H Liu L Peng Admissible wavelets associated with the Heisenberg group Pacific JMath 180 101ndash123 (1997)
[450] E Livine S Speziale Physical boundary state for the quantum tetrahedron Class QuantGrav 25 085003 (2008)
[451] F Low Complete sets of wave packets in A Passion for Physics ndash Essay in Honor ofGeoffrey Chew ed by C DeTar (World Scientific Singapore 1985) pp 17ndash22
[452] G Mack All unitary ray representations of the conformal group SU(22) with positiveenergy Commun Math Phys 55 1ndash28 (1977)
[453] GW Mackey Imprimitivity for representations of locally compact groups I Proc NatAcad Sci 35 537ndash545 (1949)
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[456] SG Mallat Multifrequency channel decompositions of images and wavelet models IEEETrans Acoust Speech Signal Proc 37 2091ndash2110 (1989)
[457] SG Mallat A theory for multiresolution signal decomposition The wavelet representa-tion IEEE Trans Pattern Anal Machine Intell 11 674ndash693 (1989)
[458] S Mallat W-L Hwang Singularity detection and processing with wavelets IEEE TransInform Theory 38 617ndash643 (1992)
[459] S Mallat Z Zhang Matching pursuits with time frequency dictionaries IEEE TransSignal Proc 41 3397ndash3415 (1993)
[460] S Mallat S Zhong Wavelet maxima representation in Wavelets and Applications (ProcMarseille 1989) ed by Y Meyer (Masson and Springer Paris and Berlin 1991) pp 207ndash284
[461] VI Manrsquoko G Marmo ECG Sudarshan F Zaccaria f -oscillators and non-linearcoherent states Phys Scr 55 528ndash541 (1997)
[462] D Marinucci D Pietrobon A Baldi P Baldi P Cabella G Kerkyacharian P Natoli DPicard N Vittorio Spherical needlets for CMB data analysis Mon Not R Astron Soc383 539ndash545 (2008)
[463] D Marion M Ikura A Bax Improved solvent suppression in one- and two-dimensionalNMR spectra by convolution of time-domain data J Magn Reson 84 425ndash430 (1989)
[464] Y Meyer Principe drsquoincertitude bases hilbertiennes et algegravebres drsquoopeacuterateurs SeacuteminaireBourbaki 662 (1985ndash1986)
[465] Y Meyer Principe drsquoincertitude bases hilbertiennes et algegravebres drsquoopeacuterateurs Asteacuterisque145ndash146 209ndash223 (1987)
[466] Y Meyer H Xu Wavelet analysis and chirps Appl Comput Harmon Anal 4 366ndash379(1997)
[467] L Michel Invariance in quantum mechanics and group extensions in Group TheoreticalConcepts and Methods in Elementary Particle Physics ed by F Guumlrsey (Gordon andBreach New York and London 1964) pp 135ndash200
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[469] MM Miller Convergence of the Sudarshan expansion for the diagonal coherent-stateweight functional J Math Phys 9 1270ndash1274 (1968)
[470] V F Molchanov Harmonic analysis on homogeneous spaces in Representation Theoryand Noncommutative Harmonic Analysis II ed by AA Kirillov (Springer Berlin 1995)
[471] MI Monastyrsky AM Perelomov Coherent states and symmetric spaces II Ann InstH Poincareacute 23 23ndash48 (1975)
[472] B Moran S Howard D Cochran Positive-operator-valued measures A general settingfor frames in Excursions in Harmonic Analysis vol 1 2 ed by TD Andrews R BalanJJ Benedetto W Czaja KA Okoudjou (Birkhaumluser Boston 2013) pp 49ndash64
[473] H Moscovici Coherent states representations of nilpotent Lie groups Commun MathPhys 54 63ndash68 (1977)
[474] H Moscovici A Verona Coherent states and square integrable representations Ann InstH Poincareacute 29 139ndash156 (1978)
[475] F Mujica R Murenzi MJT Smith J-P Leduc Robust tracking in compressed imagesequences J Electr Imaging 7 746ndash754 (1998)
[476] R Murenzi Wavelet transforms associated to the n-dimensional Euclidean group withdilations Signals in more than one dimension in Wavelets Time-Frequency Methodsand Phase Space (Proc Marseille 1987) ed by J-M Combes A Grossmann PTchamitchian 2nd edn (Springer Berlin 1990) pp 239ndash246
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[479] MA Naımark Dokl Akad Nauk SSSR 41 359ndash361 (1943) see also B Sz-NagyExtensions of linear transformations in Hilbert space which extend beyond this spaceAppendix to F Riesz B Sz-Nagy Functional Analysis (Frederick Ungar New York 1960)
[480] FJ Narcowich P Petrushev JD Ward Localized tight frames on spheres SIAM J MathAnal 38 574ndash594 (2006)
[481] M Nauenberg Quantum wave packets on Kepler elliptic orbits Phys Rev A 40 1133ndash1136 (1989)
[482] M Nauenberg C Stroud J Yeazell The classical limit of an atom Scient Amer 27024ndash29 (1994)
[483] H Neumann Transformation properties of observables Helv Phys Acta 45 811ndash819(1972)
[484] U Niederer The maximal kinematical invariance group of the free Schroumldinger equationHelv Phys Acta 45 802ndash881 (1972)
[485] MM Nieto LM Simmons Jr Coherent states for general potentials I Formalism IIConfining one-dimensional examples III Nonconfining one-dimensional examples PhysRev D 20 1321ndash1331 1332ndash1341 1342ndash1350 (1979)
[486] MM Nieto LM Simmons Jr Coherent states for general potentials Phys Rev Lett 41207ndash210 (1987)
[487] A Odzijewicz On reproducing kernels and quantization of states Commun Math Phys114 577ndash597 (1988)
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[490] A Odzijewicz M Horowski A Tereszkiewicz Integrable multi-boson systems andorthogonal polynomials J Phys A Math Gen 34 4353ndash4376 (2001)
[491] G Oacutelafsson B Oslashrsted The holomorphic discrete series for affine symmetric spaces JFunct Anal 81 126ndash159 (1988)
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[494] E Onofri Dynamical quantization of the Kepler manifold J Math Phys 17 401ndash408(1976)
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[498] Z Pasternak-Winiarski On reproducing kernels for holomorphic vector bundles inQuantization and Infinite Dimensional Systems (Proc Białowieza Poland 1993) ed by J-P Antoine ST Ali W Lisiecki IM Mladenov A Odzijewicz (Plenum Press New Yorkand London 1994) pp 109ndash112
[499] T Paul Affine coherent states and the radial Schroumldinger equation I preprint CPT-84P1710 (1984) (unpublished)
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[501] AM Perelomov On the completeness of a system of coherent states Theor Math Phys6 156ndash164 (1971)
[502] AM Perelomov Coherent states for arbitrary Lie group Commun Math Phys 26 222ndash236 (1972)
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[504] M Perroud Projective representations of the Schroumldinger group Helv Phys Acta 50 233ndash252 (1977)
[505] J Phillips A note on square-integrable representations J Funct Anal 20 83ndash92 (1975)[506] D Pietrobon P Baldi D Marinucci Integrated Sachs-Wolfe effect from the cross
correlation of WMAP3 year and the NRAO VLA sky survey data New results andconstraints on dark energy Phys Rev D 74 043524 (2006)
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[509] G Poumlschl E Teller Bemerkungen zur Quantenmechanik des anharmonischen OszillatorsZ Physik 83 143ndash151 (1933)
[510] D Potts G Steidl M Tasche Kernels of spherical harmonics and spherical frames inAdvanced Topics in Multivariate Approximation ed by F Fontanella K Jetter PJ Laurent(World Scientific Singapore 1996) pp 287ndash301
[511] E Prugovecki Consistent formulation of relativistic dynamics for massive spin-zeroparticles in external fields Phys Rev D 18 3655ndash3673 (1978) (Appendix C)
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[516] A Rahimi A Najati YN Dehghan Continuous frames in Hilbert spaces Methods FunctAnal Topol 12 170ndash182 (2006)
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[521] D Robert La coheacuterence dans tous ses eacutetats SMF Gazette 132 (2012)[522] JE Roberts The Dirac bra and ket formalism J Math Phys 7 1097ndash1104 (1966)[523] JE Roberts Rigged Hilbert spaces in quantum mechanics Commun Math Phys 3 98ndash
119 (1966)[524] S Roques F Bourzeix K Bouyoucef Soft-thresholding technique and restoration of
3C273 jet Astrophys Space Sci Nr 239 297ndash304 (1996)[525] D Rosca Haar wavelets on spherical triangulations in Advances in Multiresolution for
Geometric Modelling ed by NA Dogson MS Floater MA Sabin (Springer Berlin2005) pp 407ndash419
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501ndash511 (2007)[529] D Rosca Wavelet bases on the sphere obtained by radial projection J Fourier Anal Appl
13 421ndash434 (2007)[530] D Rosca Piecewise constant wavelets on triangulations obtained by 1ndash3 splitting Int J
Wavelets Multiresolut Inf Process 6 209ndash222 (2008)[531] D Rosca On a norm equivalence on L2(S2) Results Math 53 399ndash405 (2009)[532] D Rosca New uniform grids on the sphere Astron Astrophys 520 (2010) Art A63[533] D Rosca Uniform and refinable grids on elliptic domains and on some surfaces of
revolution Appl Math Comput 217 7812ndash7817 (2011)[534] D Rosca Wavelet analysis on some surfaces of revolution via area preserving projection
Appl Comput Harmon Anal 30 262ndash272 (2011)[535] D Rosca J-P Antoine Locally supported orthogonal wavelet bases on the sphere via
stereographic projection Math Probl Eng 2009 124904 (2009)[536] D Rosca J-P Antoine Constructing wavelet frames and orthogonal wavelet bases on the
sphere in Recent Advances in Signal Processing ed by S Miron (IN-TECH ViennaAustria and Rijeka Croatia 2010) pp 59ndash76
[537] D Rosca G Plonka Uniform spherical grids via area preserving projection from the cubeto the sphere J Comput Appl Math 236 1033ndash1041 (2011)
[538] D Rosca G Plonka An area preserving projection from the regular octahedron to thesphere Results Math 63 429ndash444 (2012)
[539] H Rossi M Vergne Analytic continuation of the holomorphic discrete series for a semi-simple Lie group Acta Math 136 1ndash59 (1976)
[540] DJ Rotenberg Application of Sturmian functions to the Schroedinger three-body prob-lem Elastic e+ndashH scattering Ann Phys (NY) 19 262ndash278 (1962)
[541] C Rovelli Zakopane lectures on loop gravity in Proceedings of 3rd Quantum Gravityand Quantum Geometry School 28 Febndash13 March 2011 (Zakopane Poland 2011)arXiv11023660v5
[542] C Rovelli S Speziale A semiclassical tetrahedron Class Quant Grav 23 5861ndash5870(2006)
[543] DJ Rowe Coherent state theory of the noncompact symplectic group J Math Phys 252662ndash2271 (1984)
[544] DJ Rowe Microscopic theory of the nuclear collective model Rep Prog Phys 48 1419ndash1480 (1985)
[545] DJ Rowe Vector coherent state representations and their inner products J Phys A MathGen 45 244003 (2012) (This paper belongs to the special issue [38])
[546] DJ Rowe J Repka Vector-coherent-state theory as a theory of induced representationsJ Math Phys 32 2614ndash2634 (1991)
[547] DJ Rowe G Rosensteel R Gilmore Vector coherent state representation theory J MathPhys 26 2787ndash2791 (1985)
[548] A Royer Phase states and phase operators for the quantum harmonic oscillator Phys RevA 53 70ndash108 (1996)
[549] J Saletan Contraction of Lie groups J Math Phys 2 1ndash21 (1961)[550] G Saracco A Grossmann P Tchamitchian Use of wavelet transforms in the study of
propagation of transient acoustic signals across a plane interface between two homoge-neous media in Wavelets Time-Frequency Methods and Phase Space (Proc Marseille1987) ed by J-M Combes A Grossmann P Tchamitchian 2nd edn (Springer Berlin1990) pp 139ndash146
[551] P Schroumlder W Sweldens Spherical wavelets Efficiently representing functions on thesphere in Computer Graphics Proceedings (SIGGRAPH95) (ACM Siggraph Los Angeles1995) pp 161ndash175
References 569
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[554] H Scutaru Coherent states and induced representations Lett Math Phys 2 101ndash107(1977)
[555] B Simon Distributions and their Hermite expansions J Math Phys 12 140ndash148 (1971)[556] B Simon The classical moment problem as a self-adjoint finite difference operator Adv
Math 137 82ndash203 (1998)[557] R Simon ECG Sudarshan N Mukunda Gaussian pure states in quantum mechanics
and the symplectic group Phys Rev A37 3028ndash3038 (1988)[558] S Sivakumar Studies on nonlinear coherent states J Opt B Quant Semiclass Opt 2
R61ndashR75 (2000)[559] E Slezak A Bijaoui G Mars Identification of structures from galaxy counts Use of the
wavelet transform Astron Astroph 227 301ndash316 (1990)[560] A Solomon A characteristic functional for deformed photon phenomenology Phys Lett
A 196 29ndash34 (1994)[561] SB Sontz Paragrassmann algebras as quantum spaces Part I Reproducing kernels in
Geometric Methods in Physics XXXI Workshop 2012 (Trends in Mathematics ed byP Kielanowski et al Birkhaumluser Verlag Basel 2013) pp 47ndash63
[562] SB Sontz Paragrassmann algebras as quantum spaces Part II Toeplitz operators J OperTh (2013 to appear) arXiv12055493
[563] SB Sontz A reproducing kernel and Toeplitz operators in the quantum plane Preprint(2013) arXiv13056986 [math-ph]
[564] SB Sontz Toeplitz quantization of an algebra with conjugation Preprint (2013)arXiv13085454 [math-ph]
[565] M Spera On a generalized Uncertainty Principle coherent states and the moment mapJ Geom Phys 12 165ndash182 (1993)
[566] J-L Starck EJ Candegraves DL Donoho The curvelet transform for image denoising IEEETrans Image Proc 11 670ndash684 (2002)
[567] J-L Starck DL Donoho E J Candegraves Astronomical image representation by the curvelettransform Astron Astroph 398 785ndash800 (2003)
[568] J-L Starck Y Moudden P Abrial M Nguyen Wavelets ridgelets and curvelets on thesphere Astron Astroph 446 1191ndash1204 (2006)
[569] MB Stenzel The Segal-Bargmann transform on a symmetric space of compact type JFunct Analysis 165 44ndash58 (1994)
[570] ECG Sudarshan Equivalence of semiclassical and quantum mechanical descriptions ofstatistical light beams Phys Rev Lett 10 277ndash279 (1963)
[571] A Suvichakorn H Ratiney A Bucur S Cavassila J-P Antoine Toward a quantitativeanalysis of in vivo magnetic resonance proton spectroscopic signals using the continuousMorlet wavelet transform Meas Sci Technol 20 (2009) Art 104029
[572] W Sweldens The lifting scheme A custom-design construction of biorthogonal waveletsApplied Comput Harmon Anal 3 1186ndash1200 (1996)
[573] W Sweldens The lifting scheme A construction of second generation wavelets SIAM JMath Anal 29 511ndash546 (1998)
[574] FH Szafraniec The reproducing kernel Hilbert space and its multiplication operatorsin Complex Analysis and Related Topics ed by E Ramirez de Arellano et al OperatorTheory Advances and Applications vol 114 (Birkhaumluser Basel 2000) pp 254ndash263
[575] FH Szafraniec Multipliers in the reproducing kernel Hilbert space subnormality andnoncommutative complex analysis in Reproducing Kernel Spaces and Applications edby D Alpay Operator Theory Advances and Applications vol 143 (Birkhaumluser Basel2003) pp 313ndash331
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[577] MC Teich BEA Saleh Squeezed states of light Quantum Opt 1 152ndash191 (1989)[578] R Terrier L Demanet IA Grenier J-P Antoine Wavelet analysis of EGRET data in
Proceedings of the 27th International Cosmic Ray Conference (ICRC 2001) (CopernicusGesellschaft DE 2001) pp 2923ndash2926
[579] T Thiemann Gauge field theory coherent states (GCS) 1 General properties Class QuantGrav 18 2025ndash2064 (2001)
[580] T Thiemann O Winkler Gauge field theory coherent states (GCS) 2 Peakednessproperties Class Quant Grav 18 2561ndash2636 (2001)
[581] T Thiemann O Winkler Gauge field theory coherent states (GCS) 3 Ehrenfest theoremsClass Quant Grav 18 4629ndash4682 (2001)
[582] T Thiemann O Winkler Gauge field theory coherent states (GCS) 4 Infinite tensorproduct and thermodynamical limit Class Quant Grav 18 4997ndash5054 (2001)
[583] K Thirulagasanthar ST Ali Regular subspaces of a quaternionic Hilbert space fromquaternionic Hermite polynomials and associated coherent states J Math Phys 54013506 (2013)
[584] K Thirulogasanthar G Honnouvo A Krzyzak Coherent states and Hermite polynomialson quaternionic Hilbert spaces J Phys A Math Theor 43 385205 (2010)
[585] Tokamak see Wikipedia httpenwikipediaorgwikiTokamak[586] B Torreacutesani Wavelets associated with representations of the affine Weyl-Heisenberg
group J Math Phys 32 1273ndash1279 (1991)[587] B Torreacutesani Time-frequency representation Wavelet packets and optimal decomposition
Ann Inst H Poincareacute 56 215ndash234 (1992)[588] B Torreacutesani Position-frequency analysis for signals defined on spheres Signal Proc 43
341ndash346 (2005)[589] DA Trifonov Generalized intelligent states and squeezing J Math Phys 35 2297ndash2308
(1994)[590] AS Trushechkin IV Volovich Localization properties of squeezed quantum states in
nanoscale space domains preprint (2013) arXiv13046277v1 [quant-ph][591] M Unser N Chenouard A unifying parametric framework for 2D steerable wavelet
transforms SIAM J Imaging Sci 6 102ndash135 (2013)[592] P Vandergheynst J-F Gobbers Directional dyadic wavelet transforms Design and
algorithms IEEE Trans Image Proc 11 363ndash372 (2002)[593] P Vandergheynst J-P Antoine E Van Vyve A Goldberg I Doghri Modelling and
simulation of an impact test using wavelets analytical and finite element models Int JSolids Struct 38 5481ndash5508 (2001)
[594] L Vanhamme RD Fierro S Van Huffel R de Beer Fast removal of residual water inproton spectra J Magn Reson 132 197ndash203 (1998)
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[598] DF Walls Squeezed states of light Nature 306 141ndash146 (1983)[599] YK Wang FT Hioe Phase transition in the Dicke maser model Phys Rev A 7 831ndash836
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Recogn Artif Intell 26 1255011 (2012)[601] I Weinreich A construction of C1-wavelets on the two-dimensional sphere Appl Comput
Harmon Anal 10 1ndash26 (2001)[602] H Weyl Quantenmechanik und Gruppentheorie Z Phys 46 1ndash46 (1927)
References 571
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[609] W Wisnoe P Gajan A Strzelecki C Lempereur J-M Matheacute The use of the two-dimensional wavelet transform in flow visualization processing in Progress in WaveletAnalysis and Applications (Proc Toulouse 1992) ed by Y Meyer S Roques (EdFrontiegraveres Gif-sur-Yvette 1993) pp 455ndash458
[610] K Woacutedkiewicz On the quantum mechanics of squeezed states J Modern Optics 34 941ndash948(1987)
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[612] JA Yeazell CR Stroud Jr Observation of fractional revivals in the evolution of aRydberg atomic wave packet Phys Rev A 43 5153ndash5156 (1991)
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[614] J Zak Balian-Low theorem for Landau levels Phys Rev Lett 79 533ndash536 (1997)[615] J Zak Orthonormal sets of localized functions for a Landau level J Math Phys 39 4195ndash
4200 (1998) and references quoted there[616] AA Zakharova On the properties of generalized frames Math Notes 83 190ndash200 (2008)[617] W-M Zhang DH Feng R Gilmore Coherent states Theory and some applications Rev
Mod Phys 26 867ndash927 (1990)[618] I Zlatev W-M Zhang DH Feng Possibility that Schroumldingerrsquos conjecture for the
hydrogen atom coherent states is not attainable Phys Rev A 50 R1973ndashR1975 (1994)[619] WH Zurek Decoherence einselection and the quantum origins of the classical Rev Mod
Phys 75 715ndash775 (2003)[620] WH Zurek S Habib JP Paz Coherent states via decoherence Phys Rev Lett 70 1187ndash
1190 (1993)[621] K Zyczkowski Squeezed states in a quantum chaotic system J Phys A Math Theor 22
of SU(11) 81 296 297HilbertClowast-modules 164holomorphic 140nonholomorphic 151nonlinear 146of affine Galilei group 505of affine Poincareacute group 509of affine Weyl-Heisenberg group GaWH
497of compact semisimple Lie groups 174of Euclidean group E(n) 266of Galilei group G (11) 290of isochronous Galilei group 237of non-semisimple Lie groups 179of noncompact semisimple Lie groups 177of Poincareacute group Puarr
+(11) 283massless case 288
of Poincareacute group Puarr+(13) 279
of Schroumldinger group 508quasi-coherent states 186quaternionic 164
ST Ali et al Coherent States Wavelets and Their Generalizations Theoreticaland Mathematical Physics DOI 101007978-1-4614-8535-3copy Springer Science+Business Media New York 2014
573
574 Index
coherent states (CS) (cont)spin or SU(2) 175square integrable covariant 166 180 264vector (VCS) 73 108 112 170weighted 184 523
of affine Weyl-Heisenberg group GaWH497
of Poincareacute group Puarr+(11) 284
cohomology group 393 403coboundaries 403cochains 402cocycle 403
algebraic 387Cauchy 418Cauchy-Paul 354 419 425conical 418difference 417 462directional 416 440kinematical 499local 488metabolite-based 355 374minimal uncertainty 425multiselective 440on a graph 493on the sphere S
2 458on the sphere S
n 479on the torus T2 481steerable 439von Mises 440
wedgelet transform 455Wigner function 322Wigner-Ville transform 349Windowed Fourier or Gabor transform 349
ZZak transform 518
References
A Books and Theses
B Articles
Index
550 References
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[91] TA Arias Multiresolution analysis of electronic structure Semicardinal and waveletbases Rev Mod Phys 71 267ndash312 (1999)
[92] A Arneacuteodo F Argoul E Bacry J Elezgaray E Freysz G Grasseau JF Muzy BPouligny Wavelet transform of fractals in Wavelets and Applications (Proc Marseille1989) ed by Y Meyer (Masson and Springer Paris and Berlin 1991) pp 286ndash352
[93] A Arneacuteodo E Bacry JF Muzy The thermodynamics of fractals revisited with waveletsPhysica A 213 232ndash275 (1995)
[94] A Arneacuteodo E Bacry JF Muzy Oscillating singularities in locally self-similar functionsPhys Rev Lett 74 4823ndash4826 (1995)
[95] A Arneacuteodo E Bacry PV Graves JF Muzy Characterizing long-range correlations inDNA sequences from wavelet analysis Phys Rev Lett 74 3293ndash3296 (1996)
[96] A Arneacuteodo Y drsquoAubenton E Bacry PV Graves JF Muzy C Thermes Wavelet basedfractal analysis of DNA sequences Physica D 96 291ndash320 (1996)
[97] A Arneacuteodo E Bacry S Jaffard JF Muzy Oscillating singularities on Cantor sets Agrand canonical multifractal formalism J Stat Phys 87 179ndash209 (1997)
[98] A Arneacuteodo E Bacry S Jaffard JF Muzy Singularity spectrum of multifractal functionsinvolving oscillating singularities J Fourier Anal Appl 4 159ndash174 (1998)
[99] N Aronszajn Theory of reproducing kernels Trans Amer Math Soc 66 337ndash404 (1950)[100] A Ashtekar J Lewandowski D Marolf J Mouratildeo T Thiemann Coherent state
transforms for spaces of connections J Funct Analysis 135 519ndash551 (1996)[101] A Askari-Hemmat MA Dehghan M Radjabalipour Generalized frames and their
redundancy Proc Amer Math Soc 129 1143ndash1147 (2001)[102] EW Aslaksen JR Klauder Unitary representations of the affine group J Math Phys 9
206ndash211 (1968)[103] EW Aslaksen JR Klauder Continuous representation theory using the affine group
J Math Phys 10 2267ndash2275 (1969)[104] D Astruc L Plantieacute R Murenzi Y Lebret D Vandromme On the use of the 3D
wavelet transform for the analysis of computational fluid dynamics results in Progressin Wavelet Analysis and Applications (Proc Toulouse 1992) ed by Y Meyer S Roques(Ed Frontiegraveres Gif-sur-Yvette 1993) pp 463ndash470
[105] PW Atkins JC Dobson Angular momentum coherent states Proc Roy Soc London A321 321ndash340 (1971)
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[107] IS Averbuch NF Perelman Fractional revivals Universality in the long-term evolutionof quantum wave packets beyond the correspondence principle dynamics Phys Lett A139 449ndash453 (1989)
[108] H Bacry J-M Leacutevy-Leblond Possible kinematics J Math Phys 9 1605ndash1614 (1968)[109] H Bacry A Grossmann J Zak Proof of the completeness of lattice states in kq
representation Phys Rev B 12 1118ndash1120 (1975)[110] L Baggett KF Taylor Groups with completely reducible regular representation Proc
Amer Math Soc 72 593ndash600 (1978)[111] VG Bagrov J-P Gazeau D Gitman A Levine Coherent states and related quantizations
for unbounded motions J Phys A Math Theor 45 125306 (2012) arXiv12010955v2[quant-ph]
[112] P Balazs J-P Antoine A Grybos Weighted and controlled frames Mutual relationshipand first numerical properties Int J Wavelets Multires Inform Proc 8 109ndash132 (2010)
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[115] P Baldi G Kerkyacharian D Marinucci D Picard High frequency asymptotics forwavelet-based tests for Gaussianity and isotropy on the torus J Multivar Anal 99 606ndash636 (2008)
[116] P Baldi G Kerkyacharian D Marinucci D Picard Asymptotics for spherical needletsAnn of Stat 37 1150ndash1171 (2009)
[117] MC Baldiotti J-P Gazeau DM Gitman Coherent states of a particle in magnetic fieldand Stieltjes moment problem Phys Lett A 373 1916ndash1920 (2009) Erratum Phys LettA 373 2600 (2009)
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[121] D Barache S De Biegravevre J-P Gazeau Affine symmetry semigroups for quasicrystalsEurophys Lett 25 435ndash440 (1994)
[122] D Barache J-P Antoine J-M Dereppe The continuous wavelet transform a tool for NMRspectroscopy J Magn Reson 128 1ndash11 (1997)
[123] V Bargmann On a Hilbert space of analytic functions and an associated integral transformPart I Commun Pure Appl Math 14 187ndash214 (1961)
[124] V Bargmann On a Hilbert space of analytic functions and an associated integral transformPart II A family of related function spaces Application to distribution theory CommunPure Appl Math 20 1ndash101 (1967)
[125] V Bargmann P Butera L Girardello JR Klauder On the completeness of coherentstates Reports Math Phys 2 221ndash228 (1971)
[126] AO Barut L Girardello New ldquocoherentrdquo states associated with non compact groupsCommun Math Phys 21 41ndash55 (1971)
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[129] G Battle Wavelets A renormalization group point of view in Wavelets and TheirApplications ed by MB Ruskai G Beylkin R Coifman I Daubechies S Mallat YMeyer L Raphael (Jones and Bartlett Boston 1992) pp 323ndash349
[130] P Bellomo CR Stroud Jr Dispersion of Klauderrsquos temporally stable coherent states forthe hydrogen atom J Phys A Math Gen 31 L445ndashL450 (1998)
[131] J Ben Geloun J R Klauder Ladder operators and coherent states for continuous spectraJ Phys A Math Theor 42 375209 (2009)
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[134] JJ Benedetto A Teolis A wavelet auditory model and data compression Appl ComputHarmon Anal 1 3ndash28 (1993)
[135] FA Berezin Quantization Math USSR Izvestija 8 1109ndash1165 (1974)[136] FA Berezin General concept of quantization Commun Math Phys 40 153ndash174 (1975)[137] H Bergeron From classical to quantum mechanics How to translate physical ideas into
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[142] H Bergeron P Siegl A Youssef New SUSYQM coherent states for Poumlschl-Tellerpotentials A detailed mathematical analysis J Phys A Math Theor 45 244028 (2012)
[143] H Bergeron J-P Gazeau A Youssef Are the Weyl and coherent state descriptionsphysically equivalent Phys Lett A 377 598ndash605 (2013)
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[145] S Bergman Uumlber die Kernfunktion eines Bereiches und ihr Verhalten am Rande I ReineAngw Math 169 1ndash42 (1933)
[146] D Bernier KF Taylor Wavelets from square-integrable representations SIAM J MathAnal 27 594ndash608 (1996)
[147] G Bernuau Wavelet bases associated to a self-similar quasicrystal J Math Phys 394213ndash4225 (1998)
[148] A Bertrand Deacuteveloppements en base de Pisot et reacutepartition modulo 1 C R Acad SciParis 285 419ndash421 (1977)
[149] J Bertrand P Bertrand Classification of affine Wigner functions via an extendedcovariance principle in Group Theoretical Methods in Physics (Proc Sainte-Adegravele 1988)ed by Y Saint-Aubin L Vinet (World Scientific Singapore 1989) pp 1380ndash1383
[150] Z Białynicka-Birula I Białynicki-Birula Space-time description of squeezing J OptSoc Am B4 1621ndash1626 (1987)
[151] E Bianchi E Magliaro C Perini Coherent spin-networks Phys Rev D 82 024012(2010)
[152] S Biskri J-P Antoine B Inhester F Mekideche Extraction of Solar coronal magneticloops with the 2-D Morlet wavelet transform Solar Phys 262 373ndash385 (2010)
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[154] I Bogdanova P Vandergheynst J-P Antoine L Jacques M Morvidone Stereographicwavelet frames on the sphere Appl Comput Harmon Anal 19 223ndash252 (2005)
[155] I Bogdanova X Bresson J-P Thiran P Vandergheynst Scale space analysis and activecontours for omnidirectional images IEEE Trans Image Process 16 1888ndash1901 (2007)
[156] I Bogdanova P Vandergheynst J-P Gazeau Continuous wavelet transform on thehyperboloid Appl Comput Harmon Anal 23 (2007) 286ndash306 (2007)
[157] P Boggiatto E Cordero Anti-Wick quantization of tempered distributions in Progress inAnalysis Berlin (2001) vol I II (World Sci Publ River Edge NJ 2003) pp 655ndash662
[158] P Boggiatto E Cordero K Groumlchenig Generalized Anti-Wick operators with symbols indistributional Sobolev spaces Int Equ Oper Theory 48 427ndash442 (2004)
[159] A Boumlhm The Rigged Hilbert Space in quantum mechanics in Lectures in TheoreticalPhysics vol IX A ed by WA Brittin et al (Gordon amp Breach New York 1967) pp255ndash315
[160] G Bohnkeacute Treillis drsquoondelettes associeacutes aux groupes de Lorentz Ann Inst H Poincareacute54 245ndash259 (1991)
[161] WR Bomstad JR Klauder Linearized quantum gravity using the projection operatorformalism Class Quantum Grav 23 5961ndash5981 (2006)
[162] VV Borzov Orthogonal polynomials and generalized oscillator algebras Int TransformSpec Funct 12 115ndash138 (2001)
[163] VV Borzov EV Damaskinsky Generalized coherent states for classical orthogonalpolynomials Day on Diffraction (2002) arXivmathQA0209181v1 (SPb 2002)
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[165] A Bouzouina S De Biegravevre Equipartition of the eigenfunctions of quantized ergodic mapson the torus Commun Math Phys 178 83ndash105 (1996)
[166] P Brault J-P Antoine A spatio-temporal Gaussian-Conical wavelet with high apertureselectivity for motion and speed analysis Appl Comput Harmon Anal 34 148ndash161(2012)
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[171] T Buumllow Multiscale image processing on the sphere in DAGM-Symposium (2002) pp609ndash617
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[174] KE Cahill R Glauber Density operators and quasiprobability distributions Phys Rev177 1882ndash1902 (1969)
[175] KE Cahill R Glauber Ordered expansions in boson amplitude operators Phys Rev 1771857ndash1881 (1969)
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[187] EJ Candegraves DL Donoho Curvelets multiresolution representation and scaling laws inWavelet Applications in Signal and Image Processing VIII ed by A Aldroubi A LaineM Unser SPIE Proceedings vol 4119 (SPIE Bellingham WA 2000) pp 1ndash12
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[197] PG Casazza D Han DR Larson Frames for Banach spaces Contemp Math 247 149ndash182 (1999)
[198] P Casazza O Christensen S Li A Lindner Riesz-Fischer sequences and lower framebounds Z Anal Anwend 21 305ndash314 (2002)
[199] PG Casazza G Kutyniok S Li Fusion frames and distributed processing ApplComputHarmon Anal 25 114ndash132 (2008)
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dimensional numerical potentials Preprint (2013) arXiv13036439v2[203] S-J Chang K-J Shi Evolution and exact eigenstates of a resonant quantum system Phys
Rev A 34 7ndash22 (1986)[204] SHH Chowdhury ST Ali All the groups of signal analysis from the (1+1) affine Galilei
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10 1ndash4 (2012)[206] C Cishahayo S De Biegravevre On the contraction of the discrete series of SU(11) Ann Inst
Fourier (Grenoble) 43 551ndash567 (1993)[207] M Clerc and S Mallat Shape from texture and shading with wavelets in Dynamical
Systems Control Coding Computer Vision Progress in Systems and Control Theory 25393ndash417 (1999)
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wavelets Commun Pure Appl Math 45 485ndash560 (1992)[210] R Coifman Y Meyer MV Wickerhauser Wavelet analysis and signal processing
in Wavelets and Their Applications ed by MB Ruskai G Beylkin R CoifmanI Daubechies S Mallat Y Meyer L Raphael (Jones and Bartlett Boston 1992)pp 153ndash178
[211] R Coifman Y Meyer MV Wickerhauser Entropy-based algorithms for best basisselection IEEE Trans Inform Theory 38 713ndash718 (1992)
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[215] N Cotfas J-P Gazeau K Goacuterska Complex and real Hermite polynomials and relatedquantizations J Phys A Math Theor 43 305304 (2010)
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[217] EMF Curado MA Rego-Monteiro LMCS Rodrigues Y Hassouni Coherent statesfor a degenerate system The hydrogen atom Physica A 371 16ndash19 (2006)
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[219] S Dahlke W Dahmen E Schmidt I Weinreich Multiresolution analysis and wavelets onS
2 and S3 Numer Funct Anal Optim 16 19ndash41 (1995)
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[221] S Dahlke G Kutyniok P Maass C Sagiv H-G Stark G Teschke The uncertaintyprinciple associated with the continuous shearlet transform Int J Wavelets MultiresolutInf Process 6 157ndash181 (2008)
[222] S Dahlke G Kutyniok G Steidl G Teschke Shearlet coorbit spaces and associatedBanach frames Appl Comput Harmon Anal 27 195ndash214 (2009)
[223] S Dahlke G Steidl G Teschke The continuous shearlet transform in arbitrary spacedimensions J Fourier Anal Appl 16 340ndash364 (2010)
[224] S Dahlke G Steidl G Teschke Shearlet coorbit spaces Compactly supported analyzingshearlets traces and embeddings J Fourier Anal Appl 17 1232ndash1355 (2011)
[225] T Dallard GR Spedding 2-D wavelet transforms Generalisation of the Hardy space andapplication to experimental studies Eur J Mech BFluids 12 107ndash134 (1993)
[226] C Daskaloyannis Generalized deformed oscillator and nonlinear algebras J Phys AMath Gen 24 L789ndashL794 (1991)
[227] C Daskaloyannis K Ypsilantis A deformed oscillator with Coulomb energy spectrumJ Phys A Math Gen 25 4157ndash4166 (1992)
[228] I Daubechies On the distributions corresponding to bounded operators in the Weylquantization Commun Math Phys 75 229ndash238 (1980)
[229] I Daubechies and A Grossmann An integral transform related to quantization I J MathPhys 21 2080ndash2090 (1980)
[230] I Daubechies A Grossmann J Reignier An integral transform related to quantization IIJ Math Phys 24 239ndash254 (1983)
[231] I Daubechies Orthonormal bases of compactly supported wavelets Commun Pure ApplMath 41 909ndash996 (1988)
[232] I Daubechies The wavelet transform time-frequency localisation and signal analysisIEEE Trans Inform Theory 36 961ndash1005 (1990)
[233] I Daubechies S Maes A nonlinear squeezing of the continuous wavelet transform basedon auditory nerve models in Wavelets in Medicine and Biology ed by A Aldroubi MUnser (CRC Press Boca Raton 1996) pp 527ndash546
[234] I Daubechies A Grossmann Y Meyer Painless nonorthogonal expansions J Math Phys27 1271ndash1283 (1986)
[235] ER Davies Introduction to texture analysis in Handbook of texture analysis ed by MMirmehdi X Xie J Suri (World Scientific Singapore 2008) pp 1ndash31
[236] R De Beer D van Ormondt FTAW Wajer S Cavassila D Graveron-Demilly S VanHuffel SVD-based modelling of medical NMR signals in SVD and Signal ProcessingIII Algorithms Architectures and Applications ed by M Moonen B De Moor (Elsevier(North-Holland) Amsterdam 1995) pp 467ndash474
[237] S De Biegravevre Coherent states over symplectic homogeneous spaces J Math Phys 301401ndash1407 (1989)
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[238] S De Biegravevre JA Gonzalez Semi-classical behaviour of the Weyl correspondence on thecircle in Group-Theoretical Methods in Physics (Proc Salamanca 1992) ed by M delOlmo M Santander J Mateos Guilarte (CIEMAT Madrid 1993) pp 343ndash346
[239] S De Biegravevre JA Gonzaacutelez Semiclassical behaviour of coherent states on the circle inQuantization and Coherent States Methods in Physics ed by A Odzijewicz et al (WorldScientific Singapore 1993)
[240] S De Biegravevre AE Gradechi Quantum mechanics and coherent states on the anti-de Sitterspace-time and their Poincareacute contraction Ann Inst H Poincareacute 57 403ndash428 (1992)
[241] J Deenen C Quesne Dynamical group of collective states I II III J Math Phys 23878ndash889 2004ndash2015 (1982)
[242] J Deenen C Quesne Dynamical group of collective states I II III J Math Phys 251638ndash1650 (1984)
[243] J Deenen C Quesne Partially coherent states of the real symplectic group J Math Phys25 2354ndash2366 (1984)
[244] J Deenen C Quesne Boson representations of the real symplectic group and theirapplication to the nuclear collective model J Math Phys 26 2705ndash2716 (1985)
[245] R Delbourgo Minimal uncertainty states for the rotation and allied groups J Phys AMath Gen 10 1837ndash1846 (1977)
[246] R Delbourgo J R Fox Maximum weight vectors possess minimal uncertainty J PhysA Math Gen 10 L233ndashL235 (1977)
[247] V Delouille J de Patoul J-F Hochedez L Jacques J-P Antoine Wavelet spectrumanalysis of EITSoHO images Solar Phys 228 301ndash321 (2005)
[248] N Delprat B Escudieacute P Guillemain R Kronland-Martinet P Tchamitchian B Tor-reacutesani Asymptotic wavelet and Gabor analysis Extraction of instantaneous frequenciesIEEE Trans Inform Theory 38 644ndash664 (1992)
[249] Th Deutsch L Genovese Wavelets for electronic structure calculations Collection SocFr Neut 12 33ndash76 (2011)
[250] B Dewitt Quantum theory of gravity I The canonical theory Phys Rev 160 1113ndash1148(1967)
[251] RH Dicke Coherence in spontaneous radiation processes Phys Rev 93 99ndash110 (1954)[252] AN Dinkelaker AL MacKinnon Wavelets intermittency and solar flare hard X-rays 1
Local intermittency measure in cascade and avalanche scenarios Solar Phys 282 471ndash481(2013)
[253] AN Dinkelaker AL MacKinnon Wavelets intermittency and solar flare hard X-rays 2LIM analysis of high time resolution BATSE data Solar Phys 282 483ndash501 (2013)
[254] MN Do M Vetterli Contourlets in Beyond Wavelets ed by GV Welland (AcademicSan Diego 2003) pp 83ndash105
[255] MN Do M Vetterli The contourlet transform An efficient directional multiresolutionimage representation IEEE Trans Image Process 14 2091ndash2106 (2005)
[256] VV Dodonov Nonclassical states in quantum optics A ldquosqueezedrdquo review of the first 75years J Opt B Quant Semiclass Opot 4 R1ndashR33 (2002)
[257] DL Donoho Nonlinear wavelet methods for recovery of signals densities and spectrafrom indirect and noisy data in Different Perspectives on Wavelets Proceedings ofSymposia in Applied Mathematics vol 38 ed by I Daubechies (American MathematicalSociety Providence RI 1993) pp 173ndash205
[258] DL Donoho Wedgelets Nearly minimax estimation of edges Ann Stat 27 859ndash897(1999)
[259] DL Donoho X Huo Beamlet pyramids A new form of multiresolution analysis suitedfor extracting lines curves and objects from very noisy image data in SPIE Proceedingsvol 5914 (SPIE Bellingham WA 2005) pp 1ndash12
References 557
[260] AH Dooley Contractions of Lie groups and applications to analysis in Topics in ModernHarmonic Analysis vol I (Istituto Nazionale di Alta Matematica Francesco Severi Roma1983) pp 483ndash515
[261] AH Dooley JW Rice Contractions of rotation groups and their representations MathProc Camb Phil Soc 94 509ndash517 (1983)
[262] AH Dooley JW Rice On contractions of semisimple Lie groups Trans Amer MathSoc 289 185ndash202 (1985)
[263] JR Driscoll DM Healy Computing Fourier transforms and convolutions on the 2-sphereAdv Appl Math 15 202ndash250 (1994)
[264] H Drissi F Regragui J-P Antoine M Bennouna Wavelet transform analysis of visualevoked potentials Some preliminary results ITBM-RBM 21 84ndash91 (2000)
[265] RJ Duffin AC Schaeffer A class of nonharmonic Fourier series Trans Amer MathSoc 72 341ndash366 (1952)
[266] M Duflo CC Moore On the regular representation of a nonunimodular locally compactgroup J Funct Anal 21 209ndash243 (1976)
[267] M Duval-Destin R Murenzi Spatio-temporal wavelets Application to the analysis ofmoving patterns in Progress in Wavelet Analysis and Applications (Proc Toulouse 1992)ed by Y Meyer S Roques (Ed Frontiegraveres Gif-sur-Yvette 1993) pp 399ndash408
[268] M Duval-Destin M-A Muschietti B Torreacutesani Continuous wavelet decompositionsmultiresolution and contrast analysis SIAM J Math Anal 24 739ndash755 (1993)
[269] SJL van Eindhoven JLH Meyers New orthogonality relations for the Hermitepolynomials and related Hilbert spaces J Math Anal Appl 146 89ndash98 (1990)
[270] M ElBaz R Fresneda J-P Gazeau Y Hassouni Coherent state quantization of para-grassmann algebras J Phys A Math Theor 43 385202 (2010) Corrigendum J PhysA Math Theor 45 (2012)
[271] A Elkharrat J-P Gazeau F Deacutenoyer Multiresolution of quasicrystal diffraction spectraActa Cryst A65 466ndash489 (2009)
[272] Q Fan Phase space analysis of the identity decompositions J Math Phys 34 3471ndash3477(1993)
[273] M Fanuel S Zonetti Affine quantization and the initial cosmological singularity Euro-phys Lett 101 10001 (2013)
[274] M Farge Wavelet transforms and their applications to turbulence Annu Rev Fluid Mech24 395ndash457 (1992)
[275] M Farge N Kevlahan V Perrier E Goirand Wavelets and turbulence Proc IEEE 84639ndash669 (1996)
[276] M Farge NK-R Kevlahan V Perrier K Schneider Turbulence analysis modellingand computing using wavelets in Wavelets in Physics Chap 4 ed by JC van den Berg(Cambridge University Press Cambridge 1999)
[277] HG Feichtinger Coherent frames and irregular sampling in Recent Advances in FourierAnalysis and Its applications ed by JS Byrnes JL Byrnes (Kluwer Dordrecht 1990)pp 427ndash440
[278] HG Feichtinger KH Groumlchenig Banach spaces related to integrable group representa-tions and their atomic decompositions I J Funct Anal 86 307ndash340 (1989)
[279] HG Feichtinger KH Groumlchenig Banach spaces related to integrable group representa-tions and their atomic decompositions II Mh Math 108 129ndash148 (1989)
[280] M Flensted-Jensen Discrete series for semisimple symmetric spaces Ann of Math 111253ndash311 (1980)
[281] K Flornes A Grossmann M Holschneider B Torreacutesani Wavelets on discrete fieldsAppl Comput Harmon Anal 1 137ndash146 (1994)
[282] V Fock Zur Theorie der Wasserstoffatoms Zs f Physik 98 145ndash54 (1936)[283] M Fornasier H Rauhut Continuous frames function spaces and the discretization
problem J Fourier Anal Appl 11 245ndash287 (2005)
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[284] W Freeden M Schreiner Orthogonal and non-orthogonal multiresolution analysis scalediscrete and exact fully discrete wavelet transform on the sphere Constr Approx 14 493ndash515 (1997)
[285] W Freeden U Windheuser Combined spherical harmonic and wavelet expansion mdash Afuture concept in Earthrsquos gravitational determination Appl Comput Harmon Anal 4 1ndash37 (1997)
[286] W Freeden T Maier S Zimmermann A survey on wavelet methods for (geo)applicationsRevista Mathematica Complutense 16 (2003) 277ndash310
[287] W Freeden M Schreiner Biorthogonal locally supported wavelets on the sphere based onzonal kernel functions J Fourier Anal Appl 13 693ndash709 (2007)
[288] WT Freeman EH Adelson The design and use of steerable filters IEEE Trans PatternAnal Machine Intell 13 891ndash906 (1991)
[289] L Freidel ER Livine U(N) coherent states for loop quantum gravity J Math Phys 52052502 (2011)
[290] J Froment S Mallat Arbitrary low bit rate image compression using wavelets in Progressin Wavelet Analysis and Applications (Proc Toulouse 1992) ed by Y Meyer S Roques(Ed Frontiegraveres Gif-sur-Yvette 1993) pp 413ndash418 and references therein
[291] L Freidel S Speziale Twisted geometries A geometric parameterisation of SU(2) phasespace Phys Rev D 82 084040 (2010)
[292] H Fuumlhr Wavelet frames and admissibility in higher dimensions J Math Phys 37 6353ndash6366 (1996)
[293] H Fuumlhr M Mayer Continuous wavelet transforms from semidirect products Cyclicrepresentations and Plancherel measure J Fourier Anal Appl 8 375ndash396 (2002)
[294] D Gabor Theory of communication J Inst Electr Engrg(London) 93 429ndash457 (1946)[295] J-P Gabardo D Han Frames associated with measurable spaces Adv Comput Math 18
127ndash147 (2003)[296] E Galapon Paulirsquos theorem and quantum canonical pairs The consistency of a bounded
self-adjoint time operator canonically conjugate to a Hamiltonian with non-empty pointspectrum Proc R Soc Lond A 458 451ndash472 (2002)
[297] PL Garciacutea de Leacuteon J-P Gazeau Coherent state quantization and phase operator PhysLett A 361 301ndash304 (2007)
[298] L Garciacutea de Leoacuten J-P Gazeau J Queacuteva The infinite well revisited Coherent states andquantization Phys Lett A 372 3597ndash3607 (2008)
[299] T Garidi J-P Gazeau E Huguet M Lachiegraveze Rey J Renaud Fuzzy spheres frominequivalent coherent states quantization J Phys A Math Theor 40 10225ndash10249 (2007)
[300] J-P Gazeau Four Euclidean conformal group in atomic calculations Exact analyticalexpressions for the bound-bound two-photon transition matrix elements in the H atomJ Math Phys 19 1041ndash1048 (1978)
[301] J-P Gazeau On the four Euclidean conformal group structure of the sturmian operatorLett Math Phys 3 285ndash292 (1979)
[302] J-P Gazeau Technique Sturmienne pour le spectre discret de lrsquoeacutequation de SchroumldingerJ Phys A Math Gen 13 3605ndash3617 (1980)
[303] J-P Gazeau Four Euclidean conformal group approach to the multiphoton processes in theH atom J Math Phys 23 156ndash164 (1982)
[304] J-P Gazeau A remarkable duality in one particle quantum mechanics between someconfining potentials and (R+Linfin
ε ) potentials Phys Lett 75A 159ndash163 (1980)[305] J-P Gazeau SL(2R)-coherent states and integrable systems in classical and quantum
physics in Quantization Coherent States and Complex Structures ed by J-P AntoineST Ali W Lisiecki IM Mladenov A Odzijewicz (Plenum Press New York and London1995) pp 147ndash158
[306] J-P Gazeau S Graffi Quantum harmonic oscillator A relativistic and statistical point ofview Boll Unione Mat Ital 11-A 815ndash839 (1997)
[307] J-P Gazeau V Hussin Poincareacute contraction of SU(11) Fock-Bargmann structure J PhysA Math Gen 25 1549ndash1573 (1992)
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[309] J-P Gazeau JR Klauder Coherent states for systems with discrete and continuousspectrum J Phys A Math Gen 32 123ndash132 (1999)
[310] J-P Gazeau P Monceau Generalized coherent states for arbitrary quantum systems inColloquium M Flato (Dijon Sept 99) vol II (Kluumlwer Dordrecht 2000) pp 131ndash144
[311] J-P Gazeau M Novello The question of mass in (Anti-) de Sitter space-times J Phys AMath Theor 41 304008 (2008)
[312] J-P Gazeau M del Olmo q-coherent states quantization of the harmonic oscillator AnnPhys (NY) 330 220ndash245 (2013) arXiv12071200 [quant-ph]
[313] J-P Gazeau J Patera Tau-wavelets of Haar J Phys A Math Gen 29 4549ndash4559 (1996)[314] J-P Gazeau W Piechocki Coherent states quantization of a particle in de Sitter space
J Phys A Math Gen 37 6977ndash6986 (2004)[315] J-P Gazeau J Renaud Lie algorithm for an interacting SU(11) elementary system and its
contraction Ann Phys (NY) 222 89ndash121 (1993)[316] J-P Gazeau J Renaud Relativistic harmonic oscillator and space curvature Phys Lett A
179 67ndash71 (1993)[317] J-P Gazeau V Spiridonov Toward discrete wavelets with irrational scaling factor J Math
plane J Phys A Math Theor 44 495201 (2011)[319] J-P Gazeau J Patera E Pelantovaacute Tau-wavelets in the plane J Math Phys 39 4201ndash
4212 (1998)[320] J-P Gazeau M Andrle C Burdiacutek R Krejcar Wavelet multiresolutions for the Fibonacci
chain J Phys A Math Gen 33 L47ndashL51 (2000)[321] J-P Gazeau M Andrle C Burdiacutek Bernuau spline wavelets and sturmian sequences
J Fourier Anal Appl 10 269ndash300 (2004)[322] J-P Gazeau F-X Josse-Michaux P Monceau Finite dimensional quantizations of the
(q p) plane new space and momentum inequalities Int J Modern Phys B 20 1778ndash1791 (2006)
[323] J-P Gazeau J Mourad J Queacuteva Fuzzy de Sitter space-times via coherent statesquantization in Proceedings of the XXVIth Colloquium on Group Theoretical Methodsin Physics New York 2006 ed by J Birman S Catto B Nicolescu (Canopus PublishingLimited London 2009)
[324] D Geller A Mayeli Continuous wavelets on compact manifolds Math Z 262 895ndash927(2009)
[325] D Geller A Mayeli Nearly tight frames and space-frequency analysis on compactmanifolds Math Z 263 235ndash264 (2009)
[326] L Genovese B Videau M Ospici Th Deutsch S Goedecker J-F Mhaut Daubechieswavelets for high performance electronic structure calculations The BigDFT project CR Mecanique 339 149ndash164 (2011)
[327] G Gentili C Stoppato Power series and analyticity over the quaternions Math Ann 352113ndash131 (2012)
[328] G Gentili DC Struppa A new theory of regular functions of a quaternionic variable AdvMath 216 279ndash301 (2007)
[329] C Geyer K Daniilidis Catadioptric projective geometry Int J Comput Vision 45 223ndash243 (2001)
[330] R Gilmore Geometry of symmetrized states Ann Phys (NY) 74 391ndash463 (1972)[331] R Gilmore On properties of coherent states Rev Mex Fis 23 143ndash187 (1974)[332] J Ginibre Statistical ensembles of complex quaternion and real matrices J Math Phys
6 440ndash449 (1965)[333] RJ Glauber The quantum theory of optical coherence Phys Rev 130 2529ndash2539 (1963)
560 References
[334] RJ Glauber Coherent and incoherent states of radiation field Phys Rev 131 2766ndash2788(1963)
[335] J Glimm Locally compact transformation groups Trans Amer Math Soc 101 124ndash138(1961)
[336] R Godement Sur les relations drsquoorthogonaliteacute de V Bargmann C R Acad Sci Paris 255521ndash523 657ndash659 (1947)
[337] C Gonnet B Torreacutesani Local frequency analysis with two-dimensional wavelet trans-form Signal Proc 37 389ndash404 (1994)
[338] JA Gonzalez MA del Olmo Coherent states on the circle J Phys A Math Gen 318841ndash8857 (1998)
[339] XGonze B Amadon et al ABINIT First-principles approach to material and nanosystemproperties Computer Physics Comm 180 2582ndash2615 (2009)
[340] KM Gograverski E Hivon AJ Banday BD Wandelt FK Hansen M Reinecke MBartelmann HEALPix A framework for high-resolution discretization and fast analysisof data distributed on the sphere Astrophys J 622 759ndash771 (2005)
[341] P Goupillaud A Grossmann J Morlet Cycle-octave and related transforms in seismicsignal analysis Geoexploration 23 85ndash102 (1984)
[342] KH Groumlchenig A new approach to irregular sampling of band-limited functions in RecentAdvances in Fourier Analysis and Its applications ed by JS Byrnes JL Byrnes (KluwerDordrecht 1990) pp 251ndash260
[343] KH Groumlchenig Gabor analysis over LCA groups in Gabor Analysis and Algorithms ndashTheory and Applications ed by HG Feichtinger T Strohmer (Birkhaumluser Boston-Basel-Berlin 1998) pp 211ndash231
[344] HJ Groenewold On the principles of elementary quantum mechanics Physica 12 405ndash460 (1946)
[345] P Grohs Continuous shearlet tight frames J Fourier Anal Appl 17 506ndash518 (2011)[346] P Grohs G Kutyniok Parabolic molecules preprint TU Berlin (2012)[347] M Grosser A note on distribution spaces on manifolds Novi Sad J Math 38 121ndash128
(2008)[348] A Grossmann Parity operator and quantization of δ -functions Commun Math Phys 48
191ndash194 (1976)[349] A Grossmann J Morlet Decomposition of Hardy functions into square integrable
wavelets of constant shape SIAM J Math Anal 15 723ndash736 (1984)[350] A Grossmann J Morlet Decomposition of functions into wavelets of constant shape and
related transforms in Mathematics + Physics Lectures on recent results I ed by L Streit(World Scientific Singapore 1985) pp 135ndash166
[351] A Grossmann J Morlet T Paul Integral transforms associated to square integrablerepresentations I General results J Math Phys 26 2473ndash2479 (1985)
[352] A Grossmann J Morlet T Paul Integral transforms associated to square integrablerepresentations II Examples Ann Inst H Poincareacute 45 293ndash309 (1986)
[353] A Grossmann R Kronland-Martinet J Morlet Reading and understanding the contin-uous wavelet transform in Wavelets Time-Frequency Methods and Phase Space (ProcMarseille 1987) ed by J-M Combes A Grossmann P Tchamitchian 2nd edn (SpringerBerlin 1990) pp 2ndash20
[354] P Guillemain R Kronland-Martinet B Martens Estimation of spectral lines with helpof the wavelet transform Application in NMR spectroscopy in Wavelets and Applications(Proc Marseille 1989) ed by Y Meyer (Masson and Springer Paris and Berlin 1991) pp38ndash60
[355] H de Guise M Bertola Coherent state realizations of su(n+ 1) on the n-torus J MathPhys 43 3425ndash3444 (2002)
[356] K Guo D Labate Representation of Fourier Integral Operators using shearlets J FourierAnal Appl 14 327ndash371 (2008)
References 561
[357] K Guo G Kutyniok D Labate Sparse multidimensional representations usinganisotropic dilation and shear operators in Wavelets and Spines (Athens GA 2005)(Nashboro Press Nashville TN 2006) pp 189ndash201
[358] K Guo D Labate W-Q Lim G Weiss E Wilson Wavelets with composite dilationsand their MRA properties Appl Comput Harmon Anal 20 202ndash236 (2006)
[359] EA Gutkin Overcomplete subspace systems and operator symbols Funct Anal Appl 9260ndash261 (1975)
[360] G Gyoumlrgyi Integration of the dynamical symmetry groups for the 1r potential Acta PhysAcad Sci Hung 27 435ndash439 (1969)
[361] BC Hall The Segal-Bargmann ldquoCoherent Staterdquo transform for compact Lie groups JFunct Analysis 122 103ndash151 (1994)
[362] B Hall JJ Mitchell Coherent states on spheres J Math Phys 43 1211ndash1236 (2002)[363] DK Hammond P Vandergheynst R Gribonval Wavelets on graphs via spectral theory
Appl Comput Harmon Anal 30 129ndash150 (2011)[364] Y Hassouni EMF Curado MA Rego-Monteiro Construction of coherent states for
physical algebraic system Phys Rev A 71 022104 (2005)[365] J He H Liu Admissible wavelets associated with the affine automorphism group of the
Siegel upper half-plane J Math Anal Appl 208 58ndash70 (1997)[366] J He H Liu Admissible wavelets associated with the classical domain of type one
Approx Appl 14 (1998) 89ndash105[367] J He L Peng Wavelet transform on the symmetric matrix space preprint Beijing (1997)
(unpublished)[368] J He L Peng Admissible wavelets on the unit disk Complex Variables 35 109ndash119
(1998)[369] DM Healy Jr FE Schroeck Jr On informational completeness of covariant localization
observables and Wigner coefficients J Math Phys 36 453ndash507 (1995)[370] C Heil D Walnut Continuous and discrete wavelet transforms SIAM Review 31 628ndash
666 (1989)[371] K Hepp EH Lieb On the superradiant phase transition for molecules in a quantized
radiation field The Dicke maser model Ann Phys (NY) 76 360ndash404 (1973)[372] K Hepp EH Lieb Equilibrium statistical mechanics of matter interacting with the
quantized radiation field Phys Rev A 8 2517ndash2525 (1973)[373] JA Hogan JD Lakey Extensions of the Heisenberg group by dilations and frames Appl
Comput Harmon Anal 2 174ndash199 (1995)[374] AL Hohoueacuteto K Thirulogasanthar ST Ali J-P Antoine Coherent states lattices and
square integrability of representations J Phys A Math Gen36 11817ndash11835 (2003)[375] M Holschneider On the wavelet transformation of fractal objects J Stat Phys 50 963ndash
993 (1988)[376] M Holschneider Wavelet analysis on the circle J Math Phys 31 39ndash44 (1990)[377] M Holschneider Inverse Radon transforms through inverse wavelet transforms Inv Probl
7 853ndash861 (1991)[378] M Holschneider Localization properties of wavelet transforms J Math Phys 34 3227ndash
3244 (1993)[379] M Holschneider General inversion formulas for wavelet transforms J Math Phys 34
4190ndash4198 (1993)[380] M Holschneider Wavelet analysis over abelian groups Applied Comput Harmon Anal
2 52ndash60 (1995)[381] M Holschneider Continuous wavelet transforms on the sphere J Math Phys 37 4156ndash
4165 (1996)[382] M Holschneider I Iglewska-Nowak Poisson wavelets on the sphere J Fourier Anal
Appl 13 405ndash419 (2007)
562 References
[383] M Holschneider R Kronland-Martinet J Morlet P Tchamitchian A real-time algorithmfor signal analysis with the help of wavelet transform in Wavelets Time-FrequencyMethods and Phase Space (Proc Marseille 1987) ed by J-M Combes A Grossmann PTchamitchian 2nd edn (Springer Berlin 1990) pp 286ndash297
[384] M Holschneider P Tchamitchian Pointwise analysis of Riemannrsquos ldquonondifferentiablerdquofunction Invent Math 105 157ndash175 (1991)
[385] GR Honarasa MK Tavassoly M Hatami R Roknizadeh Nonclassical properties ofcoherent states and excited coherent states for continuous spectra J Phys A Math Theor44 085303 (2011)
[386] M Hongoh Coherent states associated with the continuous spectrum of noncompactgroups J Math Phys 18 2081ndash2085 (1977)
[387] A Horzela FH Szafraniec A measure free approach to coherent states J Phys A MathGen 45 244018 (2012)
[388] W-L Hwang S Mallat Characterization of self-similar multifractals with waveletmaxima Appl Comput Harmon Anal 1 316ndash328 (1994)
[389] W-L Hwang C-S Lu P-C Chung Shape from texture Estimation of planar surfaceorientation through the ridge surfaces of continuous wavelet transform IEEE Trans ImageProc 7 773ndash780 (1998)
[390] I Iglewska-Nowak M Holschneider Frames of Poisson wavelets on the sphere ApplComput Harmon Anal 28 227ndash248 (2010)
[391] E Inoumlnuuml EP Wigner On the contraction of groups and their representations Proc NatAcad Sci U S 39 510ndash524 (1953)
[392] S Iqbal F Saif Generalized coherent states and their statistical characteristics in power-law potentials J Math Phys 52 082105 (2011)
[393] CJ Isham JR Klauder Coherent states for n-dimensional Euclidean groups E(n) andtheir application J MathPhys 32 607ndash620 (1991)
[394] L Jacques J-P Antoine Multiselective pyramidal decomposition of images Wavelets withadaptive angular selectivity Int J Wavelets Multires Inform Proc 5 785ndash814 (2007)
[395] L Jacques L Duval C Chaux G Peyreacute A panorama on multiscale geometric rep-resentations intertwining spatial directional and frequency selectivity Signal Proc 912699ndash2730 (2011)
[396] HR Jalali M K Tavassoly On the ladder operators and nonclassicality of generalizedcoherent state associated with a particle in an infinite square well preprint (2013)arXiv13034100v1 [quant-ph]
[397] C Johnston On the pseudo-dilation representations of Flornes Grossmann Holschneiderand Torreacutesani Appl Comput Harmon Anal 3 377ndash385 (1997)
[398] G Kaiser Phase-space approach to relativistic quantum mechanics I Coherent staterepresentation for massive scalar particles J MathPhys 18 952ndash959 (1977)
[399] G Kaiser Phase-space approach to relativistic quantum mechanics II Geometrical aspectsJ MathPhys 19 502ndash507 (1978)
[400] C Kalisa B Torreacutesani N-dimensional affine Weyl-Heisenberg wavelets Ann Inst HPoincareacute 59 201ndash236 (1993)
[401] W Kaminski J Lewandowski T Pawłowski Quantum constraints Dirac observables andevolution group averaging versus the Schroumldinger picture in LQC Class Quant Grav 26245016 (2009)
[402] MR Karim ST Ali A relativistic windowed Fourier transform preprint ConcordiaUniversity Montreacuteal (1997) (unpublished)
[403] M R Karim ST Ali M Bodruzzaman A relativistic windowed Fourier transform inProceedings of IEEE SoutheastCon 2000 Nashville Tennessee pp 253ndash260 (2000)
[404] T Kawazoe Wavelet transforms associated to a principal series representation of semisim-ple Lie groups I II Proc Japan Acad Ser A ndash Math Sci 71 154ndash157 158ndash160 (1995)
[405] T Kawazoe Wavelet transform associated to an induced representation of SL(n+ 2R)Ann Inst H Poincareacute 65 1ndash13 (1996)
References 563
[406] P Kittipoom G Kutyniok W-Q Lim Irregular shearlet frames Geometry and approxi-mation properties J Fourier Anal Appl 17 604ndash639 (2011)
[407] P Kittipoom G Kutyniok W-Q Lim Construction of compactly supported shearletframes Constr Approx 35 21ndash72 (2012)
[408] J Kiukas P Lahti K Ylinenc Phase space quantization and the operator moment problemJ Math Phys 47 072104 (2006)
[409] JR Klauder Continuous-representation theory I Postulates of continuous-representationtheory J Math Phys 4 1055ndash1058 (1963)
[410] JR Klauder Continuous-representation theory II Generalized relation between quantumand classical dynamics J Math Phys 4 1058ndash1073 (1963)
[411] JR Klauder Path integrals for affine variables in Functional Integration Theory andApplications ed by J-P Antoine E Tirapegui (Plenum Press New York and London1980) pp 101ndash119
[412] JR Klauder Are coherent states the natural language of quantum mechanics inFundamental Aspects of Quantum Theory ed by V Gorini A Frigerio NATO ASI Seriesvol B 144 (Plenum Press New York 1986) pp 1ndash12
[413] JR Klauder Quantization without quantization Ann Phys (NY) 237 147ndash160 (1995)[414] JR Klauder Coherent states for the hydrogen atom J Phys A Math Gen 29 L293ndash
L296 (1996)[415] JR Klauder An affinity for affine quantum gravity Proc Steklov Inst Math 272 169ndash176
(2011) and references therein[416] JR Klauder RF Streater A wavelet transform for the Poincareacute group J Math Phys 32
1609ndash1611 (1991)[417] JR Klauder RF Streater Wavelets and the Poincareacute half-plane J Math Phys 35 471ndash
478 (1994)[418] JR Klauder K Penson J-M Sixdeniers Constructing coherent states through solutions
of Stieltjes and Hausdorff moment problems Phys Rev A 64 013817 (2001)[419] A Kleppner RL Lipsman The Plancherel formula for group extensions Ann Ec Norm
Sup 5 459ndash516 (1972)[420] AB Klimov C Muntildeoz Coherent isotropic and squeezed states in a N-qubit system Phys
Scr 87 038110 (2013)[421] A Klyashko Dynamical symmetry approach to entanglement in Physics and Theoretical
Computer Science From Numbers and Languages to (Quantum) Cryptography - NATOSecurity through Science Series D - Information and Communication Security vol 7 edby J-P Gazeau J Nesetril B Rovan (IOS Press Washington DC 2007) pp 25ndash54
[422] S Kobayashi Irreducibility of certain unitary representations J Math Soc Japan 20 638ndash642 (1968)
[423] K Kowalski J Rembielinski LC Papaloucas Coherent states for a quantum particle ona circle J Phys A Math Gen 29 4149ndash4167 (1996)
[424] K Kowalski J Rembielinski Quantum mechanics on a sphere and coherent states J PhysA Math Gen 33 6035ndash6048 (2000)
[425] K Kowalski J Rembielinski The Bargmann representation for the quantum mechanicson a sphere J Math Phys 42 4138ndash4147 (2001)
[426] C Kristjansen J Plefka GW Semenoff M Staudacher A new double-scaling limit ofN = 4 super-Yang-Mills theory and pp-wave strings Nuclear Phys B 643 3ndash30 (2002)
[427] M Kulesh M Holschneider MS Diallo Geophysical wavelet library Applications ofthe continuous wavelet transform to the polarization and dispersion analysis of signalsComput Geosci 34 1732ndash1752 (2008)
[428] R Kunze On the Frobenius reciprocity theorem for square integrable representationsPacific J Math 53 465ndash471 (1974)
[429] Y Kuroda A Wada T Yamazaki K Nagayama Postacquisition data processing methodfor suppression of the solvent signal I J Magn Reson 84 604ndash610 (1989)
564 References
[430] Y Kuroda A Wada T Yamazaki K Nagayama Postacquisition data processing methodfor suppression of the solvent signal II The weighted first derivative J Magn Reson 88141ndash145 (1990)
[431] G Kutyniok D Labate Resolution of the wavefront set using continuous shearlets TransAmer Math Soc 361 2719ndash2754 (2009)
[432] G Kutyniok W-Q Lim Compactly supported shearlets are optimally sparse J ApproxTheory 163 1564ndash1589 (2011)
[433] D Labate W-Q Lim G Kutyniok G Weiss Sparse multidimensional representationusing shearlets in Wavelets XI (San Diego CA 2005) ed by M Papadakis A Laine MUnser SPIE Proceedings vol 5914 (SPIE Bellingham WA 2005) pp 254ndash262
[434] P Lahti J-P Pellonpaumlauml Continuous variable tomographic measurements Phys Lett A373 3435ndash3438 (2009)
[435] Lambertrsquos projection see WikipediahttpenwikipediaorgwikiLambert_azimuthal_equal-area_projection
[436] J-P Leduc F Mujica R Murenzi MJT Smith Missile-tracking algorithm using target-adapted spatio-temporal wavelets in Automatic Object Recognition VII SPIE Proceedingsvol 5914 (SPIE Bellingham WA 1997) pp 400ndash411
[437] J-P Leduc F Mujica R Murenzi MJT Smith Spatio-temporal wavelet transforms formotion tracking in IEEE ICASSP 1997 vol 4 (1997) pp 3013ndash3016
[438] J-P Leduc F Mujica R Murenzi MJT Smith Spatio-temporal continuous waveletsapplied to missile warhead detection and tracking in SPIE VCIP rsquo97 vol 3024 ed byJ Biemond EJ Delp (1997) pp 787ndash798
[439] B Leistedt JD McEwen Exact wavelets on the ball IEEE Trans Signal Proc 60 1564ndash1589 (2012)
[440] PG Lemarieacute Y Meyer Ondelettes et bases hilbertiennes Rev Math Iberoamer 2 1ndash18(1986)
[441] C Lemke A Schuck Jr J-P Antoine D Sima Metabolite-sensitive analysis of magneticresonance spectroscopic signals using the continuous wavelet transform Meas SciTechnol 22 (2011) Art 114013
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[443] J-M Leacutevy-Leblond Galilei group and Galilean invariance in Group Theory and ItsApplications vol II ed by EM Loebl (Academic New York 1971) pp 221ndash299
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[446] G Lindblad B Nagel Continuous bases for unitary irreducible representations of SU(11)Ann Inst H Poincareacute 13 27ndash56 (1970)
[447] W Lisiecki Kaumlhler coherent states orbits for representations of semisimple Lie groupsAnn Inst H Poincareacute 53 857ndash890 (1990)
[448] A Lisowska Moment-based fast wedgelet transform J Math Imaging Vis 39 180ndash192(2011)
[449] H Liu L Peng Admissible wavelets associated with the Heisenberg group Pacific JMath 180 101ndash123 (1997)
[450] E Livine S Speziale Physical boundary state for the quantum tetrahedron Class QuantGrav 25 085003 (2008)
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[554] H Scutaru Coherent states and induced representations Lett Math Phys 2 101ndash107(1977)
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R61ndashR75 (2000)[559] E Slezak A Bijaoui G Mars Identification of structures from galaxy counts Use of the
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Geometric Methods in Physics XXXI Workshop 2012 (Trends in Mathematics ed byP Kielanowski et al Birkhaumluser Verlag Basel 2013) pp 47ndash63
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[579] T Thiemann Gauge field theory coherent states (GCS) 1 General properties Class QuantGrav 18 2025ndash2064 (2001)
[580] T Thiemann O Winkler Gauge field theory coherent states (GCS) 2 Peakednessproperties Class Quant Grav 18 2561ndash2636 (2001)
[581] T Thiemann O Winkler Gauge field theory coherent states (GCS) 3 Ehrenfest theoremsClass Quant Grav 18 4629ndash4682 (2001)
[582] T Thiemann O Winkler Gauge field theory coherent states (GCS) 4 Infinite tensorproduct and thermodynamical limit Class Quant Grav 18 4997ndash5054 (2001)
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simulation of an impact test using wavelets analytical and finite element models Int JSolids Struct 38 5481ndash5508 (2001)
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Recogn Artif Intell 26 1255011 (2012)[601] I Weinreich A construction of C1-wavelets on the two-dimensional sphere Appl Comput
Harmon Anal 10 1ndash26 (2001)[602] H Weyl Quantenmechanik und Gruppentheorie Z Phys 46 1ndash46 (1927)
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[610] K Woacutedkiewicz On the quantum mechanics of squeezed states J Modern Optics 34 941ndash948(1987)
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[612] JA Yeazell CR Stroud Jr Observation of fractional revivals in the evolution of aRydberg atomic wave packet Phys Rev A 43 5153ndash5156 (1991)
[613] HP Yuen Two-photon coherent states of the radiation field Phys Rev A 13 2226ndash2243(1976)
[614] J Zak Balian-Low theorem for Landau levels Phys Rev Lett 79 533ndash536 (1997)[615] J Zak Orthonormal sets of localized functions for a Landau level J Math Phys 39 4195ndash
4200 (1998) and references quoted there[616] AA Zakharova On the properties of generalized frames Math Notes 83 190ndash200 (2008)[617] W-M Zhang DH Feng R Gilmore Coherent states Theory and some applications Rev
Mod Phys 26 867ndash927 (1990)[618] I Zlatev W-M Zhang DH Feng Possibility that Schroumldingerrsquos conjecture for the
hydrogen atom coherent states is not attainable Phys Rev A 50 R1973ndashR1975 (1994)[619] WH Zurek Decoherence einselection and the quantum origins of the classical Rev Mod
Phys 75 715ndash775 (2003)[620] WH Zurek S Habib JP Paz Coherent states via decoherence Phys Rev Lett 70 1187ndash
1190 (1993)[621] K Zyczkowski Squeezed states in a quantum chaotic system J Phys A Math Theor 22
of SU(11) 81 296 297HilbertClowast-modules 164holomorphic 140nonholomorphic 151nonlinear 146of affine Galilei group 505of affine Poincareacute group 509of affine Weyl-Heisenberg group GaWH
497of compact semisimple Lie groups 174of Euclidean group E(n) 266of Galilei group G (11) 290of isochronous Galilei group 237of non-semisimple Lie groups 179of noncompact semisimple Lie groups 177of Poincareacute group Puarr
+(11) 283massless case 288
of Poincareacute group Puarr+(13) 279
of Schroumldinger group 508quasi-coherent states 186quaternionic 164
ST Ali et al Coherent States Wavelets and Their Generalizations Theoreticaland Mathematical Physics DOI 101007978-1-4614-8535-3copy Springer Science+Business Media New York 2014
573
574 Index
coherent states (CS) (cont)spin or SU(2) 175square integrable covariant 166 180 264vector (VCS) 73 108 112 170weighted 184 523
of affine Weyl-Heisenberg group GaWH497
of Poincareacute group Puarr+(11) 284
cohomology group 393 403coboundaries 403cochains 402cocycle 403
algebraic 387Cauchy 418Cauchy-Paul 354 419 425conical 418difference 417 462directional 416 440kinematical 499local 488metabolite-based 355 374minimal uncertainty 425multiselective 440on a graph 493on the sphere S
2 458on the sphere S
n 479on the torus T2 481steerable 439von Mises 440
wedgelet transform 455Wigner function 322Wigner-Ville transform 349Windowed Fourier or Gabor transform 349
ZZak transform 518
References
A Books and Theses
B Articles
Index
References 551
[113] P Balazs DT Stoeva J-P Antoine Classification of general sequences by frame-relatedoperators Sampling Theory Signal Image Proc (STSIP) 10 151ndash170 (2011)
[114] P Balazs D Bayer A Rahimi Multipliers for continuous frames in Hilbert spaces JPhys A Math Gen 45 244023 (2012)
[115] P Baldi G Kerkyacharian D Marinucci D Picard High frequency asymptotics forwavelet-based tests for Gaussianity and isotropy on the torus J Multivar Anal 99 606ndash636 (2008)
[116] P Baldi G Kerkyacharian D Marinucci D Picard Asymptotics for spherical needletsAnn of Stat 37 1150ndash1171 (2009)
[117] MC Baldiotti J-P Gazeau DM Gitman Coherent states of a particle in magnetic fieldand Stieltjes moment problem Phys Lett A 373 1916ndash1920 (2009) Erratum Phys LettA 373 2600 (2009)
[118] MC Baldiotti J-P Gazeau DM Gitman Semiclassical and quantum description ofmotion on the noncommutative plane Phys Lett A 373 3937ndash3943 (2009)
[119] R Balian Un principe drsquoincertitude fort en theacuteorie du signal ou en meacutecanique quantiqueCR Acad Sci(Paris) 292 1357ndash1362 (1981)
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[121] D Barache S De Biegravevre J-P Gazeau Affine symmetry semigroups for quasicrystalsEurophys Lett 25 435ndash440 (1994)
[122] D Barache J-P Antoine J-M Dereppe The continuous wavelet transform a tool for NMRspectroscopy J Magn Reson 128 1ndash11 (1997)
[123] V Bargmann On a Hilbert space of analytic functions and an associated integral transformPart I Commun Pure Appl Math 14 187ndash214 (1961)
[124] V Bargmann On a Hilbert space of analytic functions and an associated integral transformPart II A family of related function spaces Application to distribution theory CommunPure Appl Math 20 1ndash101 (1967)
[125] V Bargmann P Butera L Girardello JR Klauder On the completeness of coherentstates Reports Math Phys 2 221ndash228 (1971)
[126] AO Barut L Girardello New ldquocoherentrdquo states associated with non compact groupsCommun Math Phys 21 41ndash55 (1971)
[127] AO Barut H Kleinert Transition probabilities of the hydrogen atom from noncompactdynamical groups Phys Rev 156 1541ndash1545 (1967)
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[129] G Battle Wavelets A renormalization group point of view in Wavelets and TheirApplications ed by MB Ruskai G Beylkin R Coifman I Daubechies S Mallat YMeyer L Raphael (Jones and Bartlett Boston 1992) pp 323ndash349
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[131] J Ben Geloun J R Klauder Ladder operators and coherent states for continuous spectraJ Phys A Math Theor 42 375209 (2009)
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[133] JJ Benedetto TD Andrews Intrinsic wavelet and frame applications in IndependentComponent Analyses Wavelets Neural Networks Biosystems and Nanoengineering IXed by H Szu L Dai SPIE Proceedings vol 8058 (SPIE Bellingham WA 2011) p805802
[134] JJ Benedetto A Teolis A wavelet auditory model and data compression Appl ComputHarmon Anal 1 3ndash28 (1993)
[135] FA Berezin Quantization Math USSR Izvestija 8 1109ndash1165 (1974)[136] FA Berezin General concept of quantization Commun Math Phys 40 153ndash174 (1975)[137] H Bergeron From classical to quantum mechanics How to translate physical ideas into
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[141] H Bergeron J-P Gazeau P Siegl A Youssef Semi-classical behavior of Poumlschl-Tellercoherent states Eur Phys Lett 92 60003 (2010)
[142] H Bergeron P Siegl A Youssef New SUSYQM coherent states for Poumlschl-Tellerpotentials A detailed mathematical analysis J Phys A Math Theor 45 244028 (2012)
[143] H Bergeron J-P Gazeau A Youssef Are the Weyl and coherent state descriptionsphysically equivalent Phys Lett A 377 598ndash605 (2013)
[144] H Bergeron A Dapor J-P Gazeau P Małkiewicz Wavelet quantum cosmology preprint(2013) arXiv13050653 [gr-qc]
[145] S Bergman Uumlber die Kernfunktion eines Bereiches und ihr Verhalten am Rande I ReineAngw Math 169 1ndash42 (1933)
[146] D Bernier KF Taylor Wavelets from square-integrable representations SIAM J MathAnal 27 594ndash608 (1996)
[147] G Bernuau Wavelet bases associated to a self-similar quasicrystal J Math Phys 394213ndash4225 (1998)
[148] A Bertrand Deacuteveloppements en base de Pisot et reacutepartition modulo 1 C R Acad SciParis 285 419ndash421 (1977)
[149] J Bertrand P Bertrand Classification of affine Wigner functions via an extendedcovariance principle in Group Theoretical Methods in Physics (Proc Sainte-Adegravele 1988)ed by Y Saint-Aubin L Vinet (World Scientific Singapore 1989) pp 1380ndash1383
[150] Z Białynicka-Birula I Białynicki-Birula Space-time description of squeezing J OptSoc Am B4 1621ndash1626 (1987)
[151] E Bianchi E Magliaro C Perini Coherent spin-networks Phys Rev D 82 024012(2010)
[152] S Biskri J-P Antoine B Inhester F Mekideche Extraction of Solar coronal magneticloops with the 2-D Morlet wavelet transform Solar Phys 262 373ndash385 (2010)
[153] R Bluhm VA Kostelecky JA Porter The evolution and revival structure of localizedquantum wave packets Am J Phys 64 944ndash953 (1996)
[154] I Bogdanova P Vandergheynst J-P Antoine L Jacques M Morvidone Stereographicwavelet frames on the sphere Appl Comput Harmon Anal 19 223ndash252 (2005)
[155] I Bogdanova X Bresson J-P Thiran P Vandergheynst Scale space analysis and activecontours for omnidirectional images IEEE Trans Image Process 16 1888ndash1901 (2007)
[156] I Bogdanova P Vandergheynst J-P Gazeau Continuous wavelet transform on thehyperboloid Appl Comput Harmon Anal 23 (2007) 286ndash306 (2007)
[157] P Boggiatto E Cordero Anti-Wick quantization of tempered distributions in Progress inAnalysis Berlin (2001) vol I II (World Sci Publ River Edge NJ 2003) pp 655ndash662
[158] P Boggiatto E Cordero K Groumlchenig Generalized Anti-Wick operators with symbols indistributional Sobolev spaces Int Equ Oper Theory 48 427ndash442 (2004)
[159] A Boumlhm The Rigged Hilbert Space in quantum mechanics in Lectures in TheoreticalPhysics vol IX A ed by WA Brittin et al (Gordon amp Breach New York 1967) pp255ndash315
[160] G Bohnkeacute Treillis drsquoondelettes associeacutes aux groupes de Lorentz Ann Inst H Poincareacute54 245ndash259 (1991)
[161] WR Bomstad JR Klauder Linearized quantum gravity using the projection operatorformalism Class Quantum Grav 23 5961ndash5981 (2006)
[162] VV Borzov Orthogonal polynomials and generalized oscillator algebras Int TransformSpec Funct 12 115ndash138 (2001)
[163] VV Borzov EV Damaskinsky Generalized coherent states for classical orthogonalpolynomials Day on Diffraction (2002) arXivmathQA0209181v1 (SPb 2002)
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[165] A Bouzouina S De Biegravevre Equipartition of the eigenfunctions of quantized ergodic mapson the torus Commun Math Phys 178 83ndash105 (1996)
[166] P Brault J-P Antoine A spatio-temporal Gaussian-Conical wavelet with high apertureselectivity for motion and speed analysis Appl Comput Harmon Anal 34 148ndash161(2012)
[167] A Briguet S Cavassila D Graveron-Demilly Suppression of huge signals using theCadzow enhancement procedure The NMR Newslett 440 26 (1995)
[168] CM Brislawn Fingerprints go digital Notices Amer Math Soc 42 1278ndash1283 (1995)[169] CM Brislawn On the group-theoretic structure of lifted filter banks in Excursions in
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[170] F Bruhat Sur les repreacutesentations induites des groupes de Lie Bull Soc Math France 8497ndash205 (1956)
[171] T Buumllow Multiscale image processing on the sphere in DAGM-Symposium (2002) pp609ndash617
[172] C Burdik C Frougny J-P Gazeau R Krejcar Beta-integers as natural counting systemsfor quasicrystals J Phys A Math Gen 31 6449ndash6472 (1998)
[173] KE Cahill Coherent-state representations for the photon density Phys Rev 138 B1566ndash1576 (1965)
[174] KE Cahill R Glauber Density operators and quasiprobability distributions Phys Rev177 1882ndash1902 (1969)
[175] KE Cahill R Glauber Ordered expansions in boson amplitude operators Phys Rev 1771857ndash1881 (1969)
[176] AR Calderbank I Daubechies W Sweldens BL Yeo Wavelets that map integers tointegers Appl Comput Harmon Anal 5 332ndash369 (1998)
[177] M Calixto J Guerrero Wavelet transform on the circle and the real line A unified group-theoretical treatment Appl Comput Harmon Anal 21 204ndash229 (2006)
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[180] EJ Candegraves Harmonic analysis of neural networks Appl Comput Harmon Anal 6 197ndash218 (1999)
[181] EJ Candegraves Ridgelets and the representation of mutilated Sobolev functions SIAM JMath Anal 33 347ndash368 (2001)
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[183] EJ Candegraves L Demanet The curvelet representation of wave propagators is optimallysparse Commun Pure Appl Math 58 1472ndash1528 (2004)
[184] EJ Candegraves L Demanet The curvelet representation of wave propagators is optimallysparse Commun Pure Appl Math 58 1472ndash1528 (2005)
[185] EJ Candegraves DL Donoho Curvelets ndash A surprisingly effective nonadaptive representationfor objects with edges in Curves and Surfaces ed by LL Schumaker et al (VanderbiltUniversity Press Nashville TN 1999)
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[191] EJ Candegraves F Guo New multiscale transforms minimum total variationsynthesisApplications to edge-preserving image reconstruction Signal Proc 82 1519ndash1543 (2002)
[192] EJ Candegraves L Demanet D Donoho L Ying Fast discrete curvelet transforms MultiscaleModel Simul 5 861ndash899 (2006)
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[195] P Carruthers MM Nieto Phase and angle variables in quantum mechanics Rev ModPhys 40 411ndash440 (1968)
[196] PG Casazza G Kutyniok Frames of subspaces in Wavelets Frames and Operator The-ory Contemporary Mathematics vol 345 (American Mathematical Society ProvidenceRI 2004) pp 87ndash113
[197] PG Casazza D Han DR Larson Frames for Banach spaces Contemp Math 247 149ndash182 (1999)
[198] P Casazza O Christensen S Li A Lindner Riesz-Fischer sequences and lower framebounds Z Anal Anwend 21 305ndash314 (2002)
[199] PG Casazza G Kutyniok S Li Fusion frames and distributed processing ApplComputHarmon Anal 25 114ndash132 (2008)
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Systems Control Coding Computer Vision Progress in Systems and Control Theory 25393ndash417 (1999)
[208] L Cohen General phase-space distribution functions J Math Phys 7 781ndash786 (1966)[209] A Cohen I Daubechies J-C Feauveau Biorthogonal bases of compactly supported
wavelets Commun Pure Appl Math 45 485ndash560 (1992)[210] R Coifman Y Meyer MV Wickerhauser Wavelet analysis and signal processing
in Wavelets and Their Applications ed by MB Ruskai G Beylkin R CoifmanI Daubechies S Mallat Y Meyer L Raphael (Jones and Bartlett Boston 1992)pp 153ndash178
[211] R Coifman Y Meyer MV Wickerhauser Entropy-based algorithms for best basisselection IEEE Trans Inform Theory 38 713ndash718 (1992)
[212] R Coquereaux A Jadczyk Conformal theories curved spaces relativistic wavelets andthe geometry of complex domains Rev Math Phys 2 1ndash44 (1990)
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[215] N Cotfas J-P Gazeau K Goacuterska Complex and real Hermite polynomials and relatedquantizations J Phys A Math Theor 43 305304 (2010)
[216] N Cotfas J-P Gazeau A Vourdas Finite-dimensional Hilbert space and frame quantiza-tion J Phys A Math Gen 44 175303 (2011)
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[219] S Dahlke W Dahmen E Schmidt I Weinreich Multiresolution analysis and wavelets onS
2 and S3 Numer Funct Anal Optim 16 19ndash41 (1995)
[220] S Dahlke V Lehmann G Teschke Applications of wavelet methods to the analysis ofmeteorological radar data - An overview Arabian J Sci Eng 28 3ndash44 (2003)
[221] S Dahlke G Kutyniok P Maass C Sagiv H-G Stark G Teschke The uncertaintyprinciple associated with the continuous shearlet transform Int J Wavelets MultiresolutInf Process 6 157ndash181 (2008)
[222] S Dahlke G Kutyniok G Steidl G Teschke Shearlet coorbit spaces and associatedBanach frames Appl Comput Harmon Anal 27 195ndash214 (2009)
[223] S Dahlke G Steidl G Teschke The continuous shearlet transform in arbitrary spacedimensions J Fourier Anal Appl 16 340ndash364 (2010)
[224] S Dahlke G Steidl G Teschke Shearlet coorbit spaces Compactly supported analyzingshearlets traces and embeddings J Fourier Anal Appl 17 1232ndash1355 (2011)
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[226] C Daskaloyannis Generalized deformed oscillator and nonlinear algebras J Phys AMath Gen 24 L789ndashL794 (1991)
[227] C Daskaloyannis K Ypsilantis A deformed oscillator with Coulomb energy spectrumJ Phys A Math Gen 25 4157ndash4166 (1992)
[228] I Daubechies On the distributions corresponding to bounded operators in the Weylquantization Commun Math Phys 75 229ndash238 (1980)
[229] I Daubechies and A Grossmann An integral transform related to quantization I J MathPhys 21 2080ndash2090 (1980)
[230] I Daubechies A Grossmann J Reignier An integral transform related to quantization IIJ Math Phys 24 239ndash254 (1983)
[231] I Daubechies Orthonormal bases of compactly supported wavelets Commun Pure ApplMath 41 909ndash996 (1988)
[232] I Daubechies The wavelet transform time-frequency localisation and signal analysisIEEE Trans Inform Theory 36 961ndash1005 (1990)
[233] I Daubechies S Maes A nonlinear squeezing of the continuous wavelet transform basedon auditory nerve models in Wavelets in Medicine and Biology ed by A Aldroubi MUnser (CRC Press Boca Raton 1996) pp 527ndash546
[234] I Daubechies A Grossmann Y Meyer Painless nonorthogonal expansions J Math Phys27 1271ndash1283 (1986)
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[236] R De Beer D van Ormondt FTAW Wajer S Cavassila D Graveron-Demilly S VanHuffel SVD-based modelling of medical NMR signals in SVD and Signal ProcessingIII Algorithms Architectures and Applications ed by M Moonen B De Moor (Elsevier(North-Holland) Amsterdam 1995) pp 467ndash474
[237] S De Biegravevre Coherent states over symplectic homogeneous spaces J Math Phys 301401ndash1407 (1989)
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[239] S De Biegravevre JA Gonzaacutelez Semiclassical behaviour of coherent states on the circle inQuantization and Coherent States Methods in Physics ed by A Odzijewicz et al (WorldScientific Singapore 1993)
[240] S De Biegravevre AE Gradechi Quantum mechanics and coherent states on the anti-de Sitterspace-time and their Poincareacute contraction Ann Inst H Poincareacute 57 403ndash428 (1992)
[241] J Deenen C Quesne Dynamical group of collective states I II III J Math Phys 23878ndash889 2004ndash2015 (1982)
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[246] R Delbourgo J R Fox Maximum weight vectors possess minimal uncertainty J PhysA Math Gen 10 L233ndashL235 (1977)
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[249] Th Deutsch L Genovese Wavelets for electronic structure calculations Collection SocFr Neut 12 33ndash76 (2011)
[250] B Dewitt Quantum theory of gravity I The canonical theory Phys Rev 160 1113ndash1148(1967)
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Local intermittency measure in cascade and avalanche scenarios Solar Phys 282 471ndash481(2013)
[253] AN Dinkelaker AL MacKinnon Wavelets intermittency and solar flare hard X-rays 2LIM analysis of high time resolution BATSE data Solar Phys 282 483ndash501 (2013)
[254] MN Do M Vetterli Contourlets in Beyond Wavelets ed by GV Welland (AcademicSan Diego 2003) pp 83ndash105
[255] MN Do M Vetterli The contourlet transform An efficient directional multiresolutionimage representation IEEE Trans Image Process 14 2091ndash2106 (2005)
[256] VV Dodonov Nonclassical states in quantum optics A ldquosqueezedrdquo review of the first 75years J Opt B Quant Semiclass Opot 4 R1ndashR33 (2002)
[257] DL Donoho Nonlinear wavelet methods for recovery of signals densities and spectrafrom indirect and noisy data in Different Perspectives on Wavelets Proceedings ofSymposia in Applied Mathematics vol 38 ed by I Daubechies (American MathematicalSociety Providence RI 1993) pp 173ndash205
[258] DL Donoho Wedgelets Nearly minimax estimation of edges Ann Stat 27 859ndash897(1999)
[259] DL Donoho X Huo Beamlet pyramids A new form of multiresolution analysis suitedfor extracting lines curves and objects from very noisy image data in SPIE Proceedingsvol 5914 (SPIE Bellingham WA 2005) pp 1ndash12
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[261] AH Dooley JW Rice Contractions of rotation groups and their representations MathProc Camb Phil Soc 94 509ndash517 (1983)
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[268] M Duval-Destin M-A Muschietti B Torreacutesani Continuous wavelet decompositionsmultiresolution and contrast analysis SIAM J Math Anal 24 739ndash755 (1993)
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[274] M Farge Wavelet transforms and their applications to turbulence Annu Rev Fluid Mech24 395ndash457 (1992)
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[276] M Farge NK-R Kevlahan V Perrier K Schneider Turbulence analysis modellingand computing using wavelets in Wavelets in Physics Chap 4 ed by JC van den Berg(Cambridge University Press Cambridge 1999)
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[280] M Flensted-Jensen Discrete series for semisimple symmetric spaces Ann of Math 111253ndash311 (1980)
[281] K Flornes A Grossmann M Holschneider B Torreacutesani Wavelets on discrete fieldsAppl Comput Harmon Anal 1 137ndash146 (1994)
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problem J Fourier Anal Appl 11 245ndash287 (2005)
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[286] W Freeden T Maier S Zimmermann A survey on wavelet methods for (geo)applicationsRevista Mathematica Complutense 16 (2003) 277ndash310
[287] W Freeden M Schreiner Biorthogonal locally supported wavelets on the sphere based onzonal kernel functions J Fourier Anal Appl 13 693ndash709 (2007)
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[289] L Freidel ER Livine U(N) coherent states for loop quantum gravity J Math Phys 52052502 (2011)
[290] J Froment S Mallat Arbitrary low bit rate image compression using wavelets in Progressin Wavelet Analysis and Applications (Proc Toulouse 1992) ed by Y Meyer S Roques(Ed Frontiegraveres Gif-sur-Yvette 1993) pp 413ndash418 and references therein
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[292] H Fuumlhr Wavelet frames and admissibility in higher dimensions J Math Phys 37 6353ndash6366 (1996)
[293] H Fuumlhr M Mayer Continuous wavelet transforms from semidirect products Cyclicrepresentations and Plancherel measure J Fourier Anal Appl 8 375ndash396 (2002)
[294] D Gabor Theory of communication J Inst Electr Engrg(London) 93 429ndash457 (1946)[295] J-P Gabardo D Han Frames associated with measurable spaces Adv Comput Math 18
127ndash147 (2003)[296] E Galapon Paulirsquos theorem and quantum canonical pairs The consistency of a bounded
self-adjoint time operator canonically conjugate to a Hamiltonian with non-empty pointspectrum Proc R Soc Lond A 458 451ndash472 (2002)
[297] PL Garciacutea de Leacuteon J-P Gazeau Coherent state quantization and phase operator PhysLett A 361 301ndash304 (2007)
[298] L Garciacutea de Leoacuten J-P Gazeau J Queacuteva The infinite well revisited Coherent states andquantization Phys Lett A 372 3597ndash3607 (2008)
[299] T Garidi J-P Gazeau E Huguet M Lachiegraveze Rey J Renaud Fuzzy spheres frominequivalent coherent states quantization J Phys A Math Theor 40 10225ndash10249 (2007)
[300] J-P Gazeau Four Euclidean conformal group in atomic calculations Exact analyticalexpressions for the bound-bound two-photon transition matrix elements in the H atomJ Math Phys 19 1041ndash1048 (1978)
[301] J-P Gazeau On the four Euclidean conformal group structure of the sturmian operatorLett Math Phys 3 285ndash292 (1979)
[302] J-P Gazeau Technique Sturmienne pour le spectre discret de lrsquoeacutequation de SchroumldingerJ Phys A Math Gen 13 3605ndash3617 (1980)
[303] J-P Gazeau Four Euclidean conformal group approach to the multiphoton processes in theH atom J Math Phys 23 156ndash164 (1982)
[304] J-P Gazeau A remarkable duality in one particle quantum mechanics between someconfining potentials and (R+Linfin
ε ) potentials Phys Lett 75A 159ndash163 (1980)[305] J-P Gazeau SL(2R)-coherent states and integrable systems in classical and quantum
physics in Quantization Coherent States and Complex Structures ed by J-P AntoineST Ali W Lisiecki IM Mladenov A Odzijewicz (Plenum Press New York and London1995) pp 147ndash158
[306] J-P Gazeau S Graffi Quantum harmonic oscillator A relativistic and statistical point ofview Boll Unione Mat Ital 11-A 815ndash839 (1997)
[307] J-P Gazeau V Hussin Poincareacute contraction of SU(11) Fock-Bargmann structure J PhysA Math Gen 25 1549ndash1573 (1992)
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[309] J-P Gazeau JR Klauder Coherent states for systems with discrete and continuousspectrum J Phys A Math Gen 32 123ndash132 (1999)
[310] J-P Gazeau P Monceau Generalized coherent states for arbitrary quantum systems inColloquium M Flato (Dijon Sept 99) vol II (Kluumlwer Dordrecht 2000) pp 131ndash144
[311] J-P Gazeau M Novello The question of mass in (Anti-) de Sitter space-times J Phys AMath Theor 41 304008 (2008)
[312] J-P Gazeau M del Olmo q-coherent states quantization of the harmonic oscillator AnnPhys (NY) 330 220ndash245 (2013) arXiv12071200 [quant-ph]
[313] J-P Gazeau J Patera Tau-wavelets of Haar J Phys A Math Gen 29 4549ndash4559 (1996)[314] J-P Gazeau W Piechocki Coherent states quantization of a particle in de Sitter space
J Phys A Math Gen 37 6977ndash6986 (2004)[315] J-P Gazeau J Renaud Lie algorithm for an interacting SU(11) elementary system and its
contraction Ann Phys (NY) 222 89ndash121 (1993)[316] J-P Gazeau J Renaud Relativistic harmonic oscillator and space curvature Phys Lett A
179 67ndash71 (1993)[317] J-P Gazeau V Spiridonov Toward discrete wavelets with irrational scaling factor J Math
plane J Phys A Math Theor 44 495201 (2011)[319] J-P Gazeau J Patera E Pelantovaacute Tau-wavelets in the plane J Math Phys 39 4201ndash
4212 (1998)[320] J-P Gazeau M Andrle C Burdiacutek R Krejcar Wavelet multiresolutions for the Fibonacci
chain J Phys A Math Gen 33 L47ndashL51 (2000)[321] J-P Gazeau M Andrle C Burdiacutek Bernuau spline wavelets and sturmian sequences
J Fourier Anal Appl 10 269ndash300 (2004)[322] J-P Gazeau F-X Josse-Michaux P Monceau Finite dimensional quantizations of the
(q p) plane new space and momentum inequalities Int J Modern Phys B 20 1778ndash1791 (2006)
[323] J-P Gazeau J Mourad J Queacuteva Fuzzy de Sitter space-times via coherent statesquantization in Proceedings of the XXVIth Colloquium on Group Theoretical Methodsin Physics New York 2006 ed by J Birman S Catto B Nicolescu (Canopus PublishingLimited London 2009)
[324] D Geller A Mayeli Continuous wavelets on compact manifolds Math Z 262 895ndash927(2009)
[325] D Geller A Mayeli Nearly tight frames and space-frequency analysis on compactmanifolds Math Z 263 235ndash264 (2009)
[326] L Genovese B Videau M Ospici Th Deutsch S Goedecker J-F Mhaut Daubechieswavelets for high performance electronic structure calculations The BigDFT project CR Mecanique 339 149ndash164 (2011)
[327] G Gentili C Stoppato Power series and analyticity over the quaternions Math Ann 352113ndash131 (2012)
[328] G Gentili DC Struppa A new theory of regular functions of a quaternionic variable AdvMath 216 279ndash301 (2007)
[329] C Geyer K Daniilidis Catadioptric projective geometry Int J Comput Vision 45 223ndash243 (2001)
[330] R Gilmore Geometry of symmetrized states Ann Phys (NY) 74 391ndash463 (1972)[331] R Gilmore On properties of coherent states Rev Mex Fis 23 143ndash187 (1974)[332] J Ginibre Statistical ensembles of complex quaternion and real matrices J Math Phys
6 440ndash449 (1965)[333] RJ Glauber The quantum theory of optical coherence Phys Rev 130 2529ndash2539 (1963)
560 References
[334] RJ Glauber Coherent and incoherent states of radiation field Phys Rev 131 2766ndash2788(1963)
[335] J Glimm Locally compact transformation groups Trans Amer Math Soc 101 124ndash138(1961)
[336] R Godement Sur les relations drsquoorthogonaliteacute de V Bargmann C R Acad Sci Paris 255521ndash523 657ndash659 (1947)
[337] C Gonnet B Torreacutesani Local frequency analysis with two-dimensional wavelet trans-form Signal Proc 37 389ndash404 (1994)
[338] JA Gonzalez MA del Olmo Coherent states on the circle J Phys A Math Gen 318841ndash8857 (1998)
[339] XGonze B Amadon et al ABINIT First-principles approach to material and nanosystemproperties Computer Physics Comm 180 2582ndash2615 (2009)
[340] KM Gograverski E Hivon AJ Banday BD Wandelt FK Hansen M Reinecke MBartelmann HEALPix A framework for high-resolution discretization and fast analysisof data distributed on the sphere Astrophys J 622 759ndash771 (2005)
[341] P Goupillaud A Grossmann J Morlet Cycle-octave and related transforms in seismicsignal analysis Geoexploration 23 85ndash102 (1984)
[342] KH Groumlchenig A new approach to irregular sampling of band-limited functions in RecentAdvances in Fourier Analysis and Its applications ed by JS Byrnes JL Byrnes (KluwerDordrecht 1990) pp 251ndash260
[343] KH Groumlchenig Gabor analysis over LCA groups in Gabor Analysis and Algorithms ndashTheory and Applications ed by HG Feichtinger T Strohmer (Birkhaumluser Boston-Basel-Berlin 1998) pp 211ndash231
[344] HJ Groenewold On the principles of elementary quantum mechanics Physica 12 405ndash460 (1946)
[345] P Grohs Continuous shearlet tight frames J Fourier Anal Appl 17 506ndash518 (2011)[346] P Grohs G Kutyniok Parabolic molecules preprint TU Berlin (2012)[347] M Grosser A note on distribution spaces on manifolds Novi Sad J Math 38 121ndash128
(2008)[348] A Grossmann Parity operator and quantization of δ -functions Commun Math Phys 48
191ndash194 (1976)[349] A Grossmann J Morlet Decomposition of Hardy functions into square integrable
wavelets of constant shape SIAM J Math Anal 15 723ndash736 (1984)[350] A Grossmann J Morlet Decomposition of functions into wavelets of constant shape and
related transforms in Mathematics + Physics Lectures on recent results I ed by L Streit(World Scientific Singapore 1985) pp 135ndash166
[351] A Grossmann J Morlet T Paul Integral transforms associated to square integrablerepresentations I General results J Math Phys 26 2473ndash2479 (1985)
[352] A Grossmann J Morlet T Paul Integral transforms associated to square integrablerepresentations II Examples Ann Inst H Poincareacute 45 293ndash309 (1986)
[353] A Grossmann R Kronland-Martinet J Morlet Reading and understanding the contin-uous wavelet transform in Wavelets Time-Frequency Methods and Phase Space (ProcMarseille 1987) ed by J-M Combes A Grossmann P Tchamitchian 2nd edn (SpringerBerlin 1990) pp 2ndash20
[354] P Guillemain R Kronland-Martinet B Martens Estimation of spectral lines with helpof the wavelet transform Application in NMR spectroscopy in Wavelets and Applications(Proc Marseille 1989) ed by Y Meyer (Masson and Springer Paris and Berlin 1991) pp38ndash60
[355] H de Guise M Bertola Coherent state realizations of su(n+ 1) on the n-torus J MathPhys 43 3425ndash3444 (2002)
[356] K Guo D Labate Representation of Fourier Integral Operators using shearlets J FourierAnal Appl 14 327ndash371 (2008)
References 561
[357] K Guo G Kutyniok D Labate Sparse multidimensional representations usinganisotropic dilation and shear operators in Wavelets and Spines (Athens GA 2005)(Nashboro Press Nashville TN 2006) pp 189ndash201
[358] K Guo D Labate W-Q Lim G Weiss E Wilson Wavelets with composite dilationsand their MRA properties Appl Comput Harmon Anal 20 202ndash236 (2006)
[359] EA Gutkin Overcomplete subspace systems and operator symbols Funct Anal Appl 9260ndash261 (1975)
[360] G Gyoumlrgyi Integration of the dynamical symmetry groups for the 1r potential Acta PhysAcad Sci Hung 27 435ndash439 (1969)
[361] BC Hall The Segal-Bargmann ldquoCoherent Staterdquo transform for compact Lie groups JFunct Analysis 122 103ndash151 (1994)
[362] B Hall JJ Mitchell Coherent states on spheres J Math Phys 43 1211ndash1236 (2002)[363] DK Hammond P Vandergheynst R Gribonval Wavelets on graphs via spectral theory
Appl Comput Harmon Anal 30 129ndash150 (2011)[364] Y Hassouni EMF Curado MA Rego-Monteiro Construction of coherent states for
physical algebraic system Phys Rev A 71 022104 (2005)[365] J He H Liu Admissible wavelets associated with the affine automorphism group of the
Siegel upper half-plane J Math Anal Appl 208 58ndash70 (1997)[366] J He H Liu Admissible wavelets associated with the classical domain of type one
Approx Appl 14 (1998) 89ndash105[367] J He L Peng Wavelet transform on the symmetric matrix space preprint Beijing (1997)
(unpublished)[368] J He L Peng Admissible wavelets on the unit disk Complex Variables 35 109ndash119
(1998)[369] DM Healy Jr FE Schroeck Jr On informational completeness of covariant localization
observables and Wigner coefficients J Math Phys 36 453ndash507 (1995)[370] C Heil D Walnut Continuous and discrete wavelet transforms SIAM Review 31 628ndash
666 (1989)[371] K Hepp EH Lieb On the superradiant phase transition for molecules in a quantized
radiation field The Dicke maser model Ann Phys (NY) 76 360ndash404 (1973)[372] K Hepp EH Lieb Equilibrium statistical mechanics of matter interacting with the
quantized radiation field Phys Rev A 8 2517ndash2525 (1973)[373] JA Hogan JD Lakey Extensions of the Heisenberg group by dilations and frames Appl
Comput Harmon Anal 2 174ndash199 (1995)[374] AL Hohoueacuteto K Thirulogasanthar ST Ali J-P Antoine Coherent states lattices and
square integrability of representations J Phys A Math Gen36 11817ndash11835 (2003)[375] M Holschneider On the wavelet transformation of fractal objects J Stat Phys 50 963ndash
993 (1988)[376] M Holschneider Wavelet analysis on the circle J Math Phys 31 39ndash44 (1990)[377] M Holschneider Inverse Radon transforms through inverse wavelet transforms Inv Probl
7 853ndash861 (1991)[378] M Holschneider Localization properties of wavelet transforms J Math Phys 34 3227ndash
3244 (1993)[379] M Holschneider General inversion formulas for wavelet transforms J Math Phys 34
4190ndash4198 (1993)[380] M Holschneider Wavelet analysis over abelian groups Applied Comput Harmon Anal
2 52ndash60 (1995)[381] M Holschneider Continuous wavelet transforms on the sphere J Math Phys 37 4156ndash
4165 (1996)[382] M Holschneider I Iglewska-Nowak Poisson wavelets on the sphere J Fourier Anal
Appl 13 405ndash419 (2007)
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[383] M Holschneider R Kronland-Martinet J Morlet P Tchamitchian A real-time algorithmfor signal analysis with the help of wavelet transform in Wavelets Time-FrequencyMethods and Phase Space (Proc Marseille 1987) ed by J-M Combes A Grossmann PTchamitchian 2nd edn (Springer Berlin 1990) pp 286ndash297
[384] M Holschneider P Tchamitchian Pointwise analysis of Riemannrsquos ldquonondifferentiablerdquofunction Invent Math 105 157ndash175 (1991)
[385] GR Honarasa MK Tavassoly M Hatami R Roknizadeh Nonclassical properties ofcoherent states and excited coherent states for continuous spectra J Phys A Math Theor44 085303 (2011)
[386] M Hongoh Coherent states associated with the continuous spectrum of noncompactgroups J Math Phys 18 2081ndash2085 (1977)
[387] A Horzela FH Szafraniec A measure free approach to coherent states J Phys A MathGen 45 244018 (2012)
[388] W-L Hwang S Mallat Characterization of self-similar multifractals with waveletmaxima Appl Comput Harmon Anal 1 316ndash328 (1994)
[389] W-L Hwang C-S Lu P-C Chung Shape from texture Estimation of planar surfaceorientation through the ridge surfaces of continuous wavelet transform IEEE Trans ImageProc 7 773ndash780 (1998)
[390] I Iglewska-Nowak M Holschneider Frames of Poisson wavelets on the sphere ApplComput Harmon Anal 28 227ndash248 (2010)
[391] E Inoumlnuuml EP Wigner On the contraction of groups and their representations Proc NatAcad Sci U S 39 510ndash524 (1953)
[392] S Iqbal F Saif Generalized coherent states and their statistical characteristics in power-law potentials J Math Phys 52 082105 (2011)
[393] CJ Isham JR Klauder Coherent states for n-dimensional Euclidean groups E(n) andtheir application J MathPhys 32 607ndash620 (1991)
[394] L Jacques J-P Antoine Multiselective pyramidal decomposition of images Wavelets withadaptive angular selectivity Int J Wavelets Multires Inform Proc 5 785ndash814 (2007)
[395] L Jacques L Duval C Chaux G Peyreacute A panorama on multiscale geometric rep-resentations intertwining spatial directional and frequency selectivity Signal Proc 912699ndash2730 (2011)
[396] HR Jalali M K Tavassoly On the ladder operators and nonclassicality of generalizedcoherent state associated with a particle in an infinite square well preprint (2013)arXiv13034100v1 [quant-ph]
[397] C Johnston On the pseudo-dilation representations of Flornes Grossmann Holschneiderand Torreacutesani Appl Comput Harmon Anal 3 377ndash385 (1997)
[398] G Kaiser Phase-space approach to relativistic quantum mechanics I Coherent staterepresentation for massive scalar particles J MathPhys 18 952ndash959 (1977)
[399] G Kaiser Phase-space approach to relativistic quantum mechanics II Geometrical aspectsJ MathPhys 19 502ndash507 (1978)
[400] C Kalisa B Torreacutesani N-dimensional affine Weyl-Heisenberg wavelets Ann Inst HPoincareacute 59 201ndash236 (1993)
[401] W Kaminski J Lewandowski T Pawłowski Quantum constraints Dirac observables andevolution group averaging versus the Schroumldinger picture in LQC Class Quant Grav 26245016 (2009)
[402] MR Karim ST Ali A relativistic windowed Fourier transform preprint ConcordiaUniversity Montreacuteal (1997) (unpublished)
[403] M R Karim ST Ali M Bodruzzaman A relativistic windowed Fourier transform inProceedings of IEEE SoutheastCon 2000 Nashville Tennessee pp 253ndash260 (2000)
[404] T Kawazoe Wavelet transforms associated to a principal series representation of semisim-ple Lie groups I II Proc Japan Acad Ser A ndash Math Sci 71 154ndash157 158ndash160 (1995)
[405] T Kawazoe Wavelet transform associated to an induced representation of SL(n+ 2R)Ann Inst H Poincareacute 65 1ndash13 (1996)
References 563
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[407] P Kittipoom G Kutyniok W-Q Lim Construction of compactly supported shearletframes Constr Approx 35 21ndash72 (2012)
[408] J Kiukas P Lahti K Ylinenc Phase space quantization and the operator moment problemJ Math Phys 47 072104 (2006)
[409] JR Klauder Continuous-representation theory I Postulates of continuous-representationtheory J Math Phys 4 1055ndash1058 (1963)
[410] JR Klauder Continuous-representation theory II Generalized relation between quantumand classical dynamics J Math Phys 4 1058ndash1073 (1963)
[411] JR Klauder Path integrals for affine variables in Functional Integration Theory andApplications ed by J-P Antoine E Tirapegui (Plenum Press New York and London1980) pp 101ndash119
[412] JR Klauder Are coherent states the natural language of quantum mechanics inFundamental Aspects of Quantum Theory ed by V Gorini A Frigerio NATO ASI Seriesvol B 144 (Plenum Press New York 1986) pp 1ndash12
[413] JR Klauder Quantization without quantization Ann Phys (NY) 237 147ndash160 (1995)[414] JR Klauder Coherent states for the hydrogen atom J Phys A Math Gen 29 L293ndash
L296 (1996)[415] JR Klauder An affinity for affine quantum gravity Proc Steklov Inst Math 272 169ndash176
(2011) and references therein[416] JR Klauder RF Streater A wavelet transform for the Poincareacute group J Math Phys 32
1609ndash1611 (1991)[417] JR Klauder RF Streater Wavelets and the Poincareacute half-plane J Math Phys 35 471ndash
478 (1994)[418] JR Klauder K Penson J-M Sixdeniers Constructing coherent states through solutions
of Stieltjes and Hausdorff moment problems Phys Rev A 64 013817 (2001)[419] A Kleppner RL Lipsman The Plancherel formula for group extensions Ann Ec Norm
Sup 5 459ndash516 (1972)[420] AB Klimov C Muntildeoz Coherent isotropic and squeezed states in a N-qubit system Phys
Scr 87 038110 (2013)[421] A Klyashko Dynamical symmetry approach to entanglement in Physics and Theoretical
Computer Science From Numbers and Languages to (Quantum) Cryptography - NATOSecurity through Science Series D - Information and Communication Security vol 7 edby J-P Gazeau J Nesetril B Rovan (IOS Press Washington DC 2007) pp 25ndash54
[422] S Kobayashi Irreducibility of certain unitary representations J Math Soc Japan 20 638ndash642 (1968)
[423] K Kowalski J Rembielinski LC Papaloucas Coherent states for a quantum particle ona circle J Phys A Math Gen 29 4149ndash4167 (1996)
[424] K Kowalski J Rembielinski Quantum mechanics on a sphere and coherent states J PhysA Math Gen 33 6035ndash6048 (2000)
[425] K Kowalski J Rembielinski The Bargmann representation for the quantum mechanicson a sphere J Math Phys 42 4138ndash4147 (2001)
[426] C Kristjansen J Plefka GW Semenoff M Staudacher A new double-scaling limit ofN = 4 super-Yang-Mills theory and pp-wave strings Nuclear Phys B 643 3ndash30 (2002)
[427] M Kulesh M Holschneider MS Diallo Geophysical wavelet library Applications ofthe continuous wavelet transform to the polarization and dispersion analysis of signalsComput Geosci 34 1732ndash1752 (2008)
[428] R Kunze On the Frobenius reciprocity theorem for square integrable representationsPacific J Math 53 465ndash471 (1974)
[429] Y Kuroda A Wada T Yamazaki K Nagayama Postacquisition data processing methodfor suppression of the solvent signal I J Magn Reson 84 604ndash610 (1989)
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[431] G Kutyniok D Labate Resolution of the wavefront set using continuous shearlets TransAmer Math Soc 361 2719ndash2754 (2009)
[432] G Kutyniok W-Q Lim Compactly supported shearlets are optimally sparse J ApproxTheory 163 1564ndash1589 (2011)
[433] D Labate W-Q Lim G Kutyniok G Weiss Sparse multidimensional representationusing shearlets in Wavelets XI (San Diego CA 2005) ed by M Papadakis A Laine MUnser SPIE Proceedings vol 5914 (SPIE Bellingham WA 2005) pp 254ndash262
[434] P Lahti J-P Pellonpaumlauml Continuous variable tomographic measurements Phys Lett A373 3435ndash3438 (2009)
[435] Lambertrsquos projection see WikipediahttpenwikipediaorgwikiLambert_azimuthal_equal-area_projection
[436] J-P Leduc F Mujica R Murenzi MJT Smith Missile-tracking algorithm using target-adapted spatio-temporal wavelets in Automatic Object Recognition VII SPIE Proceedingsvol 5914 (SPIE Bellingham WA 1997) pp 400ndash411
[437] J-P Leduc F Mujica R Murenzi MJT Smith Spatio-temporal wavelet transforms formotion tracking in IEEE ICASSP 1997 vol 4 (1997) pp 3013ndash3016
[438] J-P Leduc F Mujica R Murenzi MJT Smith Spatio-temporal continuous waveletsapplied to missile warhead detection and tracking in SPIE VCIP rsquo97 vol 3024 ed byJ Biemond EJ Delp (1997) pp 787ndash798
[439] B Leistedt JD McEwen Exact wavelets on the ball IEEE Trans Signal Proc 60 1564ndash1589 (2012)
[440] PG Lemarieacute Y Meyer Ondelettes et bases hilbertiennes Rev Math Iberoamer 2 1ndash18(1986)
[441] C Lemke A Schuck Jr J-P Antoine D Sima Metabolite-sensitive analysis of magneticresonance spectroscopic signals using the continuous wavelet transform Meas SciTechnol 22 (2011) Art 114013
[442] J-M Leacutevy-Leblond Galilei group and non-relativistic quantum mechanics J Math Phys4 776-788 (1963)
[443] J-M Leacutevy-Leblond Galilei group and Galilean invariance in Group Theory and ItsApplications vol II ed by EM Loebl (Academic New York 1971) pp 221ndash299
[444] J-M Leacutevy-Leblond On the conceptual nature of the physical constants Riv Nuovo Cim7 187ndash214 (1977)
[445] EH Lieb The classical limit of quantum spin systems Commun Math Phys 31 327ndash340(1973)
[446] G Lindblad B Nagel Continuous bases for unitary irreducible representations of SU(11)Ann Inst H Poincareacute 13 27ndash56 (1970)
[447] W Lisiecki Kaumlhler coherent states orbits for representations of semisimple Lie groupsAnn Inst H Poincareacute 53 857ndash890 (1990)
[448] A Lisowska Moment-based fast wedgelet transform J Math Imaging Vis 39 180ndash192(2011)
[449] H Liu L Peng Admissible wavelets associated with the Heisenberg group Pacific JMath 180 101ndash123 (1997)
[450] E Livine S Speziale Physical boundary state for the quantum tetrahedron Class QuantGrav 25 085003 (2008)
[451] F Low Complete sets of wave packets in A Passion for Physics ndash Essay in Honor ofGeoffrey Chew ed by C DeTar (World Scientific Singapore 1985) pp 17ndash22
[452] G Mack All unitary ray representations of the conformal group SU(22) with positiveenergy Commun Math Phys 55 1ndash28 (1977)
[453] GW Mackey Imprimitivity for representations of locally compact groups I Proc NatAcad Sci 35 537ndash545 (1949)
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[455] M Mallalieu CR Stroud Jr Rydberg wave packets fractional revivals and classicalorbits in Coherent States Past Present and Future (Proc Oak Ridge 1993) ed by DHFeng JR Klauder M Strayer (World Scientific Singapore 1994) pp 301ndash314
[456] SG Mallat Multifrequency channel decompositions of images and wavelet models IEEETrans Acoust Speech Signal Proc 37 2091ndash2110 (1989)
[457] SG Mallat A theory for multiresolution signal decomposition The wavelet representa-tion IEEE Trans Pattern Anal Machine Intell 11 674ndash693 (1989)
[458] S Mallat W-L Hwang Singularity detection and processing with wavelets IEEE TransInform Theory 38 617ndash643 (1992)
[459] S Mallat Z Zhang Matching pursuits with time frequency dictionaries IEEE TransSignal Proc 41 3397ndash3415 (1993)
[460] S Mallat S Zhong Wavelet maxima representation in Wavelets and Applications (ProcMarseille 1989) ed by Y Meyer (Masson and Springer Paris and Berlin 1991) pp 207ndash284
[461] VI Manrsquoko G Marmo ECG Sudarshan F Zaccaria f -oscillators and non-linearcoherent states Phys Scr 55 528ndash541 (1997)
[462] D Marinucci D Pietrobon A Baldi P Baldi P Cabella G Kerkyacharian P Natoli DPicard N Vittorio Spherical needlets for CMB data analysis Mon Not R Astron Soc383 539ndash545 (2008)
[463] D Marion M Ikura A Bax Improved solvent suppression in one- and two-dimensionalNMR spectra by convolution of time-domain data J Magn Reson 84 425ndash430 (1989)
[464] Y Meyer Principe drsquoincertitude bases hilbertiennes et algegravebres drsquoopeacuterateurs SeacuteminaireBourbaki 662 (1985ndash1986)
[465] Y Meyer Principe drsquoincertitude bases hilbertiennes et algegravebres drsquoopeacuterateurs Asteacuterisque145ndash146 209ndash223 (1987)
[466] Y Meyer H Xu Wavelet analysis and chirps Appl Comput Harmon Anal 4 366ndash379(1997)
[467] L Michel Invariance in quantum mechanics and group extensions in Group TheoreticalConcepts and Methods in Elementary Particle Physics ed by F Guumlrsey (Gordon andBreach New York and London 1964) pp 135ndash200
[468] J Mickelsson J Niederle Contractions of representations of the de Sitter groupsCommun Math Phys 27 167ndash180 (1972)
[469] MM Miller Convergence of the Sudarshan expansion for the diagonal coherent-stateweight functional J Math Phys 9 1270ndash1274 (1968)
[470] V F Molchanov Harmonic analysis on homogeneous spaces in Representation Theoryand Noncommutative Harmonic Analysis II ed by AA Kirillov (Springer Berlin 1995)
[471] MI Monastyrsky AM Perelomov Coherent states and symmetric spaces II Ann InstH Poincareacute 23 23ndash48 (1975)
[472] B Moran S Howard D Cochran Positive-operator-valued measures A general settingfor frames in Excursions in Harmonic Analysis vol 1 2 ed by TD Andrews R BalanJJ Benedetto W Czaja KA Okoudjou (Birkhaumluser Boston 2013) pp 49ndash64
[473] H Moscovici Coherent states representations of nilpotent Lie groups Commun MathPhys 54 63ndash68 (1977)
[474] H Moscovici A Verona Coherent states and square integrable representations Ann InstH Poincareacute 29 139ndash156 (1978)
[475] F Mujica R Murenzi MJT Smith J-P Leduc Robust tracking in compressed imagesequences J Electr Imaging 7 746ndash754 (1998)
[476] R Murenzi Wavelet transforms associated to the n-dimensional Euclidean group withdilations Signals in more than one dimension in Wavelets Time-Frequency Methodsand Phase Space (Proc Marseille 1987) ed by J-M Combes A Grossmann PTchamitchian 2nd edn (Springer Berlin 1990) pp 239ndash246
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[478] B Nagel Generalized eigenvectors in group representations in Studies in MathematicalPhysics (Proc Istanbul 1970) ed by AO Barut (Reidel Dordrecht and Boston 1970)pp 135ndash154
[479] MA Naımark Dokl Akad Nauk SSSR 41 359ndash361 (1943) see also B Sz-NagyExtensions of linear transformations in Hilbert space which extend beyond this spaceAppendix to F Riesz B Sz-Nagy Functional Analysis (Frederick Ungar New York 1960)
[480] FJ Narcowich P Petrushev JD Ward Localized tight frames on spheres SIAM J MathAnal 38 574ndash594 (2006)
[481] M Nauenberg Quantum wave packets on Kepler elliptic orbits Phys Rev A 40 1133ndash1136 (1989)
[482] M Nauenberg C Stroud J Yeazell The classical limit of an atom Scient Amer 27024ndash29 (1994)
[483] H Neumann Transformation properties of observables Helv Phys Acta 45 811ndash819(1972)
[484] U Niederer The maximal kinematical invariance group of the free Schroumldinger equationHelv Phys Acta 45 802ndash881 (1972)
[485] MM Nieto LM Simmons Jr Coherent states for general potentials I Formalism IIConfining one-dimensional examples III Nonconfining one-dimensional examples PhysRev D 20 1321ndash1331 1332ndash1341 1342ndash1350 (1979)
[486] MM Nieto LM Simmons Jr Coherent states for general potentials Phys Rev Lett 41207ndash210 (1987)
[487] A Odzijewicz On reproducing kernels and quantization of states Commun Math Phys114 577ndash597 (1988)
[488] A Odzijewicz Coherent states and geometric quantization Commun Math Phys 150385ndash413 (1992)
[489] A Odzijewicz Quantum algebras and q-special functions related to coherent states mapsof the disc Commun Math Phys 192 183ndash215 (1998)
[490] A Odzijewicz M Horowski A Tereszkiewicz Integrable multi-boson systems andorthogonal polynomials J Phys A Math Gen 34 4353ndash4376 (2001)
[491] G Oacutelafsson B Oslashrsted The holomorphic discrete series for affine symmetric spaces JFunct Anal 81 126ndash159 (1988)
[492] G Oacutelafsson H Schlichtkrull Representation theory Radon transform and the heatequation on a Riemannian symmetric space Contemp Math 449 315ndash344 (2008)
[493] E Onofri A note on coherent state representations of Lie groups J Math Phys 16 1087ndash1089 (1975)
[494] E Onofri Dynamical quantization of the Kepler manifold J Math Phys 17 401ndash408(1976)
[495] D Oriti R Pereira L Sindoni Coherent states in quantum gravity A construction basedon the flux representation of loop quantum gravity J Phys A Math Theor 45 244004(2012)
[496] LC Papaloucas J Rembielinski W Tybor Vectorlike coherent states with noncompactstability group J Math Phys 30 2406ndash2410 (1989)
[497] Z Pasternak-Winiarski On the dependence of the reproducing kernel on the weight ofintegration J Funct Anal 94 110ndash134 (1990)
[498] Z Pasternak-Winiarski On reproducing kernels for holomorphic vector bundles inQuantization and Infinite Dimensional Systems (Proc Białowieza Poland 1993) ed by J-P Antoine ST Ali W Lisiecki IM Mladenov A Odzijewicz (Plenum Press New Yorkand London 1994) pp 109ndash112
[499] T Paul Affine coherent states and the radial Schroumldinger equation I preprint CPT-84P1710 (1984) (unpublished)
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[500] T Paul K Seip Wavelets in quantum mechanics in Wavelets and Their Applications edby MB Ruskai G Beylkin R Coifman I Daubechies S Mallat Y Meyer L Raphael(Jones and Bartlett Boston 1992) pp 303ndash322
[501] AM Perelomov On the completeness of a system of coherent states Theor Math Phys6 156ndash164 (1971)
[502] AM Perelomov Coherent states for arbitrary Lie group Commun Math Phys 26 222ndash236 (1972)
[503] AM Perelomov Coherent states and symmetric spaces Commun Math Phys 44 197ndash210 (1975)
[504] M Perroud Projective representations of the Schroumldinger group Helv Phys Acta 50 233ndash252 (1977)
[505] J Phillips A note on square-integrable representations J Funct Anal 20 83ndash92 (1975)[506] D Pietrobon P Baldi D Marinucci Integrated Sachs-Wolfe effect from the cross
correlation of WMAP3 year and the NRAO VLA sky survey data New results andconstraints on dark energy Phys Rev D 74 043524 (2006)
[507] WWF Pijnappel A van den Boogaart R de Beer D van Ormondt SVD-basedquantification of magnetic resonance signals J Magn Reson 97 122ndash134 (1992)
[508] V Pop D Rosca Generalized piecewise constant orthogonal wavelet bases on 2D-domains Appl Anal 90 715ndash723 (2011)
[509] G Poumlschl E Teller Bemerkungen zur Quantenmechanik des anharmonischen OszillatorsZ Physik 83 143ndash151 (1933)
[510] D Potts G Steidl M Tasche Kernels of spherical harmonics and spherical frames inAdvanced Topics in Multivariate Approximation ed by F Fontanella K Jetter PJ Laurent(World Scientific Singapore 1996) pp 287ndash301
[511] E Prugovecki Consistent formulation of relativistic dynamics for massive spin-zeroparticles in external fields Phys Rev D 18 3655ndash3673 (1978) (Appendix C)
[512] E Prugovecki Relativistic quantum kinematics on stochastic phase space for massiveparticles J MathPhys 19 2261ndash2270 (1978)
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[514] C Quesne Generalized vector coherent states of sp(2NR) vector operators and ofsp(2NR) sup u(N) reduced Wigner coefficients J Phys A Math Gen 24 2697ndash2714(1991)
[515] JM Radcliffe Some properties of spin coherent states J Phys A Math Gen 4 313ndash323(1971)
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[517] H Rauhut M Roumlsler Radial multiresolution in dimension three Constr Approx 22 193ndash218 (2005)
[518] JH Rawnsley Coherent states and Kaumlhler manifolds Quart J Math Oxford 28(2) 403ndash415 (1977)
[519] J Renaud The contraction of the SU(11) discrete series of representations by means ofcoherent states J Math Phys 37 3168ndash3179 (1996)
[520] A Reacutenyi Representations for real numbers and their ergodic properties Acta Math AcadSci Hungary 8(3ndash4) 477ndash493 (1957)
[521] D Robert La coheacuterence dans tous ses eacutetats SMF Gazette 132 (2012)[522] JE Roberts The Dirac bra and ket formalism J Math Phys 7 1097ndash1104 (1966)[523] JE Roberts Rigged Hilbert spaces in quantum mechanics Commun Math Phys 3 98ndash
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[537] D Rosca G Plonka Uniform spherical grids via area preserving projection from the cubeto the sphere J Comput Appl Math 236 1033ndash1041 (2011)
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[579] T Thiemann Gauge field theory coherent states (GCS) 1 General properties Class QuantGrav 18 2025ndash2064 (2001)
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4200 (1998) and references quoted there[616] AA Zakharova On the properties of generalized frames Math Notes 83 190ndash200 (2008)[617] W-M Zhang DH Feng R Gilmore Coherent states Theory and some applications Rev
Mod Phys 26 867ndash927 (1990)[618] I Zlatev W-M Zhang DH Feng Possibility that Schroumldingerrsquos conjecture for the
hydrogen atom coherent states is not attainable Phys Rev A 50 R1973ndashR1975 (1994)[619] WH Zurek Decoherence einselection and the quantum origins of the classical Rev Mod
Phys 75 715ndash775 (2003)[620] WH Zurek S Habib JP Paz Coherent states via decoherence Phys Rev Lett 70 1187ndash
1190 (1993)[621] K Zyczkowski Squeezed states in a quantum chaotic system J Phys A Math Theor 22
of SU(11) 81 296 297HilbertClowast-modules 164holomorphic 140nonholomorphic 151nonlinear 146of affine Galilei group 505of affine Poincareacute group 509of affine Weyl-Heisenberg group GaWH
497of compact semisimple Lie groups 174of Euclidean group E(n) 266of Galilei group G (11) 290of isochronous Galilei group 237of non-semisimple Lie groups 179of noncompact semisimple Lie groups 177of Poincareacute group Puarr
+(11) 283massless case 288
of Poincareacute group Puarr+(13) 279
of Schroumldinger group 508quasi-coherent states 186quaternionic 164
ST Ali et al Coherent States Wavelets and Their Generalizations Theoreticaland Mathematical Physics DOI 101007978-1-4614-8535-3copy Springer Science+Business Media New York 2014
573
574 Index
coherent states (CS) (cont)spin or SU(2) 175square integrable covariant 166 180 264vector (VCS) 73 108 112 170weighted 184 523
of affine Weyl-Heisenberg group GaWH497
of Poincareacute group Puarr+(11) 284
cohomology group 393 403coboundaries 403cochains 402cocycle 403
algebraic 387Cauchy 418Cauchy-Paul 354 419 425conical 418difference 417 462directional 416 440kinematical 499local 488metabolite-based 355 374minimal uncertainty 425multiselective 440on a graph 493on the sphere S
2 458on the sphere S
n 479on the torus T2 481steerable 439von Mises 440
wedgelet transform 455Wigner function 322Wigner-Ville transform 349Windowed Fourier or Gabor transform 349
ZZak transform 518
References
A Books and Theses
B Articles
Index
552 References
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[198] P Casazza O Christensen S Li A Lindner Riesz-Fischer sequences and lower framebounds Z Anal Anwend 21 305ndash314 (2002)
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10 1ndash4 (2012)[206] C Cishahayo S De Biegravevre On the contraction of the discrete series of SU(11) Ann Inst
Fourier (Grenoble) 43 551ndash567 (1993)[207] M Clerc and S Mallat Shape from texture and shading with wavelets in Dynamical
Systems Control Coding Computer Vision Progress in Systems and Control Theory 25393ndash417 (1999)
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[215] N Cotfas J-P Gazeau K Goacuterska Complex and real Hermite polynomials and relatedquantizations J Phys A Math Theor 43 305304 (2010)
[216] N Cotfas J-P Gazeau A Vourdas Finite-dimensional Hilbert space and frame quantiza-tion J Phys A Math Gen 44 175303 (2011)
[217] EMF Curado MA Rego-Monteiro LMCS Rodrigues Y Hassouni Coherent statesfor a degenerate system The hydrogen atom Physica A 371 16ndash19 (2006)
[218] S Dahlke P Maass The affine uncertainty principle in one and two dimensions CompMath Appl 30 293ndash305 (1995)
[219] S Dahlke W Dahmen E Schmidt I Weinreich Multiresolution analysis and wavelets onS
2 and S3 Numer Funct Anal Optim 16 19ndash41 (1995)
[220] S Dahlke V Lehmann G Teschke Applications of wavelet methods to the analysis ofmeteorological radar data - An overview Arabian J Sci Eng 28 3ndash44 (2003)
[221] S Dahlke G Kutyniok P Maass C Sagiv H-G Stark G Teschke The uncertaintyprinciple associated with the continuous shearlet transform Int J Wavelets MultiresolutInf Process 6 157ndash181 (2008)
[222] S Dahlke G Kutyniok G Steidl G Teschke Shearlet coorbit spaces and associatedBanach frames Appl Comput Harmon Anal 27 195ndash214 (2009)
[223] S Dahlke G Steidl G Teschke The continuous shearlet transform in arbitrary spacedimensions J Fourier Anal Appl 16 340ndash364 (2010)
[224] S Dahlke G Steidl G Teschke Shearlet coorbit spaces Compactly supported analyzingshearlets traces and embeddings J Fourier Anal Appl 17 1232ndash1355 (2011)
[225] T Dallard GR Spedding 2-D wavelet transforms Generalisation of the Hardy space andapplication to experimental studies Eur J Mech BFluids 12 107ndash134 (1993)
[226] C Daskaloyannis Generalized deformed oscillator and nonlinear algebras J Phys AMath Gen 24 L789ndashL794 (1991)
[227] C Daskaloyannis K Ypsilantis A deformed oscillator with Coulomb energy spectrumJ Phys A Math Gen 25 4157ndash4166 (1992)
[228] I Daubechies On the distributions corresponding to bounded operators in the Weylquantization Commun Math Phys 75 229ndash238 (1980)
[229] I Daubechies and A Grossmann An integral transform related to quantization I J MathPhys 21 2080ndash2090 (1980)
[230] I Daubechies A Grossmann J Reignier An integral transform related to quantization IIJ Math Phys 24 239ndash254 (1983)
[231] I Daubechies Orthonormal bases of compactly supported wavelets Commun Pure ApplMath 41 909ndash996 (1988)
[232] I Daubechies The wavelet transform time-frequency localisation and signal analysisIEEE Trans Inform Theory 36 961ndash1005 (1990)
[233] I Daubechies S Maes A nonlinear squeezing of the continuous wavelet transform basedon auditory nerve models in Wavelets in Medicine and Biology ed by A Aldroubi MUnser (CRC Press Boca Raton 1996) pp 527ndash546
[234] I Daubechies A Grossmann Y Meyer Painless nonorthogonal expansions J Math Phys27 1271ndash1283 (1986)
[235] ER Davies Introduction to texture analysis in Handbook of texture analysis ed by MMirmehdi X Xie J Suri (World Scientific Singapore 2008) pp 1ndash31
[236] R De Beer D van Ormondt FTAW Wajer S Cavassila D Graveron-Demilly S VanHuffel SVD-based modelling of medical NMR signals in SVD and Signal ProcessingIII Algorithms Architectures and Applications ed by M Moonen B De Moor (Elsevier(North-Holland) Amsterdam 1995) pp 467ndash474
[237] S De Biegravevre Coherent states over symplectic homogeneous spaces J Math Phys 301401ndash1407 (1989)
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[238] S De Biegravevre JA Gonzalez Semi-classical behaviour of the Weyl correspondence on thecircle in Group-Theoretical Methods in Physics (Proc Salamanca 1992) ed by M delOlmo M Santander J Mateos Guilarte (CIEMAT Madrid 1993) pp 343ndash346
[239] S De Biegravevre JA Gonzaacutelez Semiclassical behaviour of coherent states on the circle inQuantization and Coherent States Methods in Physics ed by A Odzijewicz et al (WorldScientific Singapore 1993)
[240] S De Biegravevre AE Gradechi Quantum mechanics and coherent states on the anti-de Sitterspace-time and their Poincareacute contraction Ann Inst H Poincareacute 57 403ndash428 (1992)
[241] J Deenen C Quesne Dynamical group of collective states I II III J Math Phys 23878ndash889 2004ndash2015 (1982)
[242] J Deenen C Quesne Dynamical group of collective states I II III J Math Phys 251638ndash1650 (1984)
[243] J Deenen C Quesne Partially coherent states of the real symplectic group J Math Phys25 2354ndash2366 (1984)
[244] J Deenen C Quesne Boson representations of the real symplectic group and theirapplication to the nuclear collective model J Math Phys 26 2705ndash2716 (1985)
[245] R Delbourgo Minimal uncertainty states for the rotation and allied groups J Phys AMath Gen 10 1837ndash1846 (1977)
[246] R Delbourgo J R Fox Maximum weight vectors possess minimal uncertainty J PhysA Math Gen 10 L233ndashL235 (1977)
[247] V Delouille J de Patoul J-F Hochedez L Jacques J-P Antoine Wavelet spectrumanalysis of EITSoHO images Solar Phys 228 301ndash321 (2005)
[248] N Delprat B Escudieacute P Guillemain R Kronland-Martinet P Tchamitchian B Tor-reacutesani Asymptotic wavelet and Gabor analysis Extraction of instantaneous frequenciesIEEE Trans Inform Theory 38 644ndash664 (1992)
[249] Th Deutsch L Genovese Wavelets for electronic structure calculations Collection SocFr Neut 12 33ndash76 (2011)
[250] B Dewitt Quantum theory of gravity I The canonical theory Phys Rev 160 1113ndash1148(1967)
[251] RH Dicke Coherence in spontaneous radiation processes Phys Rev 93 99ndash110 (1954)[252] AN Dinkelaker AL MacKinnon Wavelets intermittency and solar flare hard X-rays 1
Local intermittency measure in cascade and avalanche scenarios Solar Phys 282 471ndash481(2013)
[253] AN Dinkelaker AL MacKinnon Wavelets intermittency and solar flare hard X-rays 2LIM analysis of high time resolution BATSE data Solar Phys 282 483ndash501 (2013)
[254] MN Do M Vetterli Contourlets in Beyond Wavelets ed by GV Welland (AcademicSan Diego 2003) pp 83ndash105
[255] MN Do M Vetterli The contourlet transform An efficient directional multiresolutionimage representation IEEE Trans Image Process 14 2091ndash2106 (2005)
[256] VV Dodonov Nonclassical states in quantum optics A ldquosqueezedrdquo review of the first 75years J Opt B Quant Semiclass Opot 4 R1ndashR33 (2002)
[257] DL Donoho Nonlinear wavelet methods for recovery of signals densities and spectrafrom indirect and noisy data in Different Perspectives on Wavelets Proceedings ofSymposia in Applied Mathematics vol 38 ed by I Daubechies (American MathematicalSociety Providence RI 1993) pp 173ndash205
[258] DL Donoho Wedgelets Nearly minimax estimation of edges Ann Stat 27 859ndash897(1999)
[259] DL Donoho X Huo Beamlet pyramids A new form of multiresolution analysis suitedfor extracting lines curves and objects from very noisy image data in SPIE Proceedingsvol 5914 (SPIE Bellingham WA 2005) pp 1ndash12
References 557
[260] AH Dooley Contractions of Lie groups and applications to analysis in Topics in ModernHarmonic Analysis vol I (Istituto Nazionale di Alta Matematica Francesco Severi Roma1983) pp 483ndash515
[261] AH Dooley JW Rice Contractions of rotation groups and their representations MathProc Camb Phil Soc 94 509ndash517 (1983)
[262] AH Dooley JW Rice On contractions of semisimple Lie groups Trans Amer MathSoc 289 185ndash202 (1985)
[263] JR Driscoll DM Healy Computing Fourier transforms and convolutions on the 2-sphereAdv Appl Math 15 202ndash250 (1994)
[264] H Drissi F Regragui J-P Antoine M Bennouna Wavelet transform analysis of visualevoked potentials Some preliminary results ITBM-RBM 21 84ndash91 (2000)
[265] RJ Duffin AC Schaeffer A class of nonharmonic Fourier series Trans Amer MathSoc 72 341ndash366 (1952)
[266] M Duflo CC Moore On the regular representation of a nonunimodular locally compactgroup J Funct Anal 21 209ndash243 (1976)
[267] M Duval-Destin R Murenzi Spatio-temporal wavelets Application to the analysis ofmoving patterns in Progress in Wavelet Analysis and Applications (Proc Toulouse 1992)ed by Y Meyer S Roques (Ed Frontiegraveres Gif-sur-Yvette 1993) pp 399ndash408
[268] M Duval-Destin M-A Muschietti B Torreacutesani Continuous wavelet decompositionsmultiresolution and contrast analysis SIAM J Math Anal 24 739ndash755 (1993)
[269] SJL van Eindhoven JLH Meyers New orthogonality relations for the Hermitepolynomials and related Hilbert spaces J Math Anal Appl 146 89ndash98 (1990)
[270] M ElBaz R Fresneda J-P Gazeau Y Hassouni Coherent state quantization of para-grassmann algebras J Phys A Math Theor 43 385202 (2010) Corrigendum J PhysA Math Theor 45 (2012)
[271] A Elkharrat J-P Gazeau F Deacutenoyer Multiresolution of quasicrystal diffraction spectraActa Cryst A65 466ndash489 (2009)
[272] Q Fan Phase space analysis of the identity decompositions J Math Phys 34 3471ndash3477(1993)
[273] M Fanuel S Zonetti Affine quantization and the initial cosmological singularity Euro-phys Lett 101 10001 (2013)
[274] M Farge Wavelet transforms and their applications to turbulence Annu Rev Fluid Mech24 395ndash457 (1992)
[275] M Farge N Kevlahan V Perrier E Goirand Wavelets and turbulence Proc IEEE 84639ndash669 (1996)
[276] M Farge NK-R Kevlahan V Perrier K Schneider Turbulence analysis modellingand computing using wavelets in Wavelets in Physics Chap 4 ed by JC van den Berg(Cambridge University Press Cambridge 1999)
[277] HG Feichtinger Coherent frames and irregular sampling in Recent Advances in FourierAnalysis and Its applications ed by JS Byrnes JL Byrnes (Kluwer Dordrecht 1990)pp 427ndash440
[278] HG Feichtinger KH Groumlchenig Banach spaces related to integrable group representa-tions and their atomic decompositions I J Funct Anal 86 307ndash340 (1989)
[279] HG Feichtinger KH Groumlchenig Banach spaces related to integrable group representa-tions and their atomic decompositions II Mh Math 108 129ndash148 (1989)
[280] M Flensted-Jensen Discrete series for semisimple symmetric spaces Ann of Math 111253ndash311 (1980)
[281] K Flornes A Grossmann M Holschneider B Torreacutesani Wavelets on discrete fieldsAppl Comput Harmon Anal 1 137ndash146 (1994)
[282] V Fock Zur Theorie der Wasserstoffatoms Zs f Physik 98 145ndash54 (1936)[283] M Fornasier H Rauhut Continuous frames function spaces and the discretization
problem J Fourier Anal Appl 11 245ndash287 (2005)
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[284] W Freeden M Schreiner Orthogonal and non-orthogonal multiresolution analysis scalediscrete and exact fully discrete wavelet transform on the sphere Constr Approx 14 493ndash515 (1997)
[285] W Freeden U Windheuser Combined spherical harmonic and wavelet expansion mdash Afuture concept in Earthrsquos gravitational determination Appl Comput Harmon Anal 4 1ndash37 (1997)
[286] W Freeden T Maier S Zimmermann A survey on wavelet methods for (geo)applicationsRevista Mathematica Complutense 16 (2003) 277ndash310
[287] W Freeden M Schreiner Biorthogonal locally supported wavelets on the sphere based onzonal kernel functions J Fourier Anal Appl 13 693ndash709 (2007)
[288] WT Freeman EH Adelson The design and use of steerable filters IEEE Trans PatternAnal Machine Intell 13 891ndash906 (1991)
[289] L Freidel ER Livine U(N) coherent states for loop quantum gravity J Math Phys 52052502 (2011)
[290] J Froment S Mallat Arbitrary low bit rate image compression using wavelets in Progressin Wavelet Analysis and Applications (Proc Toulouse 1992) ed by Y Meyer S Roques(Ed Frontiegraveres Gif-sur-Yvette 1993) pp 413ndash418 and references therein
[291] L Freidel S Speziale Twisted geometries A geometric parameterisation of SU(2) phasespace Phys Rev D 82 084040 (2010)
[292] H Fuumlhr Wavelet frames and admissibility in higher dimensions J Math Phys 37 6353ndash6366 (1996)
[293] H Fuumlhr M Mayer Continuous wavelet transforms from semidirect products Cyclicrepresentations and Plancherel measure J Fourier Anal Appl 8 375ndash396 (2002)
[294] D Gabor Theory of communication J Inst Electr Engrg(London) 93 429ndash457 (1946)[295] J-P Gabardo D Han Frames associated with measurable spaces Adv Comput Math 18
127ndash147 (2003)[296] E Galapon Paulirsquos theorem and quantum canonical pairs The consistency of a bounded
self-adjoint time operator canonically conjugate to a Hamiltonian with non-empty pointspectrum Proc R Soc Lond A 458 451ndash472 (2002)
[297] PL Garciacutea de Leacuteon J-P Gazeau Coherent state quantization and phase operator PhysLett A 361 301ndash304 (2007)
[298] L Garciacutea de Leoacuten J-P Gazeau J Queacuteva The infinite well revisited Coherent states andquantization Phys Lett A 372 3597ndash3607 (2008)
[299] T Garidi J-P Gazeau E Huguet M Lachiegraveze Rey J Renaud Fuzzy spheres frominequivalent coherent states quantization J Phys A Math Theor 40 10225ndash10249 (2007)
[300] J-P Gazeau Four Euclidean conformal group in atomic calculations Exact analyticalexpressions for the bound-bound two-photon transition matrix elements in the H atomJ Math Phys 19 1041ndash1048 (1978)
[301] J-P Gazeau On the four Euclidean conformal group structure of the sturmian operatorLett Math Phys 3 285ndash292 (1979)
[302] J-P Gazeau Technique Sturmienne pour le spectre discret de lrsquoeacutequation de SchroumldingerJ Phys A Math Gen 13 3605ndash3617 (1980)
[303] J-P Gazeau Four Euclidean conformal group approach to the multiphoton processes in theH atom J Math Phys 23 156ndash164 (1982)
[304] J-P Gazeau A remarkable duality in one particle quantum mechanics between someconfining potentials and (R+Linfin
ε ) potentials Phys Lett 75A 159ndash163 (1980)[305] J-P Gazeau SL(2R)-coherent states and integrable systems in classical and quantum
physics in Quantization Coherent States and Complex Structures ed by J-P AntoineST Ali W Lisiecki IM Mladenov A Odzijewicz (Plenum Press New York and London1995) pp 147ndash158
[306] J-P Gazeau S Graffi Quantum harmonic oscillator A relativistic and statistical point ofview Boll Unione Mat Ital 11-A 815ndash839 (1997)
[307] J-P Gazeau V Hussin Poincareacute contraction of SU(11) Fock-Bargmann structure J PhysA Math Gen 25 1549ndash1573 (1992)
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[309] J-P Gazeau JR Klauder Coherent states for systems with discrete and continuousspectrum J Phys A Math Gen 32 123ndash132 (1999)
[310] J-P Gazeau P Monceau Generalized coherent states for arbitrary quantum systems inColloquium M Flato (Dijon Sept 99) vol II (Kluumlwer Dordrecht 2000) pp 131ndash144
[311] J-P Gazeau M Novello The question of mass in (Anti-) de Sitter space-times J Phys AMath Theor 41 304008 (2008)
[312] J-P Gazeau M del Olmo q-coherent states quantization of the harmonic oscillator AnnPhys (NY) 330 220ndash245 (2013) arXiv12071200 [quant-ph]
[313] J-P Gazeau J Patera Tau-wavelets of Haar J Phys A Math Gen 29 4549ndash4559 (1996)[314] J-P Gazeau W Piechocki Coherent states quantization of a particle in de Sitter space
J Phys A Math Gen 37 6977ndash6986 (2004)[315] J-P Gazeau J Renaud Lie algorithm for an interacting SU(11) elementary system and its
contraction Ann Phys (NY) 222 89ndash121 (1993)[316] J-P Gazeau J Renaud Relativistic harmonic oscillator and space curvature Phys Lett A
179 67ndash71 (1993)[317] J-P Gazeau V Spiridonov Toward discrete wavelets with irrational scaling factor J Math
plane J Phys A Math Theor 44 495201 (2011)[319] J-P Gazeau J Patera E Pelantovaacute Tau-wavelets in the plane J Math Phys 39 4201ndash
4212 (1998)[320] J-P Gazeau M Andrle C Burdiacutek R Krejcar Wavelet multiresolutions for the Fibonacci
chain J Phys A Math Gen 33 L47ndashL51 (2000)[321] J-P Gazeau M Andrle C Burdiacutek Bernuau spline wavelets and sturmian sequences
J Fourier Anal Appl 10 269ndash300 (2004)[322] J-P Gazeau F-X Josse-Michaux P Monceau Finite dimensional quantizations of the
(q p) plane new space and momentum inequalities Int J Modern Phys B 20 1778ndash1791 (2006)
[323] J-P Gazeau J Mourad J Queacuteva Fuzzy de Sitter space-times via coherent statesquantization in Proceedings of the XXVIth Colloquium on Group Theoretical Methodsin Physics New York 2006 ed by J Birman S Catto B Nicolescu (Canopus PublishingLimited London 2009)
[324] D Geller A Mayeli Continuous wavelets on compact manifolds Math Z 262 895ndash927(2009)
[325] D Geller A Mayeli Nearly tight frames and space-frequency analysis on compactmanifolds Math Z 263 235ndash264 (2009)
[326] L Genovese B Videau M Ospici Th Deutsch S Goedecker J-F Mhaut Daubechieswavelets for high performance electronic structure calculations The BigDFT project CR Mecanique 339 149ndash164 (2011)
[327] G Gentili C Stoppato Power series and analyticity over the quaternions Math Ann 352113ndash131 (2012)
[328] G Gentili DC Struppa A new theory of regular functions of a quaternionic variable AdvMath 216 279ndash301 (2007)
[329] C Geyer K Daniilidis Catadioptric projective geometry Int J Comput Vision 45 223ndash243 (2001)
[330] R Gilmore Geometry of symmetrized states Ann Phys (NY) 74 391ndash463 (1972)[331] R Gilmore On properties of coherent states Rev Mex Fis 23 143ndash187 (1974)[332] J Ginibre Statistical ensembles of complex quaternion and real matrices J Math Phys
6 440ndash449 (1965)[333] RJ Glauber The quantum theory of optical coherence Phys Rev 130 2529ndash2539 (1963)
560 References
[334] RJ Glauber Coherent and incoherent states of radiation field Phys Rev 131 2766ndash2788(1963)
[335] J Glimm Locally compact transformation groups Trans Amer Math Soc 101 124ndash138(1961)
[336] R Godement Sur les relations drsquoorthogonaliteacute de V Bargmann C R Acad Sci Paris 255521ndash523 657ndash659 (1947)
[337] C Gonnet B Torreacutesani Local frequency analysis with two-dimensional wavelet trans-form Signal Proc 37 389ndash404 (1994)
[338] JA Gonzalez MA del Olmo Coherent states on the circle J Phys A Math Gen 318841ndash8857 (1998)
[339] XGonze B Amadon et al ABINIT First-principles approach to material and nanosystemproperties Computer Physics Comm 180 2582ndash2615 (2009)
[340] KM Gograverski E Hivon AJ Banday BD Wandelt FK Hansen M Reinecke MBartelmann HEALPix A framework for high-resolution discretization and fast analysisof data distributed on the sphere Astrophys J 622 759ndash771 (2005)
[341] P Goupillaud A Grossmann J Morlet Cycle-octave and related transforms in seismicsignal analysis Geoexploration 23 85ndash102 (1984)
[342] KH Groumlchenig A new approach to irregular sampling of band-limited functions in RecentAdvances in Fourier Analysis and Its applications ed by JS Byrnes JL Byrnes (KluwerDordrecht 1990) pp 251ndash260
[343] KH Groumlchenig Gabor analysis over LCA groups in Gabor Analysis and Algorithms ndashTheory and Applications ed by HG Feichtinger T Strohmer (Birkhaumluser Boston-Basel-Berlin 1998) pp 211ndash231
[344] HJ Groenewold On the principles of elementary quantum mechanics Physica 12 405ndash460 (1946)
[345] P Grohs Continuous shearlet tight frames J Fourier Anal Appl 17 506ndash518 (2011)[346] P Grohs G Kutyniok Parabolic molecules preprint TU Berlin (2012)[347] M Grosser A note on distribution spaces on manifolds Novi Sad J Math 38 121ndash128
(2008)[348] A Grossmann Parity operator and quantization of δ -functions Commun Math Phys 48
191ndash194 (1976)[349] A Grossmann J Morlet Decomposition of Hardy functions into square integrable
wavelets of constant shape SIAM J Math Anal 15 723ndash736 (1984)[350] A Grossmann J Morlet Decomposition of functions into wavelets of constant shape and
related transforms in Mathematics + Physics Lectures on recent results I ed by L Streit(World Scientific Singapore 1985) pp 135ndash166
[351] A Grossmann J Morlet T Paul Integral transforms associated to square integrablerepresentations I General results J Math Phys 26 2473ndash2479 (1985)
[352] A Grossmann J Morlet T Paul Integral transforms associated to square integrablerepresentations II Examples Ann Inst H Poincareacute 45 293ndash309 (1986)
[353] A Grossmann R Kronland-Martinet J Morlet Reading and understanding the contin-uous wavelet transform in Wavelets Time-Frequency Methods and Phase Space (ProcMarseille 1987) ed by J-M Combes A Grossmann P Tchamitchian 2nd edn (SpringerBerlin 1990) pp 2ndash20
[354] P Guillemain R Kronland-Martinet B Martens Estimation of spectral lines with helpof the wavelet transform Application in NMR spectroscopy in Wavelets and Applications(Proc Marseille 1989) ed by Y Meyer (Masson and Springer Paris and Berlin 1991) pp38ndash60
[355] H de Guise M Bertola Coherent state realizations of su(n+ 1) on the n-torus J MathPhys 43 3425ndash3444 (2002)
[356] K Guo D Labate Representation of Fourier Integral Operators using shearlets J FourierAnal Appl 14 327ndash371 (2008)
References 561
[357] K Guo G Kutyniok D Labate Sparse multidimensional representations usinganisotropic dilation and shear operators in Wavelets and Spines (Athens GA 2005)(Nashboro Press Nashville TN 2006) pp 189ndash201
[358] K Guo D Labate W-Q Lim G Weiss E Wilson Wavelets with composite dilationsand their MRA properties Appl Comput Harmon Anal 20 202ndash236 (2006)
[359] EA Gutkin Overcomplete subspace systems and operator symbols Funct Anal Appl 9260ndash261 (1975)
[360] G Gyoumlrgyi Integration of the dynamical symmetry groups for the 1r potential Acta PhysAcad Sci Hung 27 435ndash439 (1969)
[361] BC Hall The Segal-Bargmann ldquoCoherent Staterdquo transform for compact Lie groups JFunct Analysis 122 103ndash151 (1994)
[362] B Hall JJ Mitchell Coherent states on spheres J Math Phys 43 1211ndash1236 (2002)[363] DK Hammond P Vandergheynst R Gribonval Wavelets on graphs via spectral theory
Appl Comput Harmon Anal 30 129ndash150 (2011)[364] Y Hassouni EMF Curado MA Rego-Monteiro Construction of coherent states for
physical algebraic system Phys Rev A 71 022104 (2005)[365] J He H Liu Admissible wavelets associated with the affine automorphism group of the
Siegel upper half-plane J Math Anal Appl 208 58ndash70 (1997)[366] J He H Liu Admissible wavelets associated with the classical domain of type one
Approx Appl 14 (1998) 89ndash105[367] J He L Peng Wavelet transform on the symmetric matrix space preprint Beijing (1997)
(unpublished)[368] J He L Peng Admissible wavelets on the unit disk Complex Variables 35 109ndash119
(1998)[369] DM Healy Jr FE Schroeck Jr On informational completeness of covariant localization
observables and Wigner coefficients J Math Phys 36 453ndash507 (1995)[370] C Heil D Walnut Continuous and discrete wavelet transforms SIAM Review 31 628ndash
666 (1989)[371] K Hepp EH Lieb On the superradiant phase transition for molecules in a quantized
radiation field The Dicke maser model Ann Phys (NY) 76 360ndash404 (1973)[372] K Hepp EH Lieb Equilibrium statistical mechanics of matter interacting with the
quantized radiation field Phys Rev A 8 2517ndash2525 (1973)[373] JA Hogan JD Lakey Extensions of the Heisenberg group by dilations and frames Appl
Comput Harmon Anal 2 174ndash199 (1995)[374] AL Hohoueacuteto K Thirulogasanthar ST Ali J-P Antoine Coherent states lattices and
square integrability of representations J Phys A Math Gen36 11817ndash11835 (2003)[375] M Holschneider On the wavelet transformation of fractal objects J Stat Phys 50 963ndash
993 (1988)[376] M Holschneider Wavelet analysis on the circle J Math Phys 31 39ndash44 (1990)[377] M Holschneider Inverse Radon transforms through inverse wavelet transforms Inv Probl
7 853ndash861 (1991)[378] M Holschneider Localization properties of wavelet transforms J Math Phys 34 3227ndash
3244 (1993)[379] M Holschneider General inversion formulas for wavelet transforms J Math Phys 34
4190ndash4198 (1993)[380] M Holschneider Wavelet analysis over abelian groups Applied Comput Harmon Anal
2 52ndash60 (1995)[381] M Holschneider Continuous wavelet transforms on the sphere J Math Phys 37 4156ndash
4165 (1996)[382] M Holschneider I Iglewska-Nowak Poisson wavelets on the sphere J Fourier Anal
Appl 13 405ndash419 (2007)
562 References
[383] M Holschneider R Kronland-Martinet J Morlet P Tchamitchian A real-time algorithmfor signal analysis with the help of wavelet transform in Wavelets Time-FrequencyMethods and Phase Space (Proc Marseille 1987) ed by J-M Combes A Grossmann PTchamitchian 2nd edn (Springer Berlin 1990) pp 286ndash297
[384] M Holschneider P Tchamitchian Pointwise analysis of Riemannrsquos ldquonondifferentiablerdquofunction Invent Math 105 157ndash175 (1991)
[385] GR Honarasa MK Tavassoly M Hatami R Roknizadeh Nonclassical properties ofcoherent states and excited coherent states for continuous spectra J Phys A Math Theor44 085303 (2011)
[386] M Hongoh Coherent states associated with the continuous spectrum of noncompactgroups J Math Phys 18 2081ndash2085 (1977)
[387] A Horzela FH Szafraniec A measure free approach to coherent states J Phys A MathGen 45 244018 (2012)
[388] W-L Hwang S Mallat Characterization of self-similar multifractals with waveletmaxima Appl Comput Harmon Anal 1 316ndash328 (1994)
[389] W-L Hwang C-S Lu P-C Chung Shape from texture Estimation of planar surfaceorientation through the ridge surfaces of continuous wavelet transform IEEE Trans ImageProc 7 773ndash780 (1998)
[390] I Iglewska-Nowak M Holschneider Frames of Poisson wavelets on the sphere ApplComput Harmon Anal 28 227ndash248 (2010)
[391] E Inoumlnuuml EP Wigner On the contraction of groups and their representations Proc NatAcad Sci U S 39 510ndash524 (1953)
[392] S Iqbal F Saif Generalized coherent states and their statistical characteristics in power-law potentials J Math Phys 52 082105 (2011)
[393] CJ Isham JR Klauder Coherent states for n-dimensional Euclidean groups E(n) andtheir application J MathPhys 32 607ndash620 (1991)
[394] L Jacques J-P Antoine Multiselective pyramidal decomposition of images Wavelets withadaptive angular selectivity Int J Wavelets Multires Inform Proc 5 785ndash814 (2007)
[395] L Jacques L Duval C Chaux G Peyreacute A panorama on multiscale geometric rep-resentations intertwining spatial directional and frequency selectivity Signal Proc 912699ndash2730 (2011)
[396] HR Jalali M K Tavassoly On the ladder operators and nonclassicality of generalizedcoherent state associated with a particle in an infinite square well preprint (2013)arXiv13034100v1 [quant-ph]
[397] C Johnston On the pseudo-dilation representations of Flornes Grossmann Holschneiderand Torreacutesani Appl Comput Harmon Anal 3 377ndash385 (1997)
[398] G Kaiser Phase-space approach to relativistic quantum mechanics I Coherent staterepresentation for massive scalar particles J MathPhys 18 952ndash959 (1977)
[399] G Kaiser Phase-space approach to relativistic quantum mechanics II Geometrical aspectsJ MathPhys 19 502ndash507 (1978)
[400] C Kalisa B Torreacutesani N-dimensional affine Weyl-Heisenberg wavelets Ann Inst HPoincareacute 59 201ndash236 (1993)
[401] W Kaminski J Lewandowski T Pawłowski Quantum constraints Dirac observables andevolution group averaging versus the Schroumldinger picture in LQC Class Quant Grav 26245016 (2009)
[402] MR Karim ST Ali A relativistic windowed Fourier transform preprint ConcordiaUniversity Montreacuteal (1997) (unpublished)
[403] M R Karim ST Ali M Bodruzzaman A relativistic windowed Fourier transform inProceedings of IEEE SoutheastCon 2000 Nashville Tennessee pp 253ndash260 (2000)
[404] T Kawazoe Wavelet transforms associated to a principal series representation of semisim-ple Lie groups I II Proc Japan Acad Ser A ndash Math Sci 71 154ndash157 158ndash160 (1995)
[405] T Kawazoe Wavelet transform associated to an induced representation of SL(n+ 2R)Ann Inst H Poincareacute 65 1ndash13 (1996)
References 563
[406] P Kittipoom G Kutyniok W-Q Lim Irregular shearlet frames Geometry and approxi-mation properties J Fourier Anal Appl 17 604ndash639 (2011)
[407] P Kittipoom G Kutyniok W-Q Lim Construction of compactly supported shearletframes Constr Approx 35 21ndash72 (2012)
[408] J Kiukas P Lahti K Ylinenc Phase space quantization and the operator moment problemJ Math Phys 47 072104 (2006)
[409] JR Klauder Continuous-representation theory I Postulates of continuous-representationtheory J Math Phys 4 1055ndash1058 (1963)
[410] JR Klauder Continuous-representation theory II Generalized relation between quantumand classical dynamics J Math Phys 4 1058ndash1073 (1963)
[411] JR Klauder Path integrals for affine variables in Functional Integration Theory andApplications ed by J-P Antoine E Tirapegui (Plenum Press New York and London1980) pp 101ndash119
[412] JR Klauder Are coherent states the natural language of quantum mechanics inFundamental Aspects of Quantum Theory ed by V Gorini A Frigerio NATO ASI Seriesvol B 144 (Plenum Press New York 1986) pp 1ndash12
[413] JR Klauder Quantization without quantization Ann Phys (NY) 237 147ndash160 (1995)[414] JR Klauder Coherent states for the hydrogen atom J Phys A Math Gen 29 L293ndash
L296 (1996)[415] JR Klauder An affinity for affine quantum gravity Proc Steklov Inst Math 272 169ndash176
(2011) and references therein[416] JR Klauder RF Streater A wavelet transform for the Poincareacute group J Math Phys 32
1609ndash1611 (1991)[417] JR Klauder RF Streater Wavelets and the Poincareacute half-plane J Math Phys 35 471ndash
478 (1994)[418] JR Klauder K Penson J-M Sixdeniers Constructing coherent states through solutions
of Stieltjes and Hausdorff moment problems Phys Rev A 64 013817 (2001)[419] A Kleppner RL Lipsman The Plancherel formula for group extensions Ann Ec Norm
Sup 5 459ndash516 (1972)[420] AB Klimov C Muntildeoz Coherent isotropic and squeezed states in a N-qubit system Phys
Scr 87 038110 (2013)[421] A Klyashko Dynamical symmetry approach to entanglement in Physics and Theoretical
Computer Science From Numbers and Languages to (Quantum) Cryptography - NATOSecurity through Science Series D - Information and Communication Security vol 7 edby J-P Gazeau J Nesetril B Rovan (IOS Press Washington DC 2007) pp 25ndash54
[422] S Kobayashi Irreducibility of certain unitary representations J Math Soc Japan 20 638ndash642 (1968)
[423] K Kowalski J Rembielinski LC Papaloucas Coherent states for a quantum particle ona circle J Phys A Math Gen 29 4149ndash4167 (1996)
[424] K Kowalski J Rembielinski Quantum mechanics on a sphere and coherent states J PhysA Math Gen 33 6035ndash6048 (2000)
[425] K Kowalski J Rembielinski The Bargmann representation for the quantum mechanicson a sphere J Math Phys 42 4138ndash4147 (2001)
[426] C Kristjansen J Plefka GW Semenoff M Staudacher A new double-scaling limit ofN = 4 super-Yang-Mills theory and pp-wave strings Nuclear Phys B 643 3ndash30 (2002)
[427] M Kulesh M Holschneider MS Diallo Geophysical wavelet library Applications ofthe continuous wavelet transform to the polarization and dispersion analysis of signalsComput Geosci 34 1732ndash1752 (2008)
[428] R Kunze On the Frobenius reciprocity theorem for square integrable representationsPacific J Math 53 465ndash471 (1974)
[429] Y Kuroda A Wada T Yamazaki K Nagayama Postacquisition data processing methodfor suppression of the solvent signal I J Magn Reson 84 604ndash610 (1989)
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[431] G Kutyniok D Labate Resolution of the wavefront set using continuous shearlets TransAmer Math Soc 361 2719ndash2754 (2009)
[432] G Kutyniok W-Q Lim Compactly supported shearlets are optimally sparse J ApproxTheory 163 1564ndash1589 (2011)
[433] D Labate W-Q Lim G Kutyniok G Weiss Sparse multidimensional representationusing shearlets in Wavelets XI (San Diego CA 2005) ed by M Papadakis A Laine MUnser SPIE Proceedings vol 5914 (SPIE Bellingham WA 2005) pp 254ndash262
[434] P Lahti J-P Pellonpaumlauml Continuous variable tomographic measurements Phys Lett A373 3435ndash3438 (2009)
[435] Lambertrsquos projection see WikipediahttpenwikipediaorgwikiLambert_azimuthal_equal-area_projection
[436] J-P Leduc F Mujica R Murenzi MJT Smith Missile-tracking algorithm using target-adapted spatio-temporal wavelets in Automatic Object Recognition VII SPIE Proceedingsvol 5914 (SPIE Bellingham WA 1997) pp 400ndash411
[437] J-P Leduc F Mujica R Murenzi MJT Smith Spatio-temporal wavelet transforms formotion tracking in IEEE ICASSP 1997 vol 4 (1997) pp 3013ndash3016
[438] J-P Leduc F Mujica R Murenzi MJT Smith Spatio-temporal continuous waveletsapplied to missile warhead detection and tracking in SPIE VCIP rsquo97 vol 3024 ed byJ Biemond EJ Delp (1997) pp 787ndash798
[439] B Leistedt JD McEwen Exact wavelets on the ball IEEE Trans Signal Proc 60 1564ndash1589 (2012)
[440] PG Lemarieacute Y Meyer Ondelettes et bases hilbertiennes Rev Math Iberoamer 2 1ndash18(1986)
[441] C Lemke A Schuck Jr J-P Antoine D Sima Metabolite-sensitive analysis of magneticresonance spectroscopic signals using the continuous wavelet transform Meas SciTechnol 22 (2011) Art 114013
[442] J-M Leacutevy-Leblond Galilei group and non-relativistic quantum mechanics J Math Phys4 776-788 (1963)
[443] J-M Leacutevy-Leblond Galilei group and Galilean invariance in Group Theory and ItsApplications vol II ed by EM Loebl (Academic New York 1971) pp 221ndash299
[444] J-M Leacutevy-Leblond On the conceptual nature of the physical constants Riv Nuovo Cim7 187ndash214 (1977)
[445] EH Lieb The classical limit of quantum spin systems Commun Math Phys 31 327ndash340(1973)
[446] G Lindblad B Nagel Continuous bases for unitary irreducible representations of SU(11)Ann Inst H Poincareacute 13 27ndash56 (1970)
[447] W Lisiecki Kaumlhler coherent states orbits for representations of semisimple Lie groupsAnn Inst H Poincareacute 53 857ndash890 (1990)
[448] A Lisowska Moment-based fast wedgelet transform J Math Imaging Vis 39 180ndash192(2011)
[449] H Liu L Peng Admissible wavelets associated with the Heisenberg group Pacific JMath 180 101ndash123 (1997)
[450] E Livine S Speziale Physical boundary state for the quantum tetrahedron Class QuantGrav 25 085003 (2008)
[451] F Low Complete sets of wave packets in A Passion for Physics ndash Essay in Honor ofGeoffrey Chew ed by C DeTar (World Scientific Singapore 1985) pp 17ndash22
[452] G Mack All unitary ray representations of the conformal group SU(22) with positiveenergy Commun Math Phys 55 1ndash28 (1977)
[453] GW Mackey Imprimitivity for representations of locally compact groups I Proc NatAcad Sci 35 537ndash545 (1949)
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[457] SG Mallat A theory for multiresolution signal decomposition The wavelet representa-tion IEEE Trans Pattern Anal Machine Intell 11 674ndash693 (1989)
[458] S Mallat W-L Hwang Singularity detection and processing with wavelets IEEE TransInform Theory 38 617ndash643 (1992)
[459] S Mallat Z Zhang Matching pursuits with time frequency dictionaries IEEE TransSignal Proc 41 3397ndash3415 (1993)
[460] S Mallat S Zhong Wavelet maxima representation in Wavelets and Applications (ProcMarseille 1989) ed by Y Meyer (Masson and Springer Paris and Berlin 1991) pp 207ndash284
[461] VI Manrsquoko G Marmo ECG Sudarshan F Zaccaria f -oscillators and non-linearcoherent states Phys Scr 55 528ndash541 (1997)
[462] D Marinucci D Pietrobon A Baldi P Baldi P Cabella G Kerkyacharian P Natoli DPicard N Vittorio Spherical needlets for CMB data analysis Mon Not R Astron Soc383 539ndash545 (2008)
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[464] Y Meyer Principe drsquoincertitude bases hilbertiennes et algegravebres drsquoopeacuterateurs SeacuteminaireBourbaki 662 (1985ndash1986)
[465] Y Meyer Principe drsquoincertitude bases hilbertiennes et algegravebres drsquoopeacuterateurs Asteacuterisque145ndash146 209ndash223 (1987)
[466] Y Meyer H Xu Wavelet analysis and chirps Appl Comput Harmon Anal 4 366ndash379(1997)
[467] L Michel Invariance in quantum mechanics and group extensions in Group TheoreticalConcepts and Methods in Elementary Particle Physics ed by F Guumlrsey (Gordon andBreach New York and London 1964) pp 135ndash200
[468] J Mickelsson J Niederle Contractions of representations of the de Sitter groupsCommun Math Phys 27 167ndash180 (1972)
[469] MM Miller Convergence of the Sudarshan expansion for the diagonal coherent-stateweight functional J Math Phys 9 1270ndash1274 (1968)
[470] V F Molchanov Harmonic analysis on homogeneous spaces in Representation Theoryand Noncommutative Harmonic Analysis II ed by AA Kirillov (Springer Berlin 1995)
[471] MI Monastyrsky AM Perelomov Coherent states and symmetric spaces II Ann InstH Poincareacute 23 23ndash48 (1975)
[472] B Moran S Howard D Cochran Positive-operator-valued measures A general settingfor frames in Excursions in Harmonic Analysis vol 1 2 ed by TD Andrews R BalanJJ Benedetto W Czaja KA Okoudjou (Birkhaumluser Boston 2013) pp 49ndash64
[473] H Moscovici Coherent states representations of nilpotent Lie groups Commun MathPhys 54 63ndash68 (1977)
[474] H Moscovici A Verona Coherent states and square integrable representations Ann InstH Poincareacute 29 139ndash156 (1978)
[475] F Mujica R Murenzi MJT Smith J-P Leduc Robust tracking in compressed imagesequences J Electr Imaging 7 746ndash754 (1998)
[476] R Murenzi Wavelet transforms associated to the n-dimensional Euclidean group withdilations Signals in more than one dimension in Wavelets Time-Frequency Methodsand Phase Space (Proc Marseille 1987) ed by J-M Combes A Grossmann PTchamitchian 2nd edn (Springer Berlin 1990) pp 239ndash246
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[478] B Nagel Generalized eigenvectors in group representations in Studies in MathematicalPhysics (Proc Istanbul 1970) ed by AO Barut (Reidel Dordrecht and Boston 1970)pp 135ndash154
[479] MA Naımark Dokl Akad Nauk SSSR 41 359ndash361 (1943) see also B Sz-NagyExtensions of linear transformations in Hilbert space which extend beyond this spaceAppendix to F Riesz B Sz-Nagy Functional Analysis (Frederick Ungar New York 1960)
[480] FJ Narcowich P Petrushev JD Ward Localized tight frames on spheres SIAM J MathAnal 38 574ndash594 (2006)
[481] M Nauenberg Quantum wave packets on Kepler elliptic orbits Phys Rev A 40 1133ndash1136 (1989)
[482] M Nauenberg C Stroud J Yeazell The classical limit of an atom Scient Amer 27024ndash29 (1994)
[483] H Neumann Transformation properties of observables Helv Phys Acta 45 811ndash819(1972)
[484] U Niederer The maximal kinematical invariance group of the free Schroumldinger equationHelv Phys Acta 45 802ndash881 (1972)
[485] MM Nieto LM Simmons Jr Coherent states for general potentials I Formalism IIConfining one-dimensional examples III Nonconfining one-dimensional examples PhysRev D 20 1321ndash1331 1332ndash1341 1342ndash1350 (1979)
[486] MM Nieto LM Simmons Jr Coherent states for general potentials Phys Rev Lett 41207ndash210 (1987)
[487] A Odzijewicz On reproducing kernels and quantization of states Commun Math Phys114 577ndash597 (1988)
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[489] A Odzijewicz Quantum algebras and q-special functions related to coherent states mapsof the disc Commun Math Phys 192 183ndash215 (1998)
[490] A Odzijewicz M Horowski A Tereszkiewicz Integrable multi-boson systems andorthogonal polynomials J Phys A Math Gen 34 4353ndash4376 (2001)
[491] G Oacutelafsson B Oslashrsted The holomorphic discrete series for affine symmetric spaces JFunct Anal 81 126ndash159 (1988)
[492] G Oacutelafsson H Schlichtkrull Representation theory Radon transform and the heatequation on a Riemannian symmetric space Contemp Math 449 315ndash344 (2008)
[493] E Onofri A note on coherent state representations of Lie groups J Math Phys 16 1087ndash1089 (1975)
[494] E Onofri Dynamical quantization of the Kepler manifold J Math Phys 17 401ndash408(1976)
[495] D Oriti R Pereira L Sindoni Coherent states in quantum gravity A construction basedon the flux representation of loop quantum gravity J Phys A Math Theor 45 244004(2012)
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[498] Z Pasternak-Winiarski On reproducing kernels for holomorphic vector bundles inQuantization and Infinite Dimensional Systems (Proc Białowieza Poland 1993) ed by J-P Antoine ST Ali W Lisiecki IM Mladenov A Odzijewicz (Plenum Press New Yorkand London 1994) pp 109ndash112
[499] T Paul Affine coherent states and the radial Schroumldinger equation I preprint CPT-84P1710 (1984) (unpublished)
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[501] AM Perelomov On the completeness of a system of coherent states Theor Math Phys6 156ndash164 (1971)
[502] AM Perelomov Coherent states for arbitrary Lie group Commun Math Phys 26 222ndash236 (1972)
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[504] M Perroud Projective representations of the Schroumldinger group Helv Phys Acta 50 233ndash252 (1977)
[505] J Phillips A note on square-integrable representations J Funct Anal 20 83ndash92 (1975)[506] D Pietrobon P Baldi D Marinucci Integrated Sachs-Wolfe effect from the cross
correlation of WMAP3 year and the NRAO VLA sky survey data New results andconstraints on dark energy Phys Rev D 74 043524 (2006)
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[508] V Pop D Rosca Generalized piecewise constant orthogonal wavelet bases on 2D-domains Appl Anal 90 715ndash723 (2011)
[509] G Poumlschl E Teller Bemerkungen zur Quantenmechanik des anharmonischen OszillatorsZ Physik 83 143ndash151 (1933)
[510] D Potts G Steidl M Tasche Kernels of spherical harmonics and spherical frames inAdvanced Topics in Multivariate Approximation ed by F Fontanella K Jetter PJ Laurent(World Scientific Singapore 1996) pp 287ndash301
[511] E Prugovecki Consistent formulation of relativistic dynamics for massive spin-zeroparticles in external fields Phys Rev D 18 3655ndash3673 (1978) (Appendix C)
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[513] C Quesne Coherent states of the real symplectic group in a complex analytic parametriza-tion I II J Math Phys 27 428ndash441 869ndash878 (1986)
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[515] JM Radcliffe Some properties of spin coherent states J Phys A Math Gen 4 313ndash323(1971)
[516] A Rahimi A Najati YN Dehghan Continuous frames in Hilbert spaces Methods FunctAnal Topol 12 170ndash182 (2006)
[517] H Rauhut M Roumlsler Radial multiresolution in dimension three Constr Approx 22 193ndash218 (2005)
[518] JH Rawnsley Coherent states and Kaumlhler manifolds Quart J Math Oxford 28(2) 403ndash415 (1977)
[519] J Renaud The contraction of the SU(11) discrete series of representations by means ofcoherent states J Math Phys 37 3168ndash3179 (1996)
[520] A Reacutenyi Representations for real numbers and their ergodic properties Acta Math AcadSci Hungary 8(3ndash4) 477ndash493 (1957)
[521] D Robert La coheacuterence dans tous ses eacutetats SMF Gazette 132 (2012)[522] JE Roberts The Dirac bra and ket formalism J Math Phys 7 1097ndash1104 (1966)[523] JE Roberts Rigged Hilbert spaces in quantum mechanics Commun Math Phys 3 98ndash
119 (1966)[524] S Roques F Bourzeix K Bouyoucef Soft-thresholding technique and restoration of
3C273 jet Astrophys Space Sci Nr 239 297ndash304 (1996)[525] D Rosca Haar wavelets on spherical triangulations in Advances in Multiresolution for
Geometric Modelling ed by NA Dogson MS Floater MA Sabin (Springer Berlin2005) pp 407ndash419
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501ndash511 (2007)[529] D Rosca Wavelet bases on the sphere obtained by radial projection J Fourier Anal Appl
13 421ndash434 (2007)[530] D Rosca Piecewise constant wavelets on triangulations obtained by 1ndash3 splitting Int J
Wavelets Multiresolut Inf Process 6 209ndash222 (2008)[531] D Rosca On a norm equivalence on L2(S2) Results Math 53 399ndash405 (2009)[532] D Rosca New uniform grids on the sphere Astron Astrophys 520 (2010) Art A63[533] D Rosca Uniform and refinable grids on elliptic domains and on some surfaces of
revolution Appl Math Comput 217 7812ndash7817 (2011)[534] D Rosca Wavelet analysis on some surfaces of revolution via area preserving projection
Appl Comput Harmon Anal 30 262ndash272 (2011)[535] D Rosca J-P Antoine Locally supported orthogonal wavelet bases on the sphere via
stereographic projection Math Probl Eng 2009 124904 (2009)[536] D Rosca J-P Antoine Constructing wavelet frames and orthogonal wavelet bases on the
sphere in Recent Advances in Signal Processing ed by S Miron (IN-TECH ViennaAustria and Rijeka Croatia 2010) pp 59ndash76
[537] D Rosca G Plonka Uniform spherical grids via area preserving projection from the cubeto the sphere J Comput Appl Math 236 1033ndash1041 (2011)
[538] D Rosca G Plonka An area preserving projection from the regular octahedron to thesphere Results Math 63 429ndash444 (2012)
[539] H Rossi M Vergne Analytic continuation of the holomorphic discrete series for a semi-simple Lie group Acta Math 136 1ndash59 (1976)
[540] DJ Rotenberg Application of Sturmian functions to the Schroedinger three-body prob-lem Elastic e+ndashH scattering Ann Phys (NY) 19 262ndash278 (1962)
[541] C Rovelli Zakopane lectures on loop gravity in Proceedings of 3rd Quantum Gravityand Quantum Geometry School 28 Febndash13 March 2011 (Zakopane Poland 2011)arXiv11023660v5
[542] C Rovelli S Speziale A semiclassical tetrahedron Class Quant Grav 23 5861ndash5870(2006)
[543] DJ Rowe Coherent state theory of the noncompact symplectic group J Math Phys 252662ndash2271 (1984)
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[545] DJ Rowe Vector coherent state representations and their inner products J Phys A MathGen 45 244003 (2012) (This paper belongs to the special issue [38])
[546] DJ Rowe J Repka Vector-coherent-state theory as a theory of induced representationsJ Math Phys 32 2614ndash2634 (1991)
[547] DJ Rowe G Rosensteel R Gilmore Vector coherent state representation theory J MathPhys 26 2787ndash2791 (1985)
[548] A Royer Phase states and phase operators for the quantum harmonic oscillator Phys RevA 53 70ndash108 (1996)
[549] J Saletan Contraction of Lie groups J Math Phys 2 1ndash21 (1961)[550] G Saracco A Grossmann P Tchamitchian Use of wavelet transforms in the study of
propagation of transient acoustic signals across a plane interface between two homoge-neous media in Wavelets Time-Frequency Methods and Phase Space (Proc Marseille1987) ed by J-M Combes A Grossmann P Tchamitchian 2nd edn (Springer Berlin1990) pp 139ndash146
[551] P Schroumlder W Sweldens Spherical wavelets Efficiently representing functions on thesphere in Computer Graphics Proceedings (SIGGRAPH95) (ACM Siggraph Los Angeles1995) pp 161ndash175
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[554] H Scutaru Coherent states and induced representations Lett Math Phys 2 101ndash107(1977)
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Math 137 82ndash203 (1998)[557] R Simon ECG Sudarshan N Mukunda Gaussian pure states in quantum mechanics
and the symplectic group Phys Rev A37 3028ndash3038 (1988)[558] S Sivakumar Studies on nonlinear coherent states J Opt B Quant Semiclass Opt 2
R61ndashR75 (2000)[559] E Slezak A Bijaoui G Mars Identification of structures from galaxy counts Use of the
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Geometric Methods in Physics XXXI Workshop 2012 (Trends in Mathematics ed byP Kielanowski et al Birkhaumluser Verlag Basel 2013) pp 47ndash63
[562] SB Sontz Paragrassmann algebras as quantum spaces Part II Toeplitz operators J OperTh (2013 to appear) arXiv12055493
[563] SB Sontz A reproducing kernel and Toeplitz operators in the quantum plane Preprint(2013) arXiv13056986 [math-ph]
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[569] MB Stenzel The Segal-Bargmann transform on a symmetric space of compact type JFunct Analysis 165 44ndash58 (1994)
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[572] W Sweldens The lifting scheme A custom-design construction of biorthogonal waveletsApplied Comput Harmon Anal 3 1186ndash1200 (1996)
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[575] FH Szafraniec Multipliers in the reproducing kernel Hilbert space subnormality andnoncommutative complex analysis in Reproducing Kernel Spaces and Applications edby D Alpay Operator Theory Advances and Applications vol 143 (Birkhaumluser Basel2003) pp 313ndash331
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Proceedings of the 27th International Cosmic Ray Conference (ICRC 2001) (CopernicusGesellschaft DE 2001) pp 2923ndash2926
[579] T Thiemann Gauge field theory coherent states (GCS) 1 General properties Class QuantGrav 18 2025ndash2064 (2001)
[580] T Thiemann O Winkler Gauge field theory coherent states (GCS) 2 Peakednessproperties Class Quant Grav 18 2561ndash2636 (2001)
[581] T Thiemann O Winkler Gauge field theory coherent states (GCS) 3 Ehrenfest theoremsClass Quant Grav 18 4629ndash4682 (2001)
[582] T Thiemann O Winkler Gauge field theory coherent states (GCS) 4 Infinite tensorproduct and thermodynamical limit Class Quant Grav 18 4997ndash5054 (2001)
[583] K Thirulagasanthar ST Ali Regular subspaces of a quaternionic Hilbert space fromquaternionic Hermite polynomials and associated coherent states J Math Phys 54013506 (2013)
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Ann Inst H Poincareacute 56 215ndash234 (1992)[588] B Torreacutesani Position-frequency analysis for signals defined on spheres Signal Proc 43
341ndash346 (2005)[589] DA Trifonov Generalized intelligent states and squeezing J Math Phys 35 2297ndash2308
(1994)[590] AS Trushechkin IV Volovich Localization properties of squeezed quantum states in
nanoscale space domains preprint (2013) arXiv13046277v1 [quant-ph][591] M Unser N Chenouard A unifying parametric framework for 2D steerable wavelet
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simulation of an impact test using wavelets analytical and finite element models Int JSolids Struct 38 5481ndash5508 (2001)
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[596] J Voisin On some unitary representations of the Galilei group I Irreducible representa-tions J Math Phys 6 1519ndash1529 (1965)
[597] A Vourdas Analytic representations in quantum mechanics J Phys A Math Gen 39R65ndashR141 (2006)
[598] DF Walls Squeezed states of light Nature 306 141ndash146 (1983)[599] YK Wang FT Hioe Phase transition in the Dicke maser model Phys Rev A 7 831ndash836
(1973)[600] PSP Wang J Yang A review of wavelet-based edge detection methods Int J Patt
Recogn Artif Intell 26 1255011 (2012)[601] I Weinreich A construction of C1-wavelets on the two-dimensional sphere Appl Comput
Harmon Anal 10 1ndash26 (2001)[602] H Weyl Quantenmechanik und Gruppentheorie Z Phys 46 1ndash46 (1927)
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[606] WM Wieland Complex Ashtekar variables and reality conditions for Holstrsquos action AnnHenri Poincareacute 13 425ndash448 (2012)
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[609] W Wisnoe P Gajan A Strzelecki C Lempereur J-M Matheacute The use of the two-dimensional wavelet transform in flow visualization processing in Progress in WaveletAnalysis and Applications (Proc Toulouse 1992) ed by Y Meyer S Roques (EdFrontiegraveres Gif-sur-Yvette 1993) pp 455ndash458
[610] K Woacutedkiewicz On the quantum mechanics of squeezed states J Modern Optics 34 941ndash948(1987)
[611] JA Yeazell M Mallalieu CR Stroud Jr Observation of the collapse and revival of aRydberg electronic wave packet Phys Rev Lett 64 2007ndash2010 (1990)
[612] JA Yeazell CR Stroud Jr Observation of fractional revivals in the evolution of aRydberg atomic wave packet Phys Rev A 43 5153ndash5156 (1991)
[613] HP Yuen Two-photon coherent states of the radiation field Phys Rev A 13 2226ndash2243(1976)
[614] J Zak Balian-Low theorem for Landau levels Phys Rev Lett 79 533ndash536 (1997)[615] J Zak Orthonormal sets of localized functions for a Landau level J Math Phys 39 4195ndash
4200 (1998) and references quoted there[616] AA Zakharova On the properties of generalized frames Math Notes 83 190ndash200 (2008)[617] W-M Zhang DH Feng R Gilmore Coherent states Theory and some applications Rev
Mod Phys 26 867ndash927 (1990)[618] I Zlatev W-M Zhang DH Feng Possibility that Schroumldingerrsquos conjecture for the
hydrogen atom coherent states is not attainable Phys Rev A 50 R1973ndashR1975 (1994)[619] WH Zurek Decoherence einselection and the quantum origins of the classical Rev Mod
Phys 75 715ndash775 (2003)[620] WH Zurek S Habib JP Paz Coherent states via decoherence Phys Rev Lett 70 1187ndash
1190 (1993)[621] K Zyczkowski Squeezed states in a quantum chaotic system J Phys A Math Theor 22
of SU(11) 81 296 297HilbertClowast-modules 164holomorphic 140nonholomorphic 151nonlinear 146of affine Galilei group 505of affine Poincareacute group 509of affine Weyl-Heisenberg group GaWH
497of compact semisimple Lie groups 174of Euclidean group E(n) 266of Galilei group G (11) 290of isochronous Galilei group 237of non-semisimple Lie groups 179of noncompact semisimple Lie groups 177of Poincareacute group Puarr
+(11) 283massless case 288
of Poincareacute group Puarr+(13) 279
of Schroumldinger group 508quasi-coherent states 186quaternionic 164
ST Ali et al Coherent States Wavelets and Their Generalizations Theoreticaland Mathematical Physics DOI 101007978-1-4614-8535-3copy Springer Science+Business Media New York 2014
573
574 Index
coherent states (CS) (cont)spin or SU(2) 175square integrable covariant 166 180 264vector (VCS) 73 108 112 170weighted 184 523
of affine Weyl-Heisenberg group GaWH497
of Poincareacute group Puarr+(11) 284
cohomology group 393 403coboundaries 403cochains 402cocycle 403
algebraic 387Cauchy 418Cauchy-Paul 354 419 425conical 418difference 417 462directional 416 440kinematical 499local 488metabolite-based 355 374minimal uncertainty 425multiselective 440on a graph 493on the sphere S
2 458on the sphere S
n 479on the torus T2 481steerable 439von Mises 440
wedgelet transform 455Wigner function 322Wigner-Ville transform 349Windowed Fourier or Gabor transform 349
ZZak transform 518
References
A Books and Theses
B Articles
Index
References 553
[164] K Bouyoucef D Fraix-Burnaix S Roques Interactive deconvolution with error analysis(IDEA) in astronomical imaging Application to aberrated HST images on SN1987A M87and 3C66B Astron Astroph Suppl Ser 121 1ndash6 (1997)
[165] A Bouzouina S De Biegravevre Equipartition of the eigenfunctions of quantized ergodic mapson the torus Commun Math Phys 178 83ndash105 (1996)
[166] P Brault J-P Antoine A spatio-temporal Gaussian-Conical wavelet with high apertureselectivity for motion and speed analysis Appl Comput Harmon Anal 34 148ndash161(2012)
[167] A Briguet S Cavassila D Graveron-Demilly Suppression of huge signals using theCadzow enhancement procedure The NMR Newslett 440 26 (1995)
[168] CM Brislawn Fingerprints go digital Notices Amer Math Soc 42 1278ndash1283 (1995)[169] CM Brislawn On the group-theoretic structure of lifted filter banks in Excursions in
Harmonic Analysis vol 1 2 ed by TD Andrews R Balan JJ Benedetto W CzajaKA Okoudjou (Birkhaumluser Boston 2013) pp 113ndash135
[170] F Bruhat Sur les repreacutesentations induites des groupes de Lie Bull Soc Math France 8497ndash205 (1956)
[171] T Buumllow Multiscale image processing on the sphere in DAGM-Symposium (2002) pp609ndash617
[172] C Burdik C Frougny J-P Gazeau R Krejcar Beta-integers as natural counting systemsfor quasicrystals J Phys A Math Gen 31 6449ndash6472 (1998)
[173] KE Cahill Coherent-state representations for the photon density Phys Rev 138 B1566ndash1576 (1965)
[174] KE Cahill R Glauber Density operators and quasiprobability distributions Phys Rev177 1882ndash1902 (1969)
[175] KE Cahill R Glauber Ordered expansions in boson amplitude operators Phys Rev 1771857ndash1881 (1969)
[176] AR Calderbank I Daubechies W Sweldens BL Yeo Wavelets that map integers tointegers Appl Comput Harmon Anal 5 332ndash369 (1998)
[177] M Calixto J Guerrero Wavelet transform on the circle and the real line A unified group-theoretical treatment Appl Comput Harmon Anal 21 204ndash229 (2006)
[178] M Calixto E Peacuterez-Romero Extended MacMahon-Schwingerrsquos master theorem andconformal wavelets in complex Minkowski space Appl Comput Harmon Anal 31 143ndash168 (2011)
[179] M Calixto J Guerrero D Rosca Wavelet transform on the torus A group-theoreticalapproach preprint (2013)
[180] EJ Candegraves Harmonic analysis of neural networks Appl Comput Harmon Anal 6 197ndash218 (1999)
[181] EJ Candegraves Ridgelets and the representation of mutilated Sobolev functions SIAM JMath Anal 33 347ndash368 (2001)
[182] EJ Candegraves L Demanet Curvelets and Fourier integral operators CR Acad Sci ParisSeacuter I Math 336 395ndash398 (2003)
[183] EJ Candegraves L Demanet The curvelet representation of wave propagators is optimallysparse Commun Pure Appl Math 58 1472ndash1528 (2004)
[184] EJ Candegraves L Demanet The curvelet representation of wave propagators is optimallysparse Commun Pure Appl Math 58 1472ndash1528 (2005)
[185] EJ Candegraves DL Donoho Curvelets ndash A surprisingly effective nonadaptive representationfor objects with edges in Curves and Surfaces ed by LL Schumaker et al (VanderbiltUniversity Press Nashville TN 1999)
[186] EJ Candegraves DL Donoho Ridgelets A key to higher-dimensional intermittency PhilTrans R Soc Lond A 357 2495ndash2509 (1999)
[187] EJ Candegraves DL Donoho Curvelets multiresolution representation and scaling laws inWavelet Applications in Signal and Image Processing VIII ed by A Aldroubi A LaineM Unser SPIE Proceedings vol 4119 (SPIE Bellingham WA 2000) pp 1ndash12
554 References
[188] EJ Candegraves DL Donoho Recovering edges in ill-posed inverse problems Optimality ofcurvelet frames Ann Statist 30 784ndash842 (2002)
[189] EJ Candegraves DL Donoho New tight frames of curvelets and optimal representations ofobjects with piecewise C2 singularities Commun Pure Appl Math 57 219ndash266 (2004)
[190] EJ Candegraves DL Donoho Continuous curvelet transform I Resolution of the wavefrontset II Discretization and frames Appl Comput Harmon Anal 19 162ndash197 198ndash222(2005)
[191] EJ Candegraves F Guo New multiscale transforms minimum total variationsynthesisApplications to edge-preserving image reconstruction Signal Proc 82 1519ndash1543 (2002)
[192] EJ Candegraves L Demanet D Donoho L Ying Fast discrete curvelet transforms MultiscaleModel Simul 5 861ndash899 (2006)
[193] AL Carey Square integrable representations of non-unimodular groups Bull AustrMath Soc 15 1ndash12 (1976)
[194] AL Carey Group representations in reproducing kernel Hilbert spaces Rep Math Phys14 247ndash259 (1978)
[195] P Carruthers MM Nieto Phase and angle variables in quantum mechanics Rev ModPhys 40 411ndash440 (1968)
[196] PG Casazza G Kutyniok Frames of subspaces in Wavelets Frames and Operator The-ory Contemporary Mathematics vol 345 (American Mathematical Society ProvidenceRI 2004) pp 87ndash113
[197] PG Casazza D Han DR Larson Frames for Banach spaces Contemp Math 247 149ndash182 (1999)
[198] P Casazza O Christensen S Li A Lindner Riesz-Fischer sequences and lower framebounds Z Anal Anwend 21 305ndash314 (2002)
[199] PG Casazza G Kutyniok S Li Fusion frames and distributed processing ApplComputHarmon Anal 25 114ndash132 (2008)
[200] DPL Castrigiano RW Henrichs Systems of covariance and subrepresentations ofinduced representations Lett Math Phys 4 169ndash175 (1980)
[201] U Cattaneo Densities of covariant observables J Math Phys 23 659ndash664 (1982)[202] A Cerioni L Genovese I Duchemin Th Deutsch Accurate complex scaling of three
dimensional numerical potentials Preprint (2013) arXiv13036439v2[203] S-J Chang K-J Shi Evolution and exact eigenstates of a resonant quantum system Phys
Rev A 34 7ndash22 (1986)[204] SHH Chowdhury ST Ali All the groups of signal analysis from the (1+1) affine Galilei
group J Math Phys 52 103504 (2011)[205] SL Chown Antarctic marine biodiversity and deep-sea hydrothermal vents PLoS Biol
10 1ndash4 (2012)[206] C Cishahayo S De Biegravevre On the contraction of the discrete series of SU(11) Ann Inst
Fourier (Grenoble) 43 551ndash567 (1993)[207] M Clerc and S Mallat Shape from texture and shading with wavelets in Dynamical
Systems Control Coding Computer Vision Progress in Systems and Control Theory 25393ndash417 (1999)
[208] L Cohen General phase-space distribution functions J Math Phys 7 781ndash786 (1966)[209] A Cohen I Daubechies J-C Feauveau Biorthogonal bases of compactly supported
wavelets Commun Pure Appl Math 45 485ndash560 (1992)[210] R Coifman Y Meyer MV Wickerhauser Wavelet analysis and signal processing
in Wavelets and Their Applications ed by MB Ruskai G Beylkin R CoifmanI Daubechies S Mallat Y Meyer L Raphael (Jones and Bartlett Boston 1992)pp 153ndash178
[211] R Coifman Y Meyer MV Wickerhauser Entropy-based algorithms for best basisselection IEEE Trans Inform Theory 38 713ndash718 (1992)
[212] R Coquereaux A Jadczyk Conformal theories curved spaces relativistic wavelets andthe geometry of complex domains Rev Math Phys 2 1ndash44 (1990)
References 555
[213] A Coron L Vanhamme J-P Antoine P Van Hecke S Van Huffel The filtering approachto solvent peak suppression in MRS A critical review J Magn Reson 152 26ndash40 (2001)
[214] N Cotfas J-P Gazeau Finite tight frames and some applications (topical review) J PhysA Math Theor 43 193001 (2010)
[215] N Cotfas J-P Gazeau K Goacuterska Complex and real Hermite polynomials and relatedquantizations J Phys A Math Theor 43 305304 (2010)
[216] N Cotfas J-P Gazeau A Vourdas Finite-dimensional Hilbert space and frame quantiza-tion J Phys A Math Gen 44 175303 (2011)
[217] EMF Curado MA Rego-Monteiro LMCS Rodrigues Y Hassouni Coherent statesfor a degenerate system The hydrogen atom Physica A 371 16ndash19 (2006)
[218] S Dahlke P Maass The affine uncertainty principle in one and two dimensions CompMath Appl 30 293ndash305 (1995)
[219] S Dahlke W Dahmen E Schmidt I Weinreich Multiresolution analysis and wavelets onS
2 and S3 Numer Funct Anal Optim 16 19ndash41 (1995)
[220] S Dahlke V Lehmann G Teschke Applications of wavelet methods to the analysis ofmeteorological radar data - An overview Arabian J Sci Eng 28 3ndash44 (2003)
[221] S Dahlke G Kutyniok P Maass C Sagiv H-G Stark G Teschke The uncertaintyprinciple associated with the continuous shearlet transform Int J Wavelets MultiresolutInf Process 6 157ndash181 (2008)
[222] S Dahlke G Kutyniok G Steidl G Teschke Shearlet coorbit spaces and associatedBanach frames Appl Comput Harmon Anal 27 195ndash214 (2009)
[223] S Dahlke G Steidl G Teschke The continuous shearlet transform in arbitrary spacedimensions J Fourier Anal Appl 16 340ndash364 (2010)
[224] S Dahlke G Steidl G Teschke Shearlet coorbit spaces Compactly supported analyzingshearlets traces and embeddings J Fourier Anal Appl 17 1232ndash1355 (2011)
[225] T Dallard GR Spedding 2-D wavelet transforms Generalisation of the Hardy space andapplication to experimental studies Eur J Mech BFluids 12 107ndash134 (1993)
[226] C Daskaloyannis Generalized deformed oscillator and nonlinear algebras J Phys AMath Gen 24 L789ndashL794 (1991)
[227] C Daskaloyannis K Ypsilantis A deformed oscillator with Coulomb energy spectrumJ Phys A Math Gen 25 4157ndash4166 (1992)
[228] I Daubechies On the distributions corresponding to bounded operators in the Weylquantization Commun Math Phys 75 229ndash238 (1980)
[229] I Daubechies and A Grossmann An integral transform related to quantization I J MathPhys 21 2080ndash2090 (1980)
[230] I Daubechies A Grossmann J Reignier An integral transform related to quantization IIJ Math Phys 24 239ndash254 (1983)
[231] I Daubechies Orthonormal bases of compactly supported wavelets Commun Pure ApplMath 41 909ndash996 (1988)
[232] I Daubechies The wavelet transform time-frequency localisation and signal analysisIEEE Trans Inform Theory 36 961ndash1005 (1990)
[233] I Daubechies S Maes A nonlinear squeezing of the continuous wavelet transform basedon auditory nerve models in Wavelets in Medicine and Biology ed by A Aldroubi MUnser (CRC Press Boca Raton 1996) pp 527ndash546
[234] I Daubechies A Grossmann Y Meyer Painless nonorthogonal expansions J Math Phys27 1271ndash1283 (1986)
[235] ER Davies Introduction to texture analysis in Handbook of texture analysis ed by MMirmehdi X Xie J Suri (World Scientific Singapore 2008) pp 1ndash31
[236] R De Beer D van Ormondt FTAW Wajer S Cavassila D Graveron-Demilly S VanHuffel SVD-based modelling of medical NMR signals in SVD and Signal ProcessingIII Algorithms Architectures and Applications ed by M Moonen B De Moor (Elsevier(North-Holland) Amsterdam 1995) pp 467ndash474
[237] S De Biegravevre Coherent states over symplectic homogeneous spaces J Math Phys 301401ndash1407 (1989)
556 References
[238] S De Biegravevre JA Gonzalez Semi-classical behaviour of the Weyl correspondence on thecircle in Group-Theoretical Methods in Physics (Proc Salamanca 1992) ed by M delOlmo M Santander J Mateos Guilarte (CIEMAT Madrid 1993) pp 343ndash346
[239] S De Biegravevre JA Gonzaacutelez Semiclassical behaviour of coherent states on the circle inQuantization and Coherent States Methods in Physics ed by A Odzijewicz et al (WorldScientific Singapore 1993)
[240] S De Biegravevre AE Gradechi Quantum mechanics and coherent states on the anti-de Sitterspace-time and their Poincareacute contraction Ann Inst H Poincareacute 57 403ndash428 (1992)
[241] J Deenen C Quesne Dynamical group of collective states I II III J Math Phys 23878ndash889 2004ndash2015 (1982)
[242] J Deenen C Quesne Dynamical group of collective states I II III J Math Phys 251638ndash1650 (1984)
[243] J Deenen C Quesne Partially coherent states of the real symplectic group J Math Phys25 2354ndash2366 (1984)
[244] J Deenen C Quesne Boson representations of the real symplectic group and theirapplication to the nuclear collective model J Math Phys 26 2705ndash2716 (1985)
[245] R Delbourgo Minimal uncertainty states for the rotation and allied groups J Phys AMath Gen 10 1837ndash1846 (1977)
[246] R Delbourgo J R Fox Maximum weight vectors possess minimal uncertainty J PhysA Math Gen 10 L233ndashL235 (1977)
[247] V Delouille J de Patoul J-F Hochedez L Jacques J-P Antoine Wavelet spectrumanalysis of EITSoHO images Solar Phys 228 301ndash321 (2005)
[248] N Delprat B Escudieacute P Guillemain R Kronland-Martinet P Tchamitchian B Tor-reacutesani Asymptotic wavelet and Gabor analysis Extraction of instantaneous frequenciesIEEE Trans Inform Theory 38 644ndash664 (1992)
[249] Th Deutsch L Genovese Wavelets for electronic structure calculations Collection SocFr Neut 12 33ndash76 (2011)
[250] B Dewitt Quantum theory of gravity I The canonical theory Phys Rev 160 1113ndash1148(1967)
[251] RH Dicke Coherence in spontaneous radiation processes Phys Rev 93 99ndash110 (1954)[252] AN Dinkelaker AL MacKinnon Wavelets intermittency and solar flare hard X-rays 1
Local intermittency measure in cascade and avalanche scenarios Solar Phys 282 471ndash481(2013)
[253] AN Dinkelaker AL MacKinnon Wavelets intermittency and solar flare hard X-rays 2LIM analysis of high time resolution BATSE data Solar Phys 282 483ndash501 (2013)
[254] MN Do M Vetterli Contourlets in Beyond Wavelets ed by GV Welland (AcademicSan Diego 2003) pp 83ndash105
[255] MN Do M Vetterli The contourlet transform An efficient directional multiresolutionimage representation IEEE Trans Image Process 14 2091ndash2106 (2005)
[256] VV Dodonov Nonclassical states in quantum optics A ldquosqueezedrdquo review of the first 75years J Opt B Quant Semiclass Opot 4 R1ndashR33 (2002)
[257] DL Donoho Nonlinear wavelet methods for recovery of signals densities and spectrafrom indirect and noisy data in Different Perspectives on Wavelets Proceedings ofSymposia in Applied Mathematics vol 38 ed by I Daubechies (American MathematicalSociety Providence RI 1993) pp 173ndash205
[258] DL Donoho Wedgelets Nearly minimax estimation of edges Ann Stat 27 859ndash897(1999)
[259] DL Donoho X Huo Beamlet pyramids A new form of multiresolution analysis suitedfor extracting lines curves and objects from very noisy image data in SPIE Proceedingsvol 5914 (SPIE Bellingham WA 2005) pp 1ndash12
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[261] AH Dooley JW Rice Contractions of rotation groups and their representations MathProc Camb Phil Soc 94 509ndash517 (1983)
[262] AH Dooley JW Rice On contractions of semisimple Lie groups Trans Amer MathSoc 289 185ndash202 (1985)
[263] JR Driscoll DM Healy Computing Fourier transforms and convolutions on the 2-sphereAdv Appl Math 15 202ndash250 (1994)
[264] H Drissi F Regragui J-P Antoine M Bennouna Wavelet transform analysis of visualevoked potentials Some preliminary results ITBM-RBM 21 84ndash91 (2000)
[265] RJ Duffin AC Schaeffer A class of nonharmonic Fourier series Trans Amer MathSoc 72 341ndash366 (1952)
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[268] M Duval-Destin M-A Muschietti B Torreacutesani Continuous wavelet decompositionsmultiresolution and contrast analysis SIAM J Math Anal 24 739ndash755 (1993)
[269] SJL van Eindhoven JLH Meyers New orthogonality relations for the Hermitepolynomials and related Hilbert spaces J Math Anal Appl 146 89ndash98 (1990)
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[274] M Farge Wavelet transforms and their applications to turbulence Annu Rev Fluid Mech24 395ndash457 (1992)
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[280] M Flensted-Jensen Discrete series for semisimple symmetric spaces Ann of Math 111253ndash311 (1980)
[281] K Flornes A Grossmann M Holschneider B Torreacutesani Wavelets on discrete fieldsAppl Comput Harmon Anal 1 137ndash146 (1994)
[282] V Fock Zur Theorie der Wasserstoffatoms Zs f Physik 98 145ndash54 (1936)[283] M Fornasier H Rauhut Continuous frames function spaces and the discretization
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[286] W Freeden T Maier S Zimmermann A survey on wavelet methods for (geo)applicationsRevista Mathematica Complutense 16 (2003) 277ndash310
[287] W Freeden M Schreiner Biorthogonal locally supported wavelets on the sphere based onzonal kernel functions J Fourier Anal Appl 13 693ndash709 (2007)
[288] WT Freeman EH Adelson The design and use of steerable filters IEEE Trans PatternAnal Machine Intell 13 891ndash906 (1991)
[289] L Freidel ER Livine U(N) coherent states for loop quantum gravity J Math Phys 52052502 (2011)
[290] J Froment S Mallat Arbitrary low bit rate image compression using wavelets in Progressin Wavelet Analysis and Applications (Proc Toulouse 1992) ed by Y Meyer S Roques(Ed Frontiegraveres Gif-sur-Yvette 1993) pp 413ndash418 and references therein
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[292] H Fuumlhr Wavelet frames and admissibility in higher dimensions J Math Phys 37 6353ndash6366 (1996)
[293] H Fuumlhr M Mayer Continuous wavelet transforms from semidirect products Cyclicrepresentations and Plancherel measure J Fourier Anal Appl 8 375ndash396 (2002)
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127ndash147 (2003)[296] E Galapon Paulirsquos theorem and quantum canonical pairs The consistency of a bounded
self-adjoint time operator canonically conjugate to a Hamiltonian with non-empty pointspectrum Proc R Soc Lond A 458 451ndash472 (2002)
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[303] J-P Gazeau Four Euclidean conformal group approach to the multiphoton processes in theH atom J Math Phys 23 156ndash164 (1982)
[304] J-P Gazeau A remarkable duality in one particle quantum mechanics between someconfining potentials and (R+Linfin
ε ) potentials Phys Lett 75A 159ndash163 (1980)[305] J-P Gazeau SL(2R)-coherent states and integrable systems in classical and quantum
physics in Quantization Coherent States and Complex Structures ed by J-P AntoineST Ali W Lisiecki IM Mladenov A Odzijewicz (Plenum Press New York and London1995) pp 147ndash158
[306] J-P Gazeau S Graffi Quantum harmonic oscillator A relativistic and statistical point ofview Boll Unione Mat Ital 11-A 815ndash839 (1997)
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[313] J-P Gazeau J Patera Tau-wavelets of Haar J Phys A Math Gen 29 4549ndash4559 (1996)[314] J-P Gazeau W Piechocki Coherent states quantization of a particle in de Sitter space
J Phys A Math Gen 37 6977ndash6986 (2004)[315] J-P Gazeau J Renaud Lie algorithm for an interacting SU(11) elementary system and its
contraction Ann Phys (NY) 222 89ndash121 (1993)[316] J-P Gazeau J Renaud Relativistic harmonic oscillator and space curvature Phys Lett A
179 67ndash71 (1993)[317] J-P Gazeau V Spiridonov Toward discrete wavelets with irrational scaling factor J Math
plane J Phys A Math Theor 44 495201 (2011)[319] J-P Gazeau J Patera E Pelantovaacute Tau-wavelets in the plane J Math Phys 39 4201ndash
4212 (1998)[320] J-P Gazeau M Andrle C Burdiacutek R Krejcar Wavelet multiresolutions for the Fibonacci
chain J Phys A Math Gen 33 L47ndashL51 (2000)[321] J-P Gazeau M Andrle C Burdiacutek Bernuau spline wavelets and sturmian sequences
J Fourier Anal Appl 10 269ndash300 (2004)[322] J-P Gazeau F-X Josse-Michaux P Monceau Finite dimensional quantizations of the
(q p) plane new space and momentum inequalities Int J Modern Phys B 20 1778ndash1791 (2006)
[323] J-P Gazeau J Mourad J Queacuteva Fuzzy de Sitter space-times via coherent statesquantization in Proceedings of the XXVIth Colloquium on Group Theoretical Methodsin Physics New York 2006 ed by J Birman S Catto B Nicolescu (Canopus PublishingLimited London 2009)
[324] D Geller A Mayeli Continuous wavelets on compact manifolds Math Z 262 895ndash927(2009)
[325] D Geller A Mayeli Nearly tight frames and space-frequency analysis on compactmanifolds Math Z 263 235ndash264 (2009)
[326] L Genovese B Videau M Ospici Th Deutsch S Goedecker J-F Mhaut Daubechieswavelets for high performance electronic structure calculations The BigDFT project CR Mecanique 339 149ndash164 (2011)
[327] G Gentili C Stoppato Power series and analyticity over the quaternions Math Ann 352113ndash131 (2012)
[328] G Gentili DC Struppa A new theory of regular functions of a quaternionic variable AdvMath 216 279ndash301 (2007)
[329] C Geyer K Daniilidis Catadioptric projective geometry Int J Comput Vision 45 223ndash243 (2001)
[330] R Gilmore Geometry of symmetrized states Ann Phys (NY) 74 391ndash463 (1972)[331] R Gilmore On properties of coherent states Rev Mex Fis 23 143ndash187 (1974)[332] J Ginibre Statistical ensembles of complex quaternion and real matrices J Math Phys
6 440ndash449 (1965)[333] RJ Glauber The quantum theory of optical coherence Phys Rev 130 2529ndash2539 (1963)
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[335] J Glimm Locally compact transformation groups Trans Amer Math Soc 101 124ndash138(1961)
[336] R Godement Sur les relations drsquoorthogonaliteacute de V Bargmann C R Acad Sci Paris 255521ndash523 657ndash659 (1947)
[337] C Gonnet B Torreacutesani Local frequency analysis with two-dimensional wavelet trans-form Signal Proc 37 389ndash404 (1994)
[338] JA Gonzalez MA del Olmo Coherent states on the circle J Phys A Math Gen 318841ndash8857 (1998)
[339] XGonze B Amadon et al ABINIT First-principles approach to material and nanosystemproperties Computer Physics Comm 180 2582ndash2615 (2009)
[340] KM Gograverski E Hivon AJ Banday BD Wandelt FK Hansen M Reinecke MBartelmann HEALPix A framework for high-resolution discretization and fast analysisof data distributed on the sphere Astrophys J 622 759ndash771 (2005)
[341] P Goupillaud A Grossmann J Morlet Cycle-octave and related transforms in seismicsignal analysis Geoexploration 23 85ndash102 (1984)
[342] KH Groumlchenig A new approach to irregular sampling of band-limited functions in RecentAdvances in Fourier Analysis and Its applications ed by JS Byrnes JL Byrnes (KluwerDordrecht 1990) pp 251ndash260
[343] KH Groumlchenig Gabor analysis over LCA groups in Gabor Analysis and Algorithms ndashTheory and Applications ed by HG Feichtinger T Strohmer (Birkhaumluser Boston-Basel-Berlin 1998) pp 211ndash231
[344] HJ Groenewold On the principles of elementary quantum mechanics Physica 12 405ndash460 (1946)
[345] P Grohs Continuous shearlet tight frames J Fourier Anal Appl 17 506ndash518 (2011)[346] P Grohs G Kutyniok Parabolic molecules preprint TU Berlin (2012)[347] M Grosser A note on distribution spaces on manifolds Novi Sad J Math 38 121ndash128
(2008)[348] A Grossmann Parity operator and quantization of δ -functions Commun Math Phys 48
191ndash194 (1976)[349] A Grossmann J Morlet Decomposition of Hardy functions into square integrable
wavelets of constant shape SIAM J Math Anal 15 723ndash736 (1984)[350] A Grossmann J Morlet Decomposition of functions into wavelets of constant shape and
related transforms in Mathematics + Physics Lectures on recent results I ed by L Streit(World Scientific Singapore 1985) pp 135ndash166
[351] A Grossmann J Morlet T Paul Integral transforms associated to square integrablerepresentations I General results J Math Phys 26 2473ndash2479 (1985)
[352] A Grossmann J Morlet T Paul Integral transforms associated to square integrablerepresentations II Examples Ann Inst H Poincareacute 45 293ndash309 (1986)
[353] A Grossmann R Kronland-Martinet J Morlet Reading and understanding the contin-uous wavelet transform in Wavelets Time-Frequency Methods and Phase Space (ProcMarseille 1987) ed by J-M Combes A Grossmann P Tchamitchian 2nd edn (SpringerBerlin 1990) pp 2ndash20
[354] P Guillemain R Kronland-Martinet B Martens Estimation of spectral lines with helpof the wavelet transform Application in NMR spectroscopy in Wavelets and Applications(Proc Marseille 1989) ed by Y Meyer (Masson and Springer Paris and Berlin 1991) pp38ndash60
[355] H de Guise M Bertola Coherent state realizations of su(n+ 1) on the n-torus J MathPhys 43 3425ndash3444 (2002)
[356] K Guo D Labate Representation of Fourier Integral Operators using shearlets J FourierAnal Appl 14 327ndash371 (2008)
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[357] K Guo G Kutyniok D Labate Sparse multidimensional representations usinganisotropic dilation and shear operators in Wavelets and Spines (Athens GA 2005)(Nashboro Press Nashville TN 2006) pp 189ndash201
[358] K Guo D Labate W-Q Lim G Weiss E Wilson Wavelets with composite dilationsand their MRA properties Appl Comput Harmon Anal 20 202ndash236 (2006)
[359] EA Gutkin Overcomplete subspace systems and operator symbols Funct Anal Appl 9260ndash261 (1975)
[360] G Gyoumlrgyi Integration of the dynamical symmetry groups for the 1r potential Acta PhysAcad Sci Hung 27 435ndash439 (1969)
[361] BC Hall The Segal-Bargmann ldquoCoherent Staterdquo transform for compact Lie groups JFunct Analysis 122 103ndash151 (1994)
[362] B Hall JJ Mitchell Coherent states on spheres J Math Phys 43 1211ndash1236 (2002)[363] DK Hammond P Vandergheynst R Gribonval Wavelets on graphs via spectral theory
Appl Comput Harmon Anal 30 129ndash150 (2011)[364] Y Hassouni EMF Curado MA Rego-Monteiro Construction of coherent states for
physical algebraic system Phys Rev A 71 022104 (2005)[365] J He H Liu Admissible wavelets associated with the affine automorphism group of the
Siegel upper half-plane J Math Anal Appl 208 58ndash70 (1997)[366] J He H Liu Admissible wavelets associated with the classical domain of type one
Approx Appl 14 (1998) 89ndash105[367] J He L Peng Wavelet transform on the symmetric matrix space preprint Beijing (1997)
(unpublished)[368] J He L Peng Admissible wavelets on the unit disk Complex Variables 35 109ndash119
(1998)[369] DM Healy Jr FE Schroeck Jr On informational completeness of covariant localization
observables and Wigner coefficients J Math Phys 36 453ndash507 (1995)[370] C Heil D Walnut Continuous and discrete wavelet transforms SIAM Review 31 628ndash
666 (1989)[371] K Hepp EH Lieb On the superradiant phase transition for molecules in a quantized
radiation field The Dicke maser model Ann Phys (NY) 76 360ndash404 (1973)[372] K Hepp EH Lieb Equilibrium statistical mechanics of matter interacting with the
quantized radiation field Phys Rev A 8 2517ndash2525 (1973)[373] JA Hogan JD Lakey Extensions of the Heisenberg group by dilations and frames Appl
Comput Harmon Anal 2 174ndash199 (1995)[374] AL Hohoueacuteto K Thirulogasanthar ST Ali J-P Antoine Coherent states lattices and
square integrability of representations J Phys A Math Gen36 11817ndash11835 (2003)[375] M Holschneider On the wavelet transformation of fractal objects J Stat Phys 50 963ndash
993 (1988)[376] M Holschneider Wavelet analysis on the circle J Math Phys 31 39ndash44 (1990)[377] M Holschneider Inverse Radon transforms through inverse wavelet transforms Inv Probl
7 853ndash861 (1991)[378] M Holschneider Localization properties of wavelet transforms J Math Phys 34 3227ndash
3244 (1993)[379] M Holschneider General inversion formulas for wavelet transforms J Math Phys 34
4190ndash4198 (1993)[380] M Holschneider Wavelet analysis over abelian groups Applied Comput Harmon Anal
2 52ndash60 (1995)[381] M Holschneider Continuous wavelet transforms on the sphere J Math Phys 37 4156ndash
4165 (1996)[382] M Holschneider I Iglewska-Nowak Poisson wavelets on the sphere J Fourier Anal
Appl 13 405ndash419 (2007)
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[383] M Holschneider R Kronland-Martinet J Morlet P Tchamitchian A real-time algorithmfor signal analysis with the help of wavelet transform in Wavelets Time-FrequencyMethods and Phase Space (Proc Marseille 1987) ed by J-M Combes A Grossmann PTchamitchian 2nd edn (Springer Berlin 1990) pp 286ndash297
[384] M Holschneider P Tchamitchian Pointwise analysis of Riemannrsquos ldquonondifferentiablerdquofunction Invent Math 105 157ndash175 (1991)
[385] GR Honarasa MK Tavassoly M Hatami R Roknizadeh Nonclassical properties ofcoherent states and excited coherent states for continuous spectra J Phys A Math Theor44 085303 (2011)
[386] M Hongoh Coherent states associated with the continuous spectrum of noncompactgroups J Math Phys 18 2081ndash2085 (1977)
[387] A Horzela FH Szafraniec A measure free approach to coherent states J Phys A MathGen 45 244018 (2012)
[388] W-L Hwang S Mallat Characterization of self-similar multifractals with waveletmaxima Appl Comput Harmon Anal 1 316ndash328 (1994)
[389] W-L Hwang C-S Lu P-C Chung Shape from texture Estimation of planar surfaceorientation through the ridge surfaces of continuous wavelet transform IEEE Trans ImageProc 7 773ndash780 (1998)
[390] I Iglewska-Nowak M Holschneider Frames of Poisson wavelets on the sphere ApplComput Harmon Anal 28 227ndash248 (2010)
[391] E Inoumlnuuml EP Wigner On the contraction of groups and their representations Proc NatAcad Sci U S 39 510ndash524 (1953)
[392] S Iqbal F Saif Generalized coherent states and their statistical characteristics in power-law potentials J Math Phys 52 082105 (2011)
[393] CJ Isham JR Klauder Coherent states for n-dimensional Euclidean groups E(n) andtheir application J MathPhys 32 607ndash620 (1991)
[394] L Jacques J-P Antoine Multiselective pyramidal decomposition of images Wavelets withadaptive angular selectivity Int J Wavelets Multires Inform Proc 5 785ndash814 (2007)
[395] L Jacques L Duval C Chaux G Peyreacute A panorama on multiscale geometric rep-resentations intertwining spatial directional and frequency selectivity Signal Proc 912699ndash2730 (2011)
[396] HR Jalali M K Tavassoly On the ladder operators and nonclassicality of generalizedcoherent state associated with a particle in an infinite square well preprint (2013)arXiv13034100v1 [quant-ph]
[397] C Johnston On the pseudo-dilation representations of Flornes Grossmann Holschneiderand Torreacutesani Appl Comput Harmon Anal 3 377ndash385 (1997)
[398] G Kaiser Phase-space approach to relativistic quantum mechanics I Coherent staterepresentation for massive scalar particles J MathPhys 18 952ndash959 (1977)
[399] G Kaiser Phase-space approach to relativistic quantum mechanics II Geometrical aspectsJ MathPhys 19 502ndash507 (1978)
[400] C Kalisa B Torreacutesani N-dimensional affine Weyl-Heisenberg wavelets Ann Inst HPoincareacute 59 201ndash236 (1993)
[401] W Kaminski J Lewandowski T Pawłowski Quantum constraints Dirac observables andevolution group averaging versus the Schroumldinger picture in LQC Class Quant Grav 26245016 (2009)
[402] MR Karim ST Ali A relativistic windowed Fourier transform preprint ConcordiaUniversity Montreacuteal (1997) (unpublished)
[403] M R Karim ST Ali M Bodruzzaman A relativistic windowed Fourier transform inProceedings of IEEE SoutheastCon 2000 Nashville Tennessee pp 253ndash260 (2000)
[404] T Kawazoe Wavelet transforms associated to a principal series representation of semisim-ple Lie groups I II Proc Japan Acad Ser A ndash Math Sci 71 154ndash157 158ndash160 (1995)
[405] T Kawazoe Wavelet transform associated to an induced representation of SL(n+ 2R)Ann Inst H Poincareacute 65 1ndash13 (1996)
References 563
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[407] P Kittipoom G Kutyniok W-Q Lim Construction of compactly supported shearletframes Constr Approx 35 21ndash72 (2012)
[408] J Kiukas P Lahti K Ylinenc Phase space quantization and the operator moment problemJ Math Phys 47 072104 (2006)
[409] JR Klauder Continuous-representation theory I Postulates of continuous-representationtheory J Math Phys 4 1055ndash1058 (1963)
[410] JR Klauder Continuous-representation theory II Generalized relation between quantumand classical dynamics J Math Phys 4 1058ndash1073 (1963)
[411] JR Klauder Path integrals for affine variables in Functional Integration Theory andApplications ed by J-P Antoine E Tirapegui (Plenum Press New York and London1980) pp 101ndash119
[412] JR Klauder Are coherent states the natural language of quantum mechanics inFundamental Aspects of Quantum Theory ed by V Gorini A Frigerio NATO ASI Seriesvol B 144 (Plenum Press New York 1986) pp 1ndash12
[413] JR Klauder Quantization without quantization Ann Phys (NY) 237 147ndash160 (1995)[414] JR Klauder Coherent states for the hydrogen atom J Phys A Math Gen 29 L293ndash
L296 (1996)[415] JR Klauder An affinity for affine quantum gravity Proc Steklov Inst Math 272 169ndash176
(2011) and references therein[416] JR Klauder RF Streater A wavelet transform for the Poincareacute group J Math Phys 32
1609ndash1611 (1991)[417] JR Klauder RF Streater Wavelets and the Poincareacute half-plane J Math Phys 35 471ndash
478 (1994)[418] JR Klauder K Penson J-M Sixdeniers Constructing coherent states through solutions
of Stieltjes and Hausdorff moment problems Phys Rev A 64 013817 (2001)[419] A Kleppner RL Lipsman The Plancherel formula for group extensions Ann Ec Norm
Sup 5 459ndash516 (1972)[420] AB Klimov C Muntildeoz Coherent isotropic and squeezed states in a N-qubit system Phys
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Computer Science From Numbers and Languages to (Quantum) Cryptography - NATOSecurity through Science Series D - Information and Communication Security vol 7 edby J-P Gazeau J Nesetril B Rovan (IOS Press Washington DC 2007) pp 25ndash54
[422] S Kobayashi Irreducibility of certain unitary representations J Math Soc Japan 20 638ndash642 (1968)
[423] K Kowalski J Rembielinski LC Papaloucas Coherent states for a quantum particle ona circle J Phys A Math Gen 29 4149ndash4167 (1996)
[424] K Kowalski J Rembielinski Quantum mechanics on a sphere and coherent states J PhysA Math Gen 33 6035ndash6048 (2000)
[425] K Kowalski J Rembielinski The Bargmann representation for the quantum mechanicson a sphere J Math Phys 42 4138ndash4147 (2001)
[426] C Kristjansen J Plefka GW Semenoff M Staudacher A new double-scaling limit ofN = 4 super-Yang-Mills theory and pp-wave strings Nuclear Phys B 643 3ndash30 (2002)
[427] M Kulesh M Holschneider MS Diallo Geophysical wavelet library Applications ofthe continuous wavelet transform to the polarization and dispersion analysis of signalsComput Geosci 34 1732ndash1752 (2008)
[428] R Kunze On the Frobenius reciprocity theorem for square integrable representationsPacific J Math 53 465ndash471 (1974)
[429] Y Kuroda A Wada T Yamazaki K Nagayama Postacquisition data processing methodfor suppression of the solvent signal I J Magn Reson 84 604ndash610 (1989)
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[431] G Kutyniok D Labate Resolution of the wavefront set using continuous shearlets TransAmer Math Soc 361 2719ndash2754 (2009)
[432] G Kutyniok W-Q Lim Compactly supported shearlets are optimally sparse J ApproxTheory 163 1564ndash1589 (2011)
[433] D Labate W-Q Lim G Kutyniok G Weiss Sparse multidimensional representationusing shearlets in Wavelets XI (San Diego CA 2005) ed by M Papadakis A Laine MUnser SPIE Proceedings vol 5914 (SPIE Bellingham WA 2005) pp 254ndash262
[434] P Lahti J-P Pellonpaumlauml Continuous variable tomographic measurements Phys Lett A373 3435ndash3438 (2009)
[435] Lambertrsquos projection see WikipediahttpenwikipediaorgwikiLambert_azimuthal_equal-area_projection
[436] J-P Leduc F Mujica R Murenzi MJT Smith Missile-tracking algorithm using target-adapted spatio-temporal wavelets in Automatic Object Recognition VII SPIE Proceedingsvol 5914 (SPIE Bellingham WA 1997) pp 400ndash411
[437] J-P Leduc F Mujica R Murenzi MJT Smith Spatio-temporal wavelet transforms formotion tracking in IEEE ICASSP 1997 vol 4 (1997) pp 3013ndash3016
[438] J-P Leduc F Mujica R Murenzi MJT Smith Spatio-temporal continuous waveletsapplied to missile warhead detection and tracking in SPIE VCIP rsquo97 vol 3024 ed byJ Biemond EJ Delp (1997) pp 787ndash798
[439] B Leistedt JD McEwen Exact wavelets on the ball IEEE Trans Signal Proc 60 1564ndash1589 (2012)
[440] PG Lemarieacute Y Meyer Ondelettes et bases hilbertiennes Rev Math Iberoamer 2 1ndash18(1986)
[441] C Lemke A Schuck Jr J-P Antoine D Sima Metabolite-sensitive analysis of magneticresonance spectroscopic signals using the continuous wavelet transform Meas SciTechnol 22 (2011) Art 114013
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[443] J-M Leacutevy-Leblond Galilei group and Galilean invariance in Group Theory and ItsApplications vol II ed by EM Loebl (Academic New York 1971) pp 221ndash299
[444] J-M Leacutevy-Leblond On the conceptual nature of the physical constants Riv Nuovo Cim7 187ndash214 (1977)
[445] EH Lieb The classical limit of quantum spin systems Commun Math Phys 31 327ndash340(1973)
[446] G Lindblad B Nagel Continuous bases for unitary irreducible representations of SU(11)Ann Inst H Poincareacute 13 27ndash56 (1970)
[447] W Lisiecki Kaumlhler coherent states orbits for representations of semisimple Lie groupsAnn Inst H Poincareacute 53 857ndash890 (1990)
[448] A Lisowska Moment-based fast wedgelet transform J Math Imaging Vis 39 180ndash192(2011)
[449] H Liu L Peng Admissible wavelets associated with the Heisenberg group Pacific JMath 180 101ndash123 (1997)
[450] E Livine S Speziale Physical boundary state for the quantum tetrahedron Class QuantGrav 25 085003 (2008)
[451] F Low Complete sets of wave packets in A Passion for Physics ndash Essay in Honor ofGeoffrey Chew ed by C DeTar (World Scientific Singapore 1985) pp 17ndash22
[452] G Mack All unitary ray representations of the conformal group SU(22) with positiveenergy Commun Math Phys 55 1ndash28 (1977)
[453] GW Mackey Imprimitivity for representations of locally compact groups I Proc NatAcad Sci 35 537ndash545 (1949)
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[456] SG Mallat Multifrequency channel decompositions of images and wavelet models IEEETrans Acoust Speech Signal Proc 37 2091ndash2110 (1989)
[457] SG Mallat A theory for multiresolution signal decomposition The wavelet representa-tion IEEE Trans Pattern Anal Machine Intell 11 674ndash693 (1989)
[458] S Mallat W-L Hwang Singularity detection and processing with wavelets IEEE TransInform Theory 38 617ndash643 (1992)
[459] S Mallat Z Zhang Matching pursuits with time frequency dictionaries IEEE TransSignal Proc 41 3397ndash3415 (1993)
[460] S Mallat S Zhong Wavelet maxima representation in Wavelets and Applications (ProcMarseille 1989) ed by Y Meyer (Masson and Springer Paris and Berlin 1991) pp 207ndash284
[461] VI Manrsquoko G Marmo ECG Sudarshan F Zaccaria f -oscillators and non-linearcoherent states Phys Scr 55 528ndash541 (1997)
[462] D Marinucci D Pietrobon A Baldi P Baldi P Cabella G Kerkyacharian P Natoli DPicard N Vittorio Spherical needlets for CMB data analysis Mon Not R Astron Soc383 539ndash545 (2008)
[463] D Marion M Ikura A Bax Improved solvent suppression in one- and two-dimensionalNMR spectra by convolution of time-domain data J Magn Reson 84 425ndash430 (1989)
[464] Y Meyer Principe drsquoincertitude bases hilbertiennes et algegravebres drsquoopeacuterateurs SeacuteminaireBourbaki 662 (1985ndash1986)
[465] Y Meyer Principe drsquoincertitude bases hilbertiennes et algegravebres drsquoopeacuterateurs Asteacuterisque145ndash146 209ndash223 (1987)
[466] Y Meyer H Xu Wavelet analysis and chirps Appl Comput Harmon Anal 4 366ndash379(1997)
[467] L Michel Invariance in quantum mechanics and group extensions in Group TheoreticalConcepts and Methods in Elementary Particle Physics ed by F Guumlrsey (Gordon andBreach New York and London 1964) pp 135ndash200
[468] J Mickelsson J Niederle Contractions of representations of the de Sitter groupsCommun Math Phys 27 167ndash180 (1972)
[469] MM Miller Convergence of the Sudarshan expansion for the diagonal coherent-stateweight functional J Math Phys 9 1270ndash1274 (1968)
[470] V F Molchanov Harmonic analysis on homogeneous spaces in Representation Theoryand Noncommutative Harmonic Analysis II ed by AA Kirillov (Springer Berlin 1995)
[471] MI Monastyrsky AM Perelomov Coherent states and symmetric spaces II Ann InstH Poincareacute 23 23ndash48 (1975)
[472] B Moran S Howard D Cochran Positive-operator-valued measures A general settingfor frames in Excursions in Harmonic Analysis vol 1 2 ed by TD Andrews R BalanJJ Benedetto W Czaja KA Okoudjou (Birkhaumluser Boston 2013) pp 49ndash64
[473] H Moscovici Coherent states representations of nilpotent Lie groups Commun MathPhys 54 63ndash68 (1977)
[474] H Moscovici A Verona Coherent states and square integrable representations Ann InstH Poincareacute 29 139ndash156 (1978)
[475] F Mujica R Murenzi MJT Smith J-P Leduc Robust tracking in compressed imagesequences J Electr Imaging 7 746ndash754 (1998)
[476] R Murenzi Wavelet transforms associated to the n-dimensional Euclidean group withdilations Signals in more than one dimension in Wavelets Time-Frequency Methodsand Phase Space (Proc Marseille 1987) ed by J-M Combes A Grossmann PTchamitchian 2nd edn (Springer Berlin 1990) pp 239ndash246
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[479] MA Naımark Dokl Akad Nauk SSSR 41 359ndash361 (1943) see also B Sz-NagyExtensions of linear transformations in Hilbert space which extend beyond this spaceAppendix to F Riesz B Sz-Nagy Functional Analysis (Frederick Ungar New York 1960)
[480] FJ Narcowich P Petrushev JD Ward Localized tight frames on spheres SIAM J MathAnal 38 574ndash594 (2006)
[481] M Nauenberg Quantum wave packets on Kepler elliptic orbits Phys Rev A 40 1133ndash1136 (1989)
[482] M Nauenberg C Stroud J Yeazell The classical limit of an atom Scient Amer 27024ndash29 (1994)
[483] H Neumann Transformation properties of observables Helv Phys Acta 45 811ndash819(1972)
[484] U Niederer The maximal kinematical invariance group of the free Schroumldinger equationHelv Phys Acta 45 802ndash881 (1972)
[485] MM Nieto LM Simmons Jr Coherent states for general potentials I Formalism IIConfining one-dimensional examples III Nonconfining one-dimensional examples PhysRev D 20 1321ndash1331 1332ndash1341 1342ndash1350 (1979)
[486] MM Nieto LM Simmons Jr Coherent states for general potentials Phys Rev Lett 41207ndash210 (1987)
[487] A Odzijewicz On reproducing kernels and quantization of states Commun Math Phys114 577ndash597 (1988)
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[490] A Odzijewicz M Horowski A Tereszkiewicz Integrable multi-boson systems andorthogonal polynomials J Phys A Math Gen 34 4353ndash4376 (2001)
[491] G Oacutelafsson B Oslashrsted The holomorphic discrete series for affine symmetric spaces JFunct Anal 81 126ndash159 (1988)
[492] G Oacutelafsson H Schlichtkrull Representation theory Radon transform and the heatequation on a Riemannian symmetric space Contemp Math 449 315ndash344 (2008)
[493] E Onofri A note on coherent state representations of Lie groups J Math Phys 16 1087ndash1089 (1975)
[494] E Onofri Dynamical quantization of the Kepler manifold J Math Phys 17 401ndash408(1976)
[495] D Oriti R Pereira L Sindoni Coherent states in quantum gravity A construction basedon the flux representation of loop quantum gravity J Phys A Math Theor 45 244004(2012)
[496] LC Papaloucas J Rembielinski W Tybor Vectorlike coherent states with noncompactstability group J Math Phys 30 2406ndash2410 (1989)
[497] Z Pasternak-Winiarski On the dependence of the reproducing kernel on the weight ofintegration J Funct Anal 94 110ndash134 (1990)
[498] Z Pasternak-Winiarski On reproducing kernels for holomorphic vector bundles inQuantization and Infinite Dimensional Systems (Proc Białowieza Poland 1993) ed by J-P Antoine ST Ali W Lisiecki IM Mladenov A Odzijewicz (Plenum Press New Yorkand London 1994) pp 109ndash112
[499] T Paul Affine coherent states and the radial Schroumldinger equation I preprint CPT-84P1710 (1984) (unpublished)
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[501] AM Perelomov On the completeness of a system of coherent states Theor Math Phys6 156ndash164 (1971)
[502] AM Perelomov Coherent states for arbitrary Lie group Commun Math Phys 26 222ndash236 (1972)
[503] AM Perelomov Coherent states and symmetric spaces Commun Math Phys 44 197ndash210 (1975)
[504] M Perroud Projective representations of the Schroumldinger group Helv Phys Acta 50 233ndash252 (1977)
[505] J Phillips A note on square-integrable representations J Funct Anal 20 83ndash92 (1975)[506] D Pietrobon P Baldi D Marinucci Integrated Sachs-Wolfe effect from the cross
correlation of WMAP3 year and the NRAO VLA sky survey data New results andconstraints on dark energy Phys Rev D 74 043524 (2006)
[507] WWF Pijnappel A van den Boogaart R de Beer D van Ormondt SVD-basedquantification of magnetic resonance signals J Magn Reson 97 122ndash134 (1992)
[508] V Pop D Rosca Generalized piecewise constant orthogonal wavelet bases on 2D-domains Appl Anal 90 715ndash723 (2011)
[509] G Poumlschl E Teller Bemerkungen zur Quantenmechanik des anharmonischen OszillatorsZ Physik 83 143ndash151 (1933)
[510] D Potts G Steidl M Tasche Kernels of spherical harmonics and spherical frames inAdvanced Topics in Multivariate Approximation ed by F Fontanella K Jetter PJ Laurent(World Scientific Singapore 1996) pp 287ndash301
[511] E Prugovecki Consistent formulation of relativistic dynamics for massive spin-zeroparticles in external fields Phys Rev D 18 3655ndash3673 (1978) (Appendix C)
[512] E Prugovecki Relativistic quantum kinematics on stochastic phase space for massiveparticles J MathPhys 19 2261ndash2270 (1978)
[513] C Quesne Coherent states of the real symplectic group in a complex analytic parametriza-tion I II J Math Phys 27 428ndash441 869ndash878 (1986)
[514] C Quesne Generalized vector coherent states of sp(2NR) vector operators and ofsp(2NR) sup u(N) reduced Wigner coefficients J Phys A Math Gen 24 2697ndash2714(1991)
[515] JM Radcliffe Some properties of spin coherent states J Phys A Math Gen 4 313ndash323(1971)
[516] A Rahimi A Najati YN Dehghan Continuous frames in Hilbert spaces Methods FunctAnal Topol 12 170ndash182 (2006)
[517] H Rauhut M Roumlsler Radial multiresolution in dimension three Constr Approx 22 193ndash218 (2005)
[518] JH Rawnsley Coherent states and Kaumlhler manifolds Quart J Math Oxford 28(2) 403ndash415 (1977)
[519] J Renaud The contraction of the SU(11) discrete series of representations by means ofcoherent states J Math Phys 37 3168ndash3179 (1996)
[520] A Reacutenyi Representations for real numbers and their ergodic properties Acta Math AcadSci Hungary 8(3ndash4) 477ndash493 (1957)
[521] D Robert La coheacuterence dans tous ses eacutetats SMF Gazette 132 (2012)[522] JE Roberts The Dirac bra and ket formalism J Math Phys 7 1097ndash1104 (1966)[523] JE Roberts Rigged Hilbert spaces in quantum mechanics Commun Math Phys 3 98ndash
119 (1966)[524] S Roques F Bourzeix K Bouyoucef Soft-thresholding technique and restoration of
3C273 jet Astrophys Space Sci Nr 239 297ndash304 (1996)[525] D Rosca Haar wavelets on spherical triangulations in Advances in Multiresolution for
Geometric Modelling ed by NA Dogson MS Floater MA Sabin (Springer Berlin2005) pp 407ndash419
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[527] D Rosca Wavelets defined on closed surfaces J Comput Anal Appl 8 121ndash132 (2006)[528] D Rosca Weighted Haar wavelets on the sphere Int J Wavelets Multiresol Inf Proc 5
501ndash511 (2007)[529] D Rosca Wavelet bases on the sphere obtained by radial projection J Fourier Anal Appl
13 421ndash434 (2007)[530] D Rosca Piecewise constant wavelets on triangulations obtained by 1ndash3 splitting Int J
Wavelets Multiresolut Inf Process 6 209ndash222 (2008)[531] D Rosca On a norm equivalence on L2(S2) Results Math 53 399ndash405 (2009)[532] D Rosca New uniform grids on the sphere Astron Astrophys 520 (2010) Art A63[533] D Rosca Uniform and refinable grids on elliptic domains and on some surfaces of
revolution Appl Math Comput 217 7812ndash7817 (2011)[534] D Rosca Wavelet analysis on some surfaces of revolution via area preserving projection
Appl Comput Harmon Anal 30 262ndash272 (2011)[535] D Rosca J-P Antoine Locally supported orthogonal wavelet bases on the sphere via
stereographic projection Math Probl Eng 2009 124904 (2009)[536] D Rosca J-P Antoine Constructing wavelet frames and orthogonal wavelet bases on the
sphere in Recent Advances in Signal Processing ed by S Miron (IN-TECH ViennaAustria and Rijeka Croatia 2010) pp 59ndash76
[537] D Rosca G Plonka Uniform spherical grids via area preserving projection from the cubeto the sphere J Comput Appl Math 236 1033ndash1041 (2011)
[538] D Rosca G Plonka An area preserving projection from the regular octahedron to thesphere Results Math 63 429ndash444 (2012)
[539] H Rossi M Vergne Analytic continuation of the holomorphic discrete series for a semi-simple Lie group Acta Math 136 1ndash59 (1976)
[540] DJ Rotenberg Application of Sturmian functions to the Schroedinger three-body prob-lem Elastic e+ndashH scattering Ann Phys (NY) 19 262ndash278 (1962)
[541] C Rovelli Zakopane lectures on loop gravity in Proceedings of 3rd Quantum Gravityand Quantum Geometry School 28 Febndash13 March 2011 (Zakopane Poland 2011)arXiv11023660v5
[542] C Rovelli S Speziale A semiclassical tetrahedron Class Quant Grav 23 5861ndash5870(2006)
[543] DJ Rowe Coherent state theory of the noncompact symplectic group J Math Phys 252662ndash2271 (1984)
[544] DJ Rowe Microscopic theory of the nuclear collective model Rep Prog Phys 48 1419ndash1480 (1985)
[545] DJ Rowe Vector coherent state representations and their inner products J Phys A MathGen 45 244003 (2012) (This paper belongs to the special issue [38])
[546] DJ Rowe J Repka Vector-coherent-state theory as a theory of induced representationsJ Math Phys 32 2614ndash2634 (1991)
[547] DJ Rowe G Rosensteel R Gilmore Vector coherent state representation theory J MathPhys 26 2787ndash2791 (1985)
[548] A Royer Phase states and phase operators for the quantum harmonic oscillator Phys RevA 53 70ndash108 (1996)
[549] J Saletan Contraction of Lie groups J Math Phys 2 1ndash21 (1961)[550] G Saracco A Grossmann P Tchamitchian Use of wavelet transforms in the study of
propagation of transient acoustic signals across a plane interface between two homoge-neous media in Wavelets Time-Frequency Methods and Phase Space (Proc Marseille1987) ed by J-M Combes A Grossmann P Tchamitchian 2nd edn (Springer Berlin1990) pp 139ndash146
[551] P Schroumlder W Sweldens Spherical wavelets Efficiently representing functions on thesphere in Computer Graphics Proceedings (SIGGRAPH95) (ACM Siggraph Los Angeles1995) pp 161ndash175
References 569
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[553] S Scodeller Oslash Rudjord FK Hansen D Marinucci D Geller A Mayeli IntroducingMexican needlets for CMB analysis Issues for practical applications and comparison withstandard needlets Astrophys J 733 (2011) Art 121
[554] H Scutaru Coherent states and induced representations Lett Math Phys 2 101ndash107(1977)
[555] B Simon Distributions and their Hermite expansions J Math Phys 12 140ndash148 (1971)[556] B Simon The classical moment problem as a self-adjoint finite difference operator Adv
Math 137 82ndash203 (1998)[557] R Simon ECG Sudarshan N Mukunda Gaussian pure states in quantum mechanics
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R61ndashR75 (2000)[559] E Slezak A Bijaoui G Mars Identification of structures from galaxy counts Use of the
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Proceedings of the 27th International Cosmic Ray Conference (ICRC 2001) (CopernicusGesellschaft DE 2001) pp 2923ndash2926
[579] T Thiemann Gauge field theory coherent states (GCS) 1 General properties Class QuantGrav 18 2025ndash2064 (2001)
[580] T Thiemann O Winkler Gauge field theory coherent states (GCS) 2 Peakednessproperties Class Quant Grav 18 2561ndash2636 (2001)
[581] T Thiemann O Winkler Gauge field theory coherent states (GCS) 3 Ehrenfest theoremsClass Quant Grav 18 4629ndash4682 (2001)
[582] T Thiemann O Winkler Gauge field theory coherent states (GCS) 4 Infinite tensorproduct and thermodynamical limit Class Quant Grav 18 4997ndash5054 (2001)
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simulation of an impact test using wavelets analytical and finite element models Int JSolids Struct 38 5481ndash5508 (2001)
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[598] DF Walls Squeezed states of light Nature 306 141ndash146 (1983)[599] YK Wang FT Hioe Phase transition in the Dicke maser model Phys Rev A 7 831ndash836
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Harmon Anal 10 1ndash26 (2001)[602] H Weyl Quantenmechanik und Gruppentheorie Z Phys 46 1ndash46 (1927)
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[610] K Woacutedkiewicz On the quantum mechanics of squeezed states J Modern Optics 34 941ndash948(1987)
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[613] HP Yuen Two-photon coherent states of the radiation field Phys Rev A 13 2226ndash2243(1976)
[614] J Zak Balian-Low theorem for Landau levels Phys Rev Lett 79 533ndash536 (1997)[615] J Zak Orthonormal sets of localized functions for a Landau level J Math Phys 39 4195ndash
4200 (1998) and references quoted there[616] AA Zakharova On the properties of generalized frames Math Notes 83 190ndash200 (2008)[617] W-M Zhang DH Feng R Gilmore Coherent states Theory and some applications Rev
Mod Phys 26 867ndash927 (1990)[618] I Zlatev W-M Zhang DH Feng Possibility that Schroumldingerrsquos conjecture for the
hydrogen atom coherent states is not attainable Phys Rev A 50 R1973ndashR1975 (1994)[619] WH Zurek Decoherence einselection and the quantum origins of the classical Rev Mod
Phys 75 715ndash775 (2003)[620] WH Zurek S Habib JP Paz Coherent states via decoherence Phys Rev Lett 70 1187ndash
1190 (1993)[621] K Zyczkowski Squeezed states in a quantum chaotic system J Phys A Math Theor 22
of SU(11) 81 296 297HilbertClowast-modules 164holomorphic 140nonholomorphic 151nonlinear 146of affine Galilei group 505of affine Poincareacute group 509of affine Weyl-Heisenberg group GaWH
497of compact semisimple Lie groups 174of Euclidean group E(n) 266of Galilei group G (11) 290of isochronous Galilei group 237of non-semisimple Lie groups 179of noncompact semisimple Lie groups 177of Poincareacute group Puarr
+(11) 283massless case 288
of Poincareacute group Puarr+(13) 279
of Schroumldinger group 508quasi-coherent states 186quaternionic 164
ST Ali et al Coherent States Wavelets and Their Generalizations Theoreticaland Mathematical Physics DOI 101007978-1-4614-8535-3copy Springer Science+Business Media New York 2014
573
574 Index
coherent states (CS) (cont)spin or SU(2) 175square integrable covariant 166 180 264vector (VCS) 73 108 112 170weighted 184 523
of affine Weyl-Heisenberg group GaWH497
of Poincareacute group Puarr+(11) 284
cohomology group 393 403coboundaries 403cochains 402cocycle 403
algebraic 387Cauchy 418Cauchy-Paul 354 419 425conical 418difference 417 462directional 416 440kinematical 499local 488metabolite-based 355 374minimal uncertainty 425multiselective 440on a graph 493on the sphere S
2 458on the sphere S
n 479on the torus T2 481steerable 439von Mises 440
wedgelet transform 455Wigner function 322Wigner-Ville transform 349Windowed Fourier or Gabor transform 349
ZZak transform 518
References
A Books and Theses
B Articles
Index
554 References
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[191] EJ Candegraves F Guo New multiscale transforms minimum total variationsynthesisApplications to edge-preserving image reconstruction Signal Proc 82 1519ndash1543 (2002)
[192] EJ Candegraves L Demanet D Donoho L Ying Fast discrete curvelet transforms MultiscaleModel Simul 5 861ndash899 (2006)
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[196] PG Casazza G Kutyniok Frames of subspaces in Wavelets Frames and Operator The-ory Contemporary Mathematics vol 345 (American Mathematical Society ProvidenceRI 2004) pp 87ndash113
[197] PG Casazza D Han DR Larson Frames for Banach spaces Contemp Math 247 149ndash182 (1999)
[198] P Casazza O Christensen S Li A Lindner Riesz-Fischer sequences and lower framebounds Z Anal Anwend 21 305ndash314 (2002)
[199] PG Casazza G Kutyniok S Li Fusion frames and distributed processing ApplComputHarmon Anal 25 114ndash132 (2008)
[200] DPL Castrigiano RW Henrichs Systems of covariance and subrepresentations ofinduced representations Lett Math Phys 4 169ndash175 (1980)
[201] U Cattaneo Densities of covariant observables J Math Phys 23 659ndash664 (1982)[202] A Cerioni L Genovese I Duchemin Th Deutsch Accurate complex scaling of three
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Fourier (Grenoble) 43 551ndash567 (1993)[207] M Clerc and S Mallat Shape from texture and shading with wavelets in Dynamical
Systems Control Coding Computer Vision Progress in Systems and Control Theory 25393ndash417 (1999)
[208] L Cohen General phase-space distribution functions J Math Phys 7 781ndash786 (1966)[209] A Cohen I Daubechies J-C Feauveau Biorthogonal bases of compactly supported
wavelets Commun Pure Appl Math 45 485ndash560 (1992)[210] R Coifman Y Meyer MV Wickerhauser Wavelet analysis and signal processing
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[211] R Coifman Y Meyer MV Wickerhauser Entropy-based algorithms for best basisselection IEEE Trans Inform Theory 38 713ndash718 (1992)
[212] R Coquereaux A Jadczyk Conformal theories curved spaces relativistic wavelets andthe geometry of complex domains Rev Math Phys 2 1ndash44 (1990)
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[215] N Cotfas J-P Gazeau K Goacuterska Complex and real Hermite polynomials and relatedquantizations J Phys A Math Theor 43 305304 (2010)
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[219] S Dahlke W Dahmen E Schmidt I Weinreich Multiresolution analysis and wavelets onS
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[221] S Dahlke G Kutyniok P Maass C Sagiv H-G Stark G Teschke The uncertaintyprinciple associated with the continuous shearlet transform Int J Wavelets MultiresolutInf Process 6 157ndash181 (2008)
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[223] S Dahlke G Steidl G Teschke The continuous shearlet transform in arbitrary spacedimensions J Fourier Anal Appl 16 340ndash364 (2010)
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[229] I Daubechies and A Grossmann An integral transform related to quantization I J MathPhys 21 2080ndash2090 (1980)
[230] I Daubechies A Grossmann J Reignier An integral transform related to quantization IIJ Math Phys 24 239ndash254 (1983)
[231] I Daubechies Orthonormal bases of compactly supported wavelets Commun Pure ApplMath 41 909ndash996 (1988)
[232] I Daubechies The wavelet transform time-frequency localisation and signal analysisIEEE Trans Inform Theory 36 961ndash1005 (1990)
[233] I Daubechies S Maes A nonlinear squeezing of the continuous wavelet transform basedon auditory nerve models in Wavelets in Medicine and Biology ed by A Aldroubi MUnser (CRC Press Boca Raton 1996) pp 527ndash546
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[236] R De Beer D van Ormondt FTAW Wajer S Cavassila D Graveron-Demilly S VanHuffel SVD-based modelling of medical NMR signals in SVD and Signal ProcessingIII Algorithms Architectures and Applications ed by M Moonen B De Moor (Elsevier(North-Holland) Amsterdam 1995) pp 467ndash474
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[249] Th Deutsch L Genovese Wavelets for electronic structure calculations Collection SocFr Neut 12 33ndash76 (2011)
[250] B Dewitt Quantum theory of gravity I The canonical theory Phys Rev 160 1113ndash1148(1967)
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Local intermittency measure in cascade and avalanche scenarios Solar Phys 282 471ndash481(2013)
[253] AN Dinkelaker AL MacKinnon Wavelets intermittency and solar flare hard X-rays 2LIM analysis of high time resolution BATSE data Solar Phys 282 483ndash501 (2013)
[254] MN Do M Vetterli Contourlets in Beyond Wavelets ed by GV Welland (AcademicSan Diego 2003) pp 83ndash105
[255] MN Do M Vetterli The contourlet transform An efficient directional multiresolutionimage representation IEEE Trans Image Process 14 2091ndash2106 (2005)
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[257] DL Donoho Nonlinear wavelet methods for recovery of signals densities and spectrafrom indirect and noisy data in Different Perspectives on Wavelets Proceedings ofSymposia in Applied Mathematics vol 38 ed by I Daubechies (American MathematicalSociety Providence RI 1993) pp 173ndash205
[258] DL Donoho Wedgelets Nearly minimax estimation of edges Ann Stat 27 859ndash897(1999)
[259] DL Donoho X Huo Beamlet pyramids A new form of multiresolution analysis suitedfor extracting lines curves and objects from very noisy image data in SPIE Proceedingsvol 5914 (SPIE Bellingham WA 2005) pp 1ndash12
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[262] AH Dooley JW Rice On contractions of semisimple Lie groups Trans Amer MathSoc 289 185ndash202 (1985)
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[286] W Freeden T Maier S Zimmermann A survey on wavelet methods for (geo)applicationsRevista Mathematica Complutense 16 (2003) 277ndash310
[287] W Freeden M Schreiner Biorthogonal locally supported wavelets on the sphere based onzonal kernel functions J Fourier Anal Appl 13 693ndash709 (2007)
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127ndash147 (2003)[296] E Galapon Paulirsquos theorem and quantum canonical pairs The consistency of a bounded
self-adjoint time operator canonically conjugate to a Hamiltonian with non-empty pointspectrum Proc R Soc Lond A 458 451ndash472 (2002)
[297] PL Garciacutea de Leacuteon J-P Gazeau Coherent state quantization and phase operator PhysLett A 361 301ndash304 (2007)
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[299] T Garidi J-P Gazeau E Huguet M Lachiegraveze Rey J Renaud Fuzzy spheres frominequivalent coherent states quantization J Phys A Math Theor 40 10225ndash10249 (2007)
[300] J-P Gazeau Four Euclidean conformal group in atomic calculations Exact analyticalexpressions for the bound-bound two-photon transition matrix elements in the H atomJ Math Phys 19 1041ndash1048 (1978)
[301] J-P Gazeau On the four Euclidean conformal group structure of the sturmian operatorLett Math Phys 3 285ndash292 (1979)
[302] J-P Gazeau Technique Sturmienne pour le spectre discret de lrsquoeacutequation de SchroumldingerJ Phys A Math Gen 13 3605ndash3617 (1980)
[303] J-P Gazeau Four Euclidean conformal group approach to the multiphoton processes in theH atom J Math Phys 23 156ndash164 (1982)
[304] J-P Gazeau A remarkable duality in one particle quantum mechanics between someconfining potentials and (R+Linfin
ε ) potentials Phys Lett 75A 159ndash163 (1980)[305] J-P Gazeau SL(2R)-coherent states and integrable systems in classical and quantum
physics in Quantization Coherent States and Complex Structures ed by J-P AntoineST Ali W Lisiecki IM Mladenov A Odzijewicz (Plenum Press New York and London1995) pp 147ndash158
[306] J-P Gazeau S Graffi Quantum harmonic oscillator A relativistic and statistical point ofview Boll Unione Mat Ital 11-A 815ndash839 (1997)
[307] J-P Gazeau V Hussin Poincareacute contraction of SU(11) Fock-Bargmann structure J PhysA Math Gen 25 1549ndash1573 (1992)
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[309] J-P Gazeau JR Klauder Coherent states for systems with discrete and continuousspectrum J Phys A Math Gen 32 123ndash132 (1999)
[310] J-P Gazeau P Monceau Generalized coherent states for arbitrary quantum systems inColloquium M Flato (Dijon Sept 99) vol II (Kluumlwer Dordrecht 2000) pp 131ndash144
[311] J-P Gazeau M Novello The question of mass in (Anti-) de Sitter space-times J Phys AMath Theor 41 304008 (2008)
[312] J-P Gazeau M del Olmo q-coherent states quantization of the harmonic oscillator AnnPhys (NY) 330 220ndash245 (2013) arXiv12071200 [quant-ph]
[313] J-P Gazeau J Patera Tau-wavelets of Haar J Phys A Math Gen 29 4549ndash4559 (1996)[314] J-P Gazeau W Piechocki Coherent states quantization of a particle in de Sitter space
J Phys A Math Gen 37 6977ndash6986 (2004)[315] J-P Gazeau J Renaud Lie algorithm for an interacting SU(11) elementary system and its
contraction Ann Phys (NY) 222 89ndash121 (1993)[316] J-P Gazeau J Renaud Relativistic harmonic oscillator and space curvature Phys Lett A
179 67ndash71 (1993)[317] J-P Gazeau V Spiridonov Toward discrete wavelets with irrational scaling factor J Math
plane J Phys A Math Theor 44 495201 (2011)[319] J-P Gazeau J Patera E Pelantovaacute Tau-wavelets in the plane J Math Phys 39 4201ndash
4212 (1998)[320] J-P Gazeau M Andrle C Burdiacutek R Krejcar Wavelet multiresolutions for the Fibonacci
chain J Phys A Math Gen 33 L47ndashL51 (2000)[321] J-P Gazeau M Andrle C Burdiacutek Bernuau spline wavelets and sturmian sequences
J Fourier Anal Appl 10 269ndash300 (2004)[322] J-P Gazeau F-X Josse-Michaux P Monceau Finite dimensional quantizations of the
(q p) plane new space and momentum inequalities Int J Modern Phys B 20 1778ndash1791 (2006)
[323] J-P Gazeau J Mourad J Queacuteva Fuzzy de Sitter space-times via coherent statesquantization in Proceedings of the XXVIth Colloquium on Group Theoretical Methodsin Physics New York 2006 ed by J Birman S Catto B Nicolescu (Canopus PublishingLimited London 2009)
[324] D Geller A Mayeli Continuous wavelets on compact manifolds Math Z 262 895ndash927(2009)
[325] D Geller A Mayeli Nearly tight frames and space-frequency analysis on compactmanifolds Math Z 263 235ndash264 (2009)
[326] L Genovese B Videau M Ospici Th Deutsch S Goedecker J-F Mhaut Daubechieswavelets for high performance electronic structure calculations The BigDFT project CR Mecanique 339 149ndash164 (2011)
[327] G Gentili C Stoppato Power series and analyticity over the quaternions Math Ann 352113ndash131 (2012)
[328] G Gentili DC Struppa A new theory of regular functions of a quaternionic variable AdvMath 216 279ndash301 (2007)
[329] C Geyer K Daniilidis Catadioptric projective geometry Int J Comput Vision 45 223ndash243 (2001)
[330] R Gilmore Geometry of symmetrized states Ann Phys (NY) 74 391ndash463 (1972)[331] R Gilmore On properties of coherent states Rev Mex Fis 23 143ndash187 (1974)[332] J Ginibre Statistical ensembles of complex quaternion and real matrices J Math Phys
6 440ndash449 (1965)[333] RJ Glauber The quantum theory of optical coherence Phys Rev 130 2529ndash2539 (1963)
560 References
[334] RJ Glauber Coherent and incoherent states of radiation field Phys Rev 131 2766ndash2788(1963)
[335] J Glimm Locally compact transformation groups Trans Amer Math Soc 101 124ndash138(1961)
[336] R Godement Sur les relations drsquoorthogonaliteacute de V Bargmann C R Acad Sci Paris 255521ndash523 657ndash659 (1947)
[337] C Gonnet B Torreacutesani Local frequency analysis with two-dimensional wavelet trans-form Signal Proc 37 389ndash404 (1994)
[338] JA Gonzalez MA del Olmo Coherent states on the circle J Phys A Math Gen 318841ndash8857 (1998)
[339] XGonze B Amadon et al ABINIT First-principles approach to material and nanosystemproperties Computer Physics Comm 180 2582ndash2615 (2009)
[340] KM Gograverski E Hivon AJ Banday BD Wandelt FK Hansen M Reinecke MBartelmann HEALPix A framework for high-resolution discretization and fast analysisof data distributed on the sphere Astrophys J 622 759ndash771 (2005)
[341] P Goupillaud A Grossmann J Morlet Cycle-octave and related transforms in seismicsignal analysis Geoexploration 23 85ndash102 (1984)
[342] KH Groumlchenig A new approach to irregular sampling of band-limited functions in RecentAdvances in Fourier Analysis and Its applications ed by JS Byrnes JL Byrnes (KluwerDordrecht 1990) pp 251ndash260
[343] KH Groumlchenig Gabor analysis over LCA groups in Gabor Analysis and Algorithms ndashTheory and Applications ed by HG Feichtinger T Strohmer (Birkhaumluser Boston-Basel-Berlin 1998) pp 211ndash231
[344] HJ Groenewold On the principles of elementary quantum mechanics Physica 12 405ndash460 (1946)
[345] P Grohs Continuous shearlet tight frames J Fourier Anal Appl 17 506ndash518 (2011)[346] P Grohs G Kutyniok Parabolic molecules preprint TU Berlin (2012)[347] M Grosser A note on distribution spaces on manifolds Novi Sad J Math 38 121ndash128
(2008)[348] A Grossmann Parity operator and quantization of δ -functions Commun Math Phys 48
191ndash194 (1976)[349] A Grossmann J Morlet Decomposition of Hardy functions into square integrable
wavelets of constant shape SIAM J Math Anal 15 723ndash736 (1984)[350] A Grossmann J Morlet Decomposition of functions into wavelets of constant shape and
related transforms in Mathematics + Physics Lectures on recent results I ed by L Streit(World Scientific Singapore 1985) pp 135ndash166
[351] A Grossmann J Morlet T Paul Integral transforms associated to square integrablerepresentations I General results J Math Phys 26 2473ndash2479 (1985)
[352] A Grossmann J Morlet T Paul Integral transforms associated to square integrablerepresentations II Examples Ann Inst H Poincareacute 45 293ndash309 (1986)
[353] A Grossmann R Kronland-Martinet J Morlet Reading and understanding the contin-uous wavelet transform in Wavelets Time-Frequency Methods and Phase Space (ProcMarseille 1987) ed by J-M Combes A Grossmann P Tchamitchian 2nd edn (SpringerBerlin 1990) pp 2ndash20
[354] P Guillemain R Kronland-Martinet B Martens Estimation of spectral lines with helpof the wavelet transform Application in NMR spectroscopy in Wavelets and Applications(Proc Marseille 1989) ed by Y Meyer (Masson and Springer Paris and Berlin 1991) pp38ndash60
[355] H de Guise M Bertola Coherent state realizations of su(n+ 1) on the n-torus J MathPhys 43 3425ndash3444 (2002)
[356] K Guo D Labate Representation of Fourier Integral Operators using shearlets J FourierAnal Appl 14 327ndash371 (2008)
References 561
[357] K Guo G Kutyniok D Labate Sparse multidimensional representations usinganisotropic dilation and shear operators in Wavelets and Spines (Athens GA 2005)(Nashboro Press Nashville TN 2006) pp 189ndash201
[358] K Guo D Labate W-Q Lim G Weiss E Wilson Wavelets with composite dilationsand their MRA properties Appl Comput Harmon Anal 20 202ndash236 (2006)
[359] EA Gutkin Overcomplete subspace systems and operator symbols Funct Anal Appl 9260ndash261 (1975)
[360] G Gyoumlrgyi Integration of the dynamical symmetry groups for the 1r potential Acta PhysAcad Sci Hung 27 435ndash439 (1969)
[361] BC Hall The Segal-Bargmann ldquoCoherent Staterdquo transform for compact Lie groups JFunct Analysis 122 103ndash151 (1994)
[362] B Hall JJ Mitchell Coherent states on spheres J Math Phys 43 1211ndash1236 (2002)[363] DK Hammond P Vandergheynst R Gribonval Wavelets on graphs via spectral theory
Appl Comput Harmon Anal 30 129ndash150 (2011)[364] Y Hassouni EMF Curado MA Rego-Monteiro Construction of coherent states for
physical algebraic system Phys Rev A 71 022104 (2005)[365] J He H Liu Admissible wavelets associated with the affine automorphism group of the
Siegel upper half-plane J Math Anal Appl 208 58ndash70 (1997)[366] J He H Liu Admissible wavelets associated with the classical domain of type one
Approx Appl 14 (1998) 89ndash105[367] J He L Peng Wavelet transform on the symmetric matrix space preprint Beijing (1997)
(unpublished)[368] J He L Peng Admissible wavelets on the unit disk Complex Variables 35 109ndash119
(1998)[369] DM Healy Jr FE Schroeck Jr On informational completeness of covariant localization
observables and Wigner coefficients J Math Phys 36 453ndash507 (1995)[370] C Heil D Walnut Continuous and discrete wavelet transforms SIAM Review 31 628ndash
666 (1989)[371] K Hepp EH Lieb On the superradiant phase transition for molecules in a quantized
radiation field The Dicke maser model Ann Phys (NY) 76 360ndash404 (1973)[372] K Hepp EH Lieb Equilibrium statistical mechanics of matter interacting with the
quantized radiation field Phys Rev A 8 2517ndash2525 (1973)[373] JA Hogan JD Lakey Extensions of the Heisenberg group by dilations and frames Appl
Comput Harmon Anal 2 174ndash199 (1995)[374] AL Hohoueacuteto K Thirulogasanthar ST Ali J-P Antoine Coherent states lattices and
square integrability of representations J Phys A Math Gen36 11817ndash11835 (2003)[375] M Holschneider On the wavelet transformation of fractal objects J Stat Phys 50 963ndash
993 (1988)[376] M Holschneider Wavelet analysis on the circle J Math Phys 31 39ndash44 (1990)[377] M Holschneider Inverse Radon transforms through inverse wavelet transforms Inv Probl
7 853ndash861 (1991)[378] M Holschneider Localization properties of wavelet transforms J Math Phys 34 3227ndash
3244 (1993)[379] M Holschneider General inversion formulas for wavelet transforms J Math Phys 34
4190ndash4198 (1993)[380] M Holschneider Wavelet analysis over abelian groups Applied Comput Harmon Anal
2 52ndash60 (1995)[381] M Holschneider Continuous wavelet transforms on the sphere J Math Phys 37 4156ndash
4165 (1996)[382] M Holschneider I Iglewska-Nowak Poisson wavelets on the sphere J Fourier Anal
Appl 13 405ndash419 (2007)
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[383] M Holschneider R Kronland-Martinet J Morlet P Tchamitchian A real-time algorithmfor signal analysis with the help of wavelet transform in Wavelets Time-FrequencyMethods and Phase Space (Proc Marseille 1987) ed by J-M Combes A Grossmann PTchamitchian 2nd edn (Springer Berlin 1990) pp 286ndash297
[384] M Holschneider P Tchamitchian Pointwise analysis of Riemannrsquos ldquonondifferentiablerdquofunction Invent Math 105 157ndash175 (1991)
[385] GR Honarasa MK Tavassoly M Hatami R Roknizadeh Nonclassical properties ofcoherent states and excited coherent states for continuous spectra J Phys A Math Theor44 085303 (2011)
[386] M Hongoh Coherent states associated with the continuous spectrum of noncompactgroups J Math Phys 18 2081ndash2085 (1977)
[387] A Horzela FH Szafraniec A measure free approach to coherent states J Phys A MathGen 45 244018 (2012)
[388] W-L Hwang S Mallat Characterization of self-similar multifractals with waveletmaxima Appl Comput Harmon Anal 1 316ndash328 (1994)
[389] W-L Hwang C-S Lu P-C Chung Shape from texture Estimation of planar surfaceorientation through the ridge surfaces of continuous wavelet transform IEEE Trans ImageProc 7 773ndash780 (1998)
[390] I Iglewska-Nowak M Holschneider Frames of Poisson wavelets on the sphere ApplComput Harmon Anal 28 227ndash248 (2010)
[391] E Inoumlnuuml EP Wigner On the contraction of groups and their representations Proc NatAcad Sci U S 39 510ndash524 (1953)
[392] S Iqbal F Saif Generalized coherent states and their statistical characteristics in power-law potentials J Math Phys 52 082105 (2011)
[393] CJ Isham JR Klauder Coherent states for n-dimensional Euclidean groups E(n) andtheir application J MathPhys 32 607ndash620 (1991)
[394] L Jacques J-P Antoine Multiselective pyramidal decomposition of images Wavelets withadaptive angular selectivity Int J Wavelets Multires Inform Proc 5 785ndash814 (2007)
[395] L Jacques L Duval C Chaux G Peyreacute A panorama on multiscale geometric rep-resentations intertwining spatial directional and frequency selectivity Signal Proc 912699ndash2730 (2011)
[396] HR Jalali M K Tavassoly On the ladder operators and nonclassicality of generalizedcoherent state associated with a particle in an infinite square well preprint (2013)arXiv13034100v1 [quant-ph]
[397] C Johnston On the pseudo-dilation representations of Flornes Grossmann Holschneiderand Torreacutesani Appl Comput Harmon Anal 3 377ndash385 (1997)
[398] G Kaiser Phase-space approach to relativistic quantum mechanics I Coherent staterepresentation for massive scalar particles J MathPhys 18 952ndash959 (1977)
[399] G Kaiser Phase-space approach to relativistic quantum mechanics II Geometrical aspectsJ MathPhys 19 502ndash507 (1978)
[400] C Kalisa B Torreacutesani N-dimensional affine Weyl-Heisenberg wavelets Ann Inst HPoincareacute 59 201ndash236 (1993)
[401] W Kaminski J Lewandowski T Pawłowski Quantum constraints Dirac observables andevolution group averaging versus the Schroumldinger picture in LQC Class Quant Grav 26245016 (2009)
[402] MR Karim ST Ali A relativistic windowed Fourier transform preprint ConcordiaUniversity Montreacuteal (1997) (unpublished)
[403] M R Karim ST Ali M Bodruzzaman A relativistic windowed Fourier transform inProceedings of IEEE SoutheastCon 2000 Nashville Tennessee pp 253ndash260 (2000)
[404] T Kawazoe Wavelet transforms associated to a principal series representation of semisim-ple Lie groups I II Proc Japan Acad Ser A ndash Math Sci 71 154ndash157 158ndash160 (1995)
[405] T Kawazoe Wavelet transform associated to an induced representation of SL(n+ 2R)Ann Inst H Poincareacute 65 1ndash13 (1996)
References 563
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[407] P Kittipoom G Kutyniok W-Q Lim Construction of compactly supported shearletframes Constr Approx 35 21ndash72 (2012)
[408] J Kiukas P Lahti K Ylinenc Phase space quantization and the operator moment problemJ Math Phys 47 072104 (2006)
[409] JR Klauder Continuous-representation theory I Postulates of continuous-representationtheory J Math Phys 4 1055ndash1058 (1963)
[410] JR Klauder Continuous-representation theory II Generalized relation between quantumand classical dynamics J Math Phys 4 1058ndash1073 (1963)
[411] JR Klauder Path integrals for affine variables in Functional Integration Theory andApplications ed by J-P Antoine E Tirapegui (Plenum Press New York and London1980) pp 101ndash119
[412] JR Klauder Are coherent states the natural language of quantum mechanics inFundamental Aspects of Quantum Theory ed by V Gorini A Frigerio NATO ASI Seriesvol B 144 (Plenum Press New York 1986) pp 1ndash12
[413] JR Klauder Quantization without quantization Ann Phys (NY) 237 147ndash160 (1995)[414] JR Klauder Coherent states for the hydrogen atom J Phys A Math Gen 29 L293ndash
L296 (1996)[415] JR Klauder An affinity for affine quantum gravity Proc Steklov Inst Math 272 169ndash176
(2011) and references therein[416] JR Klauder RF Streater A wavelet transform for the Poincareacute group J Math Phys 32
1609ndash1611 (1991)[417] JR Klauder RF Streater Wavelets and the Poincareacute half-plane J Math Phys 35 471ndash
478 (1994)[418] JR Klauder K Penson J-M Sixdeniers Constructing coherent states through solutions
of Stieltjes and Hausdorff moment problems Phys Rev A 64 013817 (2001)[419] A Kleppner RL Lipsman The Plancherel formula for group extensions Ann Ec Norm
Sup 5 459ndash516 (1972)[420] AB Klimov C Muntildeoz Coherent isotropic and squeezed states in a N-qubit system Phys
Scr 87 038110 (2013)[421] A Klyashko Dynamical symmetry approach to entanglement in Physics and Theoretical
Computer Science From Numbers and Languages to (Quantum) Cryptography - NATOSecurity through Science Series D - Information and Communication Security vol 7 edby J-P Gazeau J Nesetril B Rovan (IOS Press Washington DC 2007) pp 25ndash54
[422] S Kobayashi Irreducibility of certain unitary representations J Math Soc Japan 20 638ndash642 (1968)
[423] K Kowalski J Rembielinski LC Papaloucas Coherent states for a quantum particle ona circle J Phys A Math Gen 29 4149ndash4167 (1996)
[424] K Kowalski J Rembielinski Quantum mechanics on a sphere and coherent states J PhysA Math Gen 33 6035ndash6048 (2000)
[425] K Kowalski J Rembielinski The Bargmann representation for the quantum mechanicson a sphere J Math Phys 42 4138ndash4147 (2001)
[426] C Kristjansen J Plefka GW Semenoff M Staudacher A new double-scaling limit ofN = 4 super-Yang-Mills theory and pp-wave strings Nuclear Phys B 643 3ndash30 (2002)
[427] M Kulesh M Holschneider MS Diallo Geophysical wavelet library Applications ofthe continuous wavelet transform to the polarization and dispersion analysis of signalsComput Geosci 34 1732ndash1752 (2008)
[428] R Kunze On the Frobenius reciprocity theorem for square integrable representationsPacific J Math 53 465ndash471 (1974)
[429] Y Kuroda A Wada T Yamazaki K Nagayama Postacquisition data processing methodfor suppression of the solvent signal I J Magn Reson 84 604ndash610 (1989)
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[430] Y Kuroda A Wada T Yamazaki K Nagayama Postacquisition data processing methodfor suppression of the solvent signal II The weighted first derivative J Magn Reson 88141ndash145 (1990)
[431] G Kutyniok D Labate Resolution of the wavefront set using continuous shearlets TransAmer Math Soc 361 2719ndash2754 (2009)
[432] G Kutyniok W-Q Lim Compactly supported shearlets are optimally sparse J ApproxTheory 163 1564ndash1589 (2011)
[433] D Labate W-Q Lim G Kutyniok G Weiss Sparse multidimensional representationusing shearlets in Wavelets XI (San Diego CA 2005) ed by M Papadakis A Laine MUnser SPIE Proceedings vol 5914 (SPIE Bellingham WA 2005) pp 254ndash262
[434] P Lahti J-P Pellonpaumlauml Continuous variable tomographic measurements Phys Lett A373 3435ndash3438 (2009)
[435] Lambertrsquos projection see WikipediahttpenwikipediaorgwikiLambert_azimuthal_equal-area_projection
[436] J-P Leduc F Mujica R Murenzi MJT Smith Missile-tracking algorithm using target-adapted spatio-temporal wavelets in Automatic Object Recognition VII SPIE Proceedingsvol 5914 (SPIE Bellingham WA 1997) pp 400ndash411
[437] J-P Leduc F Mujica R Murenzi MJT Smith Spatio-temporal wavelet transforms formotion tracking in IEEE ICASSP 1997 vol 4 (1997) pp 3013ndash3016
[438] J-P Leduc F Mujica R Murenzi MJT Smith Spatio-temporal continuous waveletsapplied to missile warhead detection and tracking in SPIE VCIP rsquo97 vol 3024 ed byJ Biemond EJ Delp (1997) pp 787ndash798
[439] B Leistedt JD McEwen Exact wavelets on the ball IEEE Trans Signal Proc 60 1564ndash1589 (2012)
[440] PG Lemarieacute Y Meyer Ondelettes et bases hilbertiennes Rev Math Iberoamer 2 1ndash18(1986)
[441] C Lemke A Schuck Jr J-P Antoine D Sima Metabolite-sensitive analysis of magneticresonance spectroscopic signals using the continuous wavelet transform Meas SciTechnol 22 (2011) Art 114013
[442] J-M Leacutevy-Leblond Galilei group and non-relativistic quantum mechanics J Math Phys4 776-788 (1963)
[443] J-M Leacutevy-Leblond Galilei group and Galilean invariance in Group Theory and ItsApplications vol II ed by EM Loebl (Academic New York 1971) pp 221ndash299
[444] J-M Leacutevy-Leblond On the conceptual nature of the physical constants Riv Nuovo Cim7 187ndash214 (1977)
[445] EH Lieb The classical limit of quantum spin systems Commun Math Phys 31 327ndash340(1973)
[446] G Lindblad B Nagel Continuous bases for unitary irreducible representations of SU(11)Ann Inst H Poincareacute 13 27ndash56 (1970)
[447] W Lisiecki Kaumlhler coherent states orbits for representations of semisimple Lie groupsAnn Inst H Poincareacute 53 857ndash890 (1990)
[448] A Lisowska Moment-based fast wedgelet transform J Math Imaging Vis 39 180ndash192(2011)
[449] H Liu L Peng Admissible wavelets associated with the Heisenberg group Pacific JMath 180 101ndash123 (1997)
[450] E Livine S Speziale Physical boundary state for the quantum tetrahedron Class QuantGrav 25 085003 (2008)
[451] F Low Complete sets of wave packets in A Passion for Physics ndash Essay in Honor ofGeoffrey Chew ed by C DeTar (World Scientific Singapore 1985) pp 17ndash22
[452] G Mack All unitary ray representations of the conformal group SU(22) with positiveenergy Commun Math Phys 55 1ndash28 (1977)
[453] GW Mackey Imprimitivity for representations of locally compact groups I Proc NatAcad Sci 35 537ndash545 (1949)
References 565
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[455] M Mallalieu CR Stroud Jr Rydberg wave packets fractional revivals and classicalorbits in Coherent States Past Present and Future (Proc Oak Ridge 1993) ed by DHFeng JR Klauder M Strayer (World Scientific Singapore 1994) pp 301ndash314
[456] SG Mallat Multifrequency channel decompositions of images and wavelet models IEEETrans Acoust Speech Signal Proc 37 2091ndash2110 (1989)
[457] SG Mallat A theory for multiresolution signal decomposition The wavelet representa-tion IEEE Trans Pattern Anal Machine Intell 11 674ndash693 (1989)
[458] S Mallat W-L Hwang Singularity detection and processing with wavelets IEEE TransInform Theory 38 617ndash643 (1992)
[459] S Mallat Z Zhang Matching pursuits with time frequency dictionaries IEEE TransSignal Proc 41 3397ndash3415 (1993)
[460] S Mallat S Zhong Wavelet maxima representation in Wavelets and Applications (ProcMarseille 1989) ed by Y Meyer (Masson and Springer Paris and Berlin 1991) pp 207ndash284
[461] VI Manrsquoko G Marmo ECG Sudarshan F Zaccaria f -oscillators and non-linearcoherent states Phys Scr 55 528ndash541 (1997)
[462] D Marinucci D Pietrobon A Baldi P Baldi P Cabella G Kerkyacharian P Natoli DPicard N Vittorio Spherical needlets for CMB data analysis Mon Not R Astron Soc383 539ndash545 (2008)
[463] D Marion M Ikura A Bax Improved solvent suppression in one- and two-dimensionalNMR spectra by convolution of time-domain data J Magn Reson 84 425ndash430 (1989)
[464] Y Meyer Principe drsquoincertitude bases hilbertiennes et algegravebres drsquoopeacuterateurs SeacuteminaireBourbaki 662 (1985ndash1986)
[465] Y Meyer Principe drsquoincertitude bases hilbertiennes et algegravebres drsquoopeacuterateurs Asteacuterisque145ndash146 209ndash223 (1987)
[466] Y Meyer H Xu Wavelet analysis and chirps Appl Comput Harmon Anal 4 366ndash379(1997)
[467] L Michel Invariance in quantum mechanics and group extensions in Group TheoreticalConcepts and Methods in Elementary Particle Physics ed by F Guumlrsey (Gordon andBreach New York and London 1964) pp 135ndash200
[468] J Mickelsson J Niederle Contractions of representations of the de Sitter groupsCommun Math Phys 27 167ndash180 (1972)
[469] MM Miller Convergence of the Sudarshan expansion for the diagonal coherent-stateweight functional J Math Phys 9 1270ndash1274 (1968)
[470] V F Molchanov Harmonic analysis on homogeneous spaces in Representation Theoryand Noncommutative Harmonic Analysis II ed by AA Kirillov (Springer Berlin 1995)
[471] MI Monastyrsky AM Perelomov Coherent states and symmetric spaces II Ann InstH Poincareacute 23 23ndash48 (1975)
[472] B Moran S Howard D Cochran Positive-operator-valued measures A general settingfor frames in Excursions in Harmonic Analysis vol 1 2 ed by TD Andrews R BalanJJ Benedetto W Czaja KA Okoudjou (Birkhaumluser Boston 2013) pp 49ndash64
[473] H Moscovici Coherent states representations of nilpotent Lie groups Commun MathPhys 54 63ndash68 (1977)
[474] H Moscovici A Verona Coherent states and square integrable representations Ann InstH Poincareacute 29 139ndash156 (1978)
[475] F Mujica R Murenzi MJT Smith J-P Leduc Robust tracking in compressed imagesequences J Electr Imaging 7 746ndash754 (1998)
[476] R Murenzi Wavelet transforms associated to the n-dimensional Euclidean group withdilations Signals in more than one dimension in Wavelets Time-Frequency Methodsand Phase Space (Proc Marseille 1987) ed by J-M Combes A Grossmann PTchamitchian 2nd edn (Springer Berlin 1990) pp 239ndash246
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[478] B Nagel Generalized eigenvectors in group representations in Studies in MathematicalPhysics (Proc Istanbul 1970) ed by AO Barut (Reidel Dordrecht and Boston 1970)pp 135ndash154
[479] MA Naımark Dokl Akad Nauk SSSR 41 359ndash361 (1943) see also B Sz-NagyExtensions of linear transformations in Hilbert space which extend beyond this spaceAppendix to F Riesz B Sz-Nagy Functional Analysis (Frederick Ungar New York 1960)
[480] FJ Narcowich P Petrushev JD Ward Localized tight frames on spheres SIAM J MathAnal 38 574ndash594 (2006)
[481] M Nauenberg Quantum wave packets on Kepler elliptic orbits Phys Rev A 40 1133ndash1136 (1989)
[482] M Nauenberg C Stroud J Yeazell The classical limit of an atom Scient Amer 27024ndash29 (1994)
[483] H Neumann Transformation properties of observables Helv Phys Acta 45 811ndash819(1972)
[484] U Niederer The maximal kinematical invariance group of the free Schroumldinger equationHelv Phys Acta 45 802ndash881 (1972)
[485] MM Nieto LM Simmons Jr Coherent states for general potentials I Formalism IIConfining one-dimensional examples III Nonconfining one-dimensional examples PhysRev D 20 1321ndash1331 1332ndash1341 1342ndash1350 (1979)
[486] MM Nieto LM Simmons Jr Coherent states for general potentials Phys Rev Lett 41207ndash210 (1987)
[487] A Odzijewicz On reproducing kernels and quantization of states Commun Math Phys114 577ndash597 (1988)
[488] A Odzijewicz Coherent states and geometric quantization Commun Math Phys 150385ndash413 (1992)
[489] A Odzijewicz Quantum algebras and q-special functions related to coherent states mapsof the disc Commun Math Phys 192 183ndash215 (1998)
[490] A Odzijewicz M Horowski A Tereszkiewicz Integrable multi-boson systems andorthogonal polynomials J Phys A Math Gen 34 4353ndash4376 (2001)
[491] G Oacutelafsson B Oslashrsted The holomorphic discrete series for affine symmetric spaces JFunct Anal 81 126ndash159 (1988)
[492] G Oacutelafsson H Schlichtkrull Representation theory Radon transform and the heatequation on a Riemannian symmetric space Contemp Math 449 315ndash344 (2008)
[493] E Onofri A note on coherent state representations of Lie groups J Math Phys 16 1087ndash1089 (1975)
[494] E Onofri Dynamical quantization of the Kepler manifold J Math Phys 17 401ndash408(1976)
[495] D Oriti R Pereira L Sindoni Coherent states in quantum gravity A construction basedon the flux representation of loop quantum gravity J Phys A Math Theor 45 244004(2012)
[496] LC Papaloucas J Rembielinski W Tybor Vectorlike coherent states with noncompactstability group J Math Phys 30 2406ndash2410 (1989)
[497] Z Pasternak-Winiarski On the dependence of the reproducing kernel on the weight ofintegration J Funct Anal 94 110ndash134 (1990)
[498] Z Pasternak-Winiarski On reproducing kernels for holomorphic vector bundles inQuantization and Infinite Dimensional Systems (Proc Białowieza Poland 1993) ed by J-P Antoine ST Ali W Lisiecki IM Mladenov A Odzijewicz (Plenum Press New Yorkand London 1994) pp 109ndash112
[499] T Paul Affine coherent states and the radial Schroumldinger equation I preprint CPT-84P1710 (1984) (unpublished)
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[507] WWF Pijnappel A van den Boogaart R de Beer D van Ormondt SVD-basedquantification of magnetic resonance signals J Magn Reson 97 122ndash134 (1992)
[508] V Pop D Rosca Generalized piecewise constant orthogonal wavelet bases on 2D-domains Appl Anal 90 715ndash723 (2011)
[509] G Poumlschl E Teller Bemerkungen zur Quantenmechanik des anharmonischen OszillatorsZ Physik 83 143ndash151 (1933)
[510] D Potts G Steidl M Tasche Kernels of spherical harmonics and spherical frames inAdvanced Topics in Multivariate Approximation ed by F Fontanella K Jetter PJ Laurent(World Scientific Singapore 1996) pp 287ndash301
[511] E Prugovecki Consistent formulation of relativistic dynamics for massive spin-zeroparticles in external fields Phys Rev D 18 3655ndash3673 (1978) (Appendix C)
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Wavelets Multiresolut Inf Process 6 209ndash222 (2008)[531] D Rosca On a norm equivalence on L2(S2) Results Math 53 399ndash405 (2009)[532] D Rosca New uniform grids on the sphere Astron Astrophys 520 (2010) Art A63[533] D Rosca Uniform and refinable grids on elliptic domains and on some surfaces of
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Appl Comput Harmon Anal 30 262ndash272 (2011)[535] D Rosca J-P Antoine Locally supported orthogonal wavelet bases on the sphere via
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sphere in Recent Advances in Signal Processing ed by S Miron (IN-TECH ViennaAustria and Rijeka Croatia 2010) pp 59ndash76
[537] D Rosca G Plonka Uniform spherical grids via area preserving projection from the cubeto the sphere J Comput Appl Math 236 1033ndash1041 (2011)
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[541] C Rovelli Zakopane lectures on loop gravity in Proceedings of 3rd Quantum Gravityand Quantum Geometry School 28 Febndash13 March 2011 (Zakopane Poland 2011)arXiv11023660v5
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[547] DJ Rowe G Rosensteel R Gilmore Vector coherent state representation theory J MathPhys 26 2787ndash2791 (1985)
[548] A Royer Phase states and phase operators for the quantum harmonic oscillator Phys RevA 53 70ndash108 (1996)
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[551] P Schroumlder W Sweldens Spherical wavelets Efficiently representing functions on thesphere in Computer Graphics Proceedings (SIGGRAPH95) (ACM Siggraph Los Angeles1995) pp 161ndash175
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[579] T Thiemann Gauge field theory coherent states (GCS) 1 General properties Class QuantGrav 18 2025ndash2064 (2001)
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[581] T Thiemann O Winkler Gauge field theory coherent states (GCS) 3 Ehrenfest theoremsClass Quant Grav 18 4629ndash4682 (2001)
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[614] J Zak Balian-Low theorem for Landau levels Phys Rev Lett 79 533ndash536 (1997)[615] J Zak Orthonormal sets of localized functions for a Landau level J Math Phys 39 4195ndash
4200 (1998) and references quoted there[616] AA Zakharova On the properties of generalized frames Math Notes 83 190ndash200 (2008)[617] W-M Zhang DH Feng R Gilmore Coherent states Theory and some applications Rev
Mod Phys 26 867ndash927 (1990)[618] I Zlatev W-M Zhang DH Feng Possibility that Schroumldingerrsquos conjecture for the
hydrogen atom coherent states is not attainable Phys Rev A 50 R1973ndashR1975 (1994)[619] WH Zurek Decoherence einselection and the quantum origins of the classical Rev Mod
Phys 75 715ndash775 (2003)[620] WH Zurek S Habib JP Paz Coherent states via decoherence Phys Rev Lett 70 1187ndash
1190 (1993)[621] K Zyczkowski Squeezed states in a quantum chaotic system J Phys A Math Theor 22
of SU(11) 81 296 297HilbertClowast-modules 164holomorphic 140nonholomorphic 151nonlinear 146of affine Galilei group 505of affine Poincareacute group 509of affine Weyl-Heisenberg group GaWH
497of compact semisimple Lie groups 174of Euclidean group E(n) 266of Galilei group G (11) 290of isochronous Galilei group 237of non-semisimple Lie groups 179of noncompact semisimple Lie groups 177of Poincareacute group Puarr
+(11) 283massless case 288
of Poincareacute group Puarr+(13) 279
of Schroumldinger group 508quasi-coherent states 186quaternionic 164
ST Ali et al Coherent States Wavelets and Their Generalizations Theoreticaland Mathematical Physics DOI 101007978-1-4614-8535-3copy Springer Science+Business Media New York 2014
573
574 Index
coherent states (CS) (cont)spin or SU(2) 175square integrable covariant 166 180 264vector (VCS) 73 108 112 170weighted 184 523
of affine Weyl-Heisenberg group GaWH497
of Poincareacute group Puarr+(11) 284
cohomology group 393 403coboundaries 403cochains 402cocycle 403
algebraic 387Cauchy 418Cauchy-Paul 354 419 425conical 418difference 417 462directional 416 440kinematical 499local 488metabolite-based 355 374minimal uncertainty 425multiselective 440on a graph 493on the sphere S
2 458on the sphere S
n 479on the torus T2 481steerable 439von Mises 440
wedgelet transform 455Wigner function 322Wigner-Ville transform 349Windowed Fourier or Gabor transform 349
ZZak transform 518
References
A Books and Theses
B Articles
Index
References 555
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[214] N Cotfas J-P Gazeau Finite tight frames and some applications (topical review) J PhysA Math Theor 43 193001 (2010)
[215] N Cotfas J-P Gazeau K Goacuterska Complex and real Hermite polynomials and relatedquantizations J Phys A Math Theor 43 305304 (2010)
[216] N Cotfas J-P Gazeau A Vourdas Finite-dimensional Hilbert space and frame quantiza-tion J Phys A Math Gen 44 175303 (2011)
[217] EMF Curado MA Rego-Monteiro LMCS Rodrigues Y Hassouni Coherent statesfor a degenerate system The hydrogen atom Physica A 371 16ndash19 (2006)
[218] S Dahlke P Maass The affine uncertainty principle in one and two dimensions CompMath Appl 30 293ndash305 (1995)
[219] S Dahlke W Dahmen E Schmidt I Weinreich Multiresolution analysis and wavelets onS
2 and S3 Numer Funct Anal Optim 16 19ndash41 (1995)
[220] S Dahlke V Lehmann G Teschke Applications of wavelet methods to the analysis ofmeteorological radar data - An overview Arabian J Sci Eng 28 3ndash44 (2003)
[221] S Dahlke G Kutyniok P Maass C Sagiv H-G Stark G Teschke The uncertaintyprinciple associated with the continuous shearlet transform Int J Wavelets MultiresolutInf Process 6 157ndash181 (2008)
[222] S Dahlke G Kutyniok G Steidl G Teschke Shearlet coorbit spaces and associatedBanach frames Appl Comput Harmon Anal 27 195ndash214 (2009)
[223] S Dahlke G Steidl G Teschke The continuous shearlet transform in arbitrary spacedimensions J Fourier Anal Appl 16 340ndash364 (2010)
[224] S Dahlke G Steidl G Teschke Shearlet coorbit spaces Compactly supported analyzingshearlets traces and embeddings J Fourier Anal Appl 17 1232ndash1355 (2011)
[225] T Dallard GR Spedding 2-D wavelet transforms Generalisation of the Hardy space andapplication to experimental studies Eur J Mech BFluids 12 107ndash134 (1993)
[226] C Daskaloyannis Generalized deformed oscillator and nonlinear algebras J Phys AMath Gen 24 L789ndashL794 (1991)
[227] C Daskaloyannis K Ypsilantis A deformed oscillator with Coulomb energy spectrumJ Phys A Math Gen 25 4157ndash4166 (1992)
[228] I Daubechies On the distributions corresponding to bounded operators in the Weylquantization Commun Math Phys 75 229ndash238 (1980)
[229] I Daubechies and A Grossmann An integral transform related to quantization I J MathPhys 21 2080ndash2090 (1980)
[230] I Daubechies A Grossmann J Reignier An integral transform related to quantization IIJ Math Phys 24 239ndash254 (1983)
[231] I Daubechies Orthonormal bases of compactly supported wavelets Commun Pure ApplMath 41 909ndash996 (1988)
[232] I Daubechies The wavelet transform time-frequency localisation and signal analysisIEEE Trans Inform Theory 36 961ndash1005 (1990)
[233] I Daubechies S Maes A nonlinear squeezing of the continuous wavelet transform basedon auditory nerve models in Wavelets in Medicine and Biology ed by A Aldroubi MUnser (CRC Press Boca Raton 1996) pp 527ndash546
[234] I Daubechies A Grossmann Y Meyer Painless nonorthogonal expansions J Math Phys27 1271ndash1283 (1986)
[235] ER Davies Introduction to texture analysis in Handbook of texture analysis ed by MMirmehdi X Xie J Suri (World Scientific Singapore 2008) pp 1ndash31
[236] R De Beer D van Ormondt FTAW Wajer S Cavassila D Graveron-Demilly S VanHuffel SVD-based modelling of medical NMR signals in SVD and Signal ProcessingIII Algorithms Architectures and Applications ed by M Moonen B De Moor (Elsevier(North-Holland) Amsterdam 1995) pp 467ndash474
[237] S De Biegravevre Coherent states over symplectic homogeneous spaces J Math Phys 301401ndash1407 (1989)
556 References
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[239] S De Biegravevre JA Gonzaacutelez Semiclassical behaviour of coherent states on the circle inQuantization and Coherent States Methods in Physics ed by A Odzijewicz et al (WorldScientific Singapore 1993)
[240] S De Biegravevre AE Gradechi Quantum mechanics and coherent states on the anti-de Sitterspace-time and their Poincareacute contraction Ann Inst H Poincareacute 57 403ndash428 (1992)
[241] J Deenen C Quesne Dynamical group of collective states I II III J Math Phys 23878ndash889 2004ndash2015 (1982)
[242] J Deenen C Quesne Dynamical group of collective states I II III J Math Phys 251638ndash1650 (1984)
[243] J Deenen C Quesne Partially coherent states of the real symplectic group J Math Phys25 2354ndash2366 (1984)
[244] J Deenen C Quesne Boson representations of the real symplectic group and theirapplication to the nuclear collective model J Math Phys 26 2705ndash2716 (1985)
[245] R Delbourgo Minimal uncertainty states for the rotation and allied groups J Phys AMath Gen 10 1837ndash1846 (1977)
[246] R Delbourgo J R Fox Maximum weight vectors possess minimal uncertainty J PhysA Math Gen 10 L233ndashL235 (1977)
[247] V Delouille J de Patoul J-F Hochedez L Jacques J-P Antoine Wavelet spectrumanalysis of EITSoHO images Solar Phys 228 301ndash321 (2005)
[248] N Delprat B Escudieacute P Guillemain R Kronland-Martinet P Tchamitchian B Tor-reacutesani Asymptotic wavelet and Gabor analysis Extraction of instantaneous frequenciesIEEE Trans Inform Theory 38 644ndash664 (1992)
[249] Th Deutsch L Genovese Wavelets for electronic structure calculations Collection SocFr Neut 12 33ndash76 (2011)
[250] B Dewitt Quantum theory of gravity I The canonical theory Phys Rev 160 1113ndash1148(1967)
[251] RH Dicke Coherence in spontaneous radiation processes Phys Rev 93 99ndash110 (1954)[252] AN Dinkelaker AL MacKinnon Wavelets intermittency and solar flare hard X-rays 1
Local intermittency measure in cascade and avalanche scenarios Solar Phys 282 471ndash481(2013)
[253] AN Dinkelaker AL MacKinnon Wavelets intermittency and solar flare hard X-rays 2LIM analysis of high time resolution BATSE data Solar Phys 282 483ndash501 (2013)
[254] MN Do M Vetterli Contourlets in Beyond Wavelets ed by GV Welland (AcademicSan Diego 2003) pp 83ndash105
[255] MN Do M Vetterli The contourlet transform An efficient directional multiresolutionimage representation IEEE Trans Image Process 14 2091ndash2106 (2005)
[256] VV Dodonov Nonclassical states in quantum optics A ldquosqueezedrdquo review of the first 75years J Opt B Quant Semiclass Opot 4 R1ndashR33 (2002)
[257] DL Donoho Nonlinear wavelet methods for recovery of signals densities and spectrafrom indirect and noisy data in Different Perspectives on Wavelets Proceedings ofSymposia in Applied Mathematics vol 38 ed by I Daubechies (American MathematicalSociety Providence RI 1993) pp 173ndash205
[258] DL Donoho Wedgelets Nearly minimax estimation of edges Ann Stat 27 859ndash897(1999)
[259] DL Donoho X Huo Beamlet pyramids A new form of multiresolution analysis suitedfor extracting lines curves and objects from very noisy image data in SPIE Proceedingsvol 5914 (SPIE Bellingham WA 2005) pp 1ndash12
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[268] M Duval-Destin M-A Muschietti B Torreacutesani Continuous wavelet decompositionsmultiresolution and contrast analysis SIAM J Math Anal 24 739ndash755 (1993)
[269] SJL van Eindhoven JLH Meyers New orthogonality relations for the Hermitepolynomials and related Hilbert spaces J Math Anal Appl 146 89ndash98 (1990)
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[271] A Elkharrat J-P Gazeau F Deacutenoyer Multiresolution of quasicrystal diffraction spectraActa Cryst A65 466ndash489 (2009)
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[273] M Fanuel S Zonetti Affine quantization and the initial cosmological singularity Euro-phys Lett 101 10001 (2013)
[274] M Farge Wavelet transforms and their applications to turbulence Annu Rev Fluid Mech24 395ndash457 (1992)
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[276] M Farge NK-R Kevlahan V Perrier K Schneider Turbulence analysis modellingand computing using wavelets in Wavelets in Physics Chap 4 ed by JC van den Berg(Cambridge University Press Cambridge 1999)
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[279] HG Feichtinger KH Groumlchenig Banach spaces related to integrable group representa-tions and their atomic decompositions II Mh Math 108 129ndash148 (1989)
[280] M Flensted-Jensen Discrete series for semisimple symmetric spaces Ann of Math 111253ndash311 (1980)
[281] K Flornes A Grossmann M Holschneider B Torreacutesani Wavelets on discrete fieldsAppl Comput Harmon Anal 1 137ndash146 (1994)
[282] V Fock Zur Theorie der Wasserstoffatoms Zs f Physik 98 145ndash54 (1936)[283] M Fornasier H Rauhut Continuous frames function spaces and the discretization
problem J Fourier Anal Appl 11 245ndash287 (2005)
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[284] W Freeden M Schreiner Orthogonal and non-orthogonal multiresolution analysis scalediscrete and exact fully discrete wavelet transform on the sphere Constr Approx 14 493ndash515 (1997)
[285] W Freeden U Windheuser Combined spherical harmonic and wavelet expansion mdash Afuture concept in Earthrsquos gravitational determination Appl Comput Harmon Anal 4 1ndash37 (1997)
[286] W Freeden T Maier S Zimmermann A survey on wavelet methods for (geo)applicationsRevista Mathematica Complutense 16 (2003) 277ndash310
[287] W Freeden M Schreiner Biorthogonal locally supported wavelets on the sphere based onzonal kernel functions J Fourier Anal Appl 13 693ndash709 (2007)
[288] WT Freeman EH Adelson The design and use of steerable filters IEEE Trans PatternAnal Machine Intell 13 891ndash906 (1991)
[289] L Freidel ER Livine U(N) coherent states for loop quantum gravity J Math Phys 52052502 (2011)
[290] J Froment S Mallat Arbitrary low bit rate image compression using wavelets in Progressin Wavelet Analysis and Applications (Proc Toulouse 1992) ed by Y Meyer S Roques(Ed Frontiegraveres Gif-sur-Yvette 1993) pp 413ndash418 and references therein
[291] L Freidel S Speziale Twisted geometries A geometric parameterisation of SU(2) phasespace Phys Rev D 82 084040 (2010)
[292] H Fuumlhr Wavelet frames and admissibility in higher dimensions J Math Phys 37 6353ndash6366 (1996)
[293] H Fuumlhr M Mayer Continuous wavelet transforms from semidirect products Cyclicrepresentations and Plancherel measure J Fourier Anal Appl 8 375ndash396 (2002)
[294] D Gabor Theory of communication J Inst Electr Engrg(London) 93 429ndash457 (1946)[295] J-P Gabardo D Han Frames associated with measurable spaces Adv Comput Math 18
127ndash147 (2003)[296] E Galapon Paulirsquos theorem and quantum canonical pairs The consistency of a bounded
self-adjoint time operator canonically conjugate to a Hamiltonian with non-empty pointspectrum Proc R Soc Lond A 458 451ndash472 (2002)
[297] PL Garciacutea de Leacuteon J-P Gazeau Coherent state quantization and phase operator PhysLett A 361 301ndash304 (2007)
[298] L Garciacutea de Leoacuten J-P Gazeau J Queacuteva The infinite well revisited Coherent states andquantization Phys Lett A 372 3597ndash3607 (2008)
[299] T Garidi J-P Gazeau E Huguet M Lachiegraveze Rey J Renaud Fuzzy spheres frominequivalent coherent states quantization J Phys A Math Theor 40 10225ndash10249 (2007)
[300] J-P Gazeau Four Euclidean conformal group in atomic calculations Exact analyticalexpressions for the bound-bound two-photon transition matrix elements in the H atomJ Math Phys 19 1041ndash1048 (1978)
[301] J-P Gazeau On the four Euclidean conformal group structure of the sturmian operatorLett Math Phys 3 285ndash292 (1979)
[302] J-P Gazeau Technique Sturmienne pour le spectre discret de lrsquoeacutequation de SchroumldingerJ Phys A Math Gen 13 3605ndash3617 (1980)
[303] J-P Gazeau Four Euclidean conformal group approach to the multiphoton processes in theH atom J Math Phys 23 156ndash164 (1982)
[304] J-P Gazeau A remarkable duality in one particle quantum mechanics between someconfining potentials and (R+Linfin
ε ) potentials Phys Lett 75A 159ndash163 (1980)[305] J-P Gazeau SL(2R)-coherent states and integrable systems in classical and quantum
physics in Quantization Coherent States and Complex Structures ed by J-P AntoineST Ali W Lisiecki IM Mladenov A Odzijewicz (Plenum Press New York and London1995) pp 147ndash158
[306] J-P Gazeau S Graffi Quantum harmonic oscillator A relativistic and statistical point ofview Boll Unione Mat Ital 11-A 815ndash839 (1997)
[307] J-P Gazeau V Hussin Poincareacute contraction of SU(11) Fock-Bargmann structure J PhysA Math Gen 25 1549ndash1573 (1992)
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[309] J-P Gazeau JR Klauder Coherent states for systems with discrete and continuousspectrum J Phys A Math Gen 32 123ndash132 (1999)
[310] J-P Gazeau P Monceau Generalized coherent states for arbitrary quantum systems inColloquium M Flato (Dijon Sept 99) vol II (Kluumlwer Dordrecht 2000) pp 131ndash144
[311] J-P Gazeau M Novello The question of mass in (Anti-) de Sitter space-times J Phys AMath Theor 41 304008 (2008)
[312] J-P Gazeau M del Olmo q-coherent states quantization of the harmonic oscillator AnnPhys (NY) 330 220ndash245 (2013) arXiv12071200 [quant-ph]
[313] J-P Gazeau J Patera Tau-wavelets of Haar J Phys A Math Gen 29 4549ndash4559 (1996)[314] J-P Gazeau W Piechocki Coherent states quantization of a particle in de Sitter space
J Phys A Math Gen 37 6977ndash6986 (2004)[315] J-P Gazeau J Renaud Lie algorithm for an interacting SU(11) elementary system and its
contraction Ann Phys (NY) 222 89ndash121 (1993)[316] J-P Gazeau J Renaud Relativistic harmonic oscillator and space curvature Phys Lett A
179 67ndash71 (1993)[317] J-P Gazeau V Spiridonov Toward discrete wavelets with irrational scaling factor J Math
plane J Phys A Math Theor 44 495201 (2011)[319] J-P Gazeau J Patera E Pelantovaacute Tau-wavelets in the plane J Math Phys 39 4201ndash
4212 (1998)[320] J-P Gazeau M Andrle C Burdiacutek R Krejcar Wavelet multiresolutions for the Fibonacci
chain J Phys A Math Gen 33 L47ndashL51 (2000)[321] J-P Gazeau M Andrle C Burdiacutek Bernuau spline wavelets and sturmian sequences
J Fourier Anal Appl 10 269ndash300 (2004)[322] J-P Gazeau F-X Josse-Michaux P Monceau Finite dimensional quantizations of the
(q p) plane new space and momentum inequalities Int J Modern Phys B 20 1778ndash1791 (2006)
[323] J-P Gazeau J Mourad J Queacuteva Fuzzy de Sitter space-times via coherent statesquantization in Proceedings of the XXVIth Colloquium on Group Theoretical Methodsin Physics New York 2006 ed by J Birman S Catto B Nicolescu (Canopus PublishingLimited London 2009)
[324] D Geller A Mayeli Continuous wavelets on compact manifolds Math Z 262 895ndash927(2009)
[325] D Geller A Mayeli Nearly tight frames and space-frequency analysis on compactmanifolds Math Z 263 235ndash264 (2009)
[326] L Genovese B Videau M Ospici Th Deutsch S Goedecker J-F Mhaut Daubechieswavelets for high performance electronic structure calculations The BigDFT project CR Mecanique 339 149ndash164 (2011)
[327] G Gentili C Stoppato Power series and analyticity over the quaternions Math Ann 352113ndash131 (2012)
[328] G Gentili DC Struppa A new theory of regular functions of a quaternionic variable AdvMath 216 279ndash301 (2007)
[329] C Geyer K Daniilidis Catadioptric projective geometry Int J Comput Vision 45 223ndash243 (2001)
[330] R Gilmore Geometry of symmetrized states Ann Phys (NY) 74 391ndash463 (1972)[331] R Gilmore On properties of coherent states Rev Mex Fis 23 143ndash187 (1974)[332] J Ginibre Statistical ensembles of complex quaternion and real matrices J Math Phys
6 440ndash449 (1965)[333] RJ Glauber The quantum theory of optical coherence Phys Rev 130 2529ndash2539 (1963)
560 References
[334] RJ Glauber Coherent and incoherent states of radiation field Phys Rev 131 2766ndash2788(1963)
[335] J Glimm Locally compact transformation groups Trans Amer Math Soc 101 124ndash138(1961)
[336] R Godement Sur les relations drsquoorthogonaliteacute de V Bargmann C R Acad Sci Paris 255521ndash523 657ndash659 (1947)
[337] C Gonnet B Torreacutesani Local frequency analysis with two-dimensional wavelet trans-form Signal Proc 37 389ndash404 (1994)
[338] JA Gonzalez MA del Olmo Coherent states on the circle J Phys A Math Gen 318841ndash8857 (1998)
[339] XGonze B Amadon et al ABINIT First-principles approach to material and nanosystemproperties Computer Physics Comm 180 2582ndash2615 (2009)
[340] KM Gograverski E Hivon AJ Banday BD Wandelt FK Hansen M Reinecke MBartelmann HEALPix A framework for high-resolution discretization and fast analysisof data distributed on the sphere Astrophys J 622 759ndash771 (2005)
[341] P Goupillaud A Grossmann J Morlet Cycle-octave and related transforms in seismicsignal analysis Geoexploration 23 85ndash102 (1984)
[342] KH Groumlchenig A new approach to irregular sampling of band-limited functions in RecentAdvances in Fourier Analysis and Its applications ed by JS Byrnes JL Byrnes (KluwerDordrecht 1990) pp 251ndash260
[343] KH Groumlchenig Gabor analysis over LCA groups in Gabor Analysis and Algorithms ndashTheory and Applications ed by HG Feichtinger T Strohmer (Birkhaumluser Boston-Basel-Berlin 1998) pp 211ndash231
[344] HJ Groenewold On the principles of elementary quantum mechanics Physica 12 405ndash460 (1946)
[345] P Grohs Continuous shearlet tight frames J Fourier Anal Appl 17 506ndash518 (2011)[346] P Grohs G Kutyniok Parabolic molecules preprint TU Berlin (2012)[347] M Grosser A note on distribution spaces on manifolds Novi Sad J Math 38 121ndash128
(2008)[348] A Grossmann Parity operator and quantization of δ -functions Commun Math Phys 48
191ndash194 (1976)[349] A Grossmann J Morlet Decomposition of Hardy functions into square integrable
wavelets of constant shape SIAM J Math Anal 15 723ndash736 (1984)[350] A Grossmann J Morlet Decomposition of functions into wavelets of constant shape and
related transforms in Mathematics + Physics Lectures on recent results I ed by L Streit(World Scientific Singapore 1985) pp 135ndash166
[351] A Grossmann J Morlet T Paul Integral transforms associated to square integrablerepresentations I General results J Math Phys 26 2473ndash2479 (1985)
[352] A Grossmann J Morlet T Paul Integral transforms associated to square integrablerepresentations II Examples Ann Inst H Poincareacute 45 293ndash309 (1986)
[353] A Grossmann R Kronland-Martinet J Morlet Reading and understanding the contin-uous wavelet transform in Wavelets Time-Frequency Methods and Phase Space (ProcMarseille 1987) ed by J-M Combes A Grossmann P Tchamitchian 2nd edn (SpringerBerlin 1990) pp 2ndash20
[354] P Guillemain R Kronland-Martinet B Martens Estimation of spectral lines with helpof the wavelet transform Application in NMR spectroscopy in Wavelets and Applications(Proc Marseille 1989) ed by Y Meyer (Masson and Springer Paris and Berlin 1991) pp38ndash60
[355] H de Guise M Bertola Coherent state realizations of su(n+ 1) on the n-torus J MathPhys 43 3425ndash3444 (2002)
[356] K Guo D Labate Representation of Fourier Integral Operators using shearlets J FourierAnal Appl 14 327ndash371 (2008)
References 561
[357] K Guo G Kutyniok D Labate Sparse multidimensional representations usinganisotropic dilation and shear operators in Wavelets and Spines (Athens GA 2005)(Nashboro Press Nashville TN 2006) pp 189ndash201
[358] K Guo D Labate W-Q Lim G Weiss E Wilson Wavelets with composite dilationsand their MRA properties Appl Comput Harmon Anal 20 202ndash236 (2006)
[359] EA Gutkin Overcomplete subspace systems and operator symbols Funct Anal Appl 9260ndash261 (1975)
[360] G Gyoumlrgyi Integration of the dynamical symmetry groups for the 1r potential Acta PhysAcad Sci Hung 27 435ndash439 (1969)
[361] BC Hall The Segal-Bargmann ldquoCoherent Staterdquo transform for compact Lie groups JFunct Analysis 122 103ndash151 (1994)
[362] B Hall JJ Mitchell Coherent states on spheres J Math Phys 43 1211ndash1236 (2002)[363] DK Hammond P Vandergheynst R Gribonval Wavelets on graphs via spectral theory
Appl Comput Harmon Anal 30 129ndash150 (2011)[364] Y Hassouni EMF Curado MA Rego-Monteiro Construction of coherent states for
physical algebraic system Phys Rev A 71 022104 (2005)[365] J He H Liu Admissible wavelets associated with the affine automorphism group of the
Siegel upper half-plane J Math Anal Appl 208 58ndash70 (1997)[366] J He H Liu Admissible wavelets associated with the classical domain of type one
Approx Appl 14 (1998) 89ndash105[367] J He L Peng Wavelet transform on the symmetric matrix space preprint Beijing (1997)
(unpublished)[368] J He L Peng Admissible wavelets on the unit disk Complex Variables 35 109ndash119
(1998)[369] DM Healy Jr FE Schroeck Jr On informational completeness of covariant localization
observables and Wigner coefficients J Math Phys 36 453ndash507 (1995)[370] C Heil D Walnut Continuous and discrete wavelet transforms SIAM Review 31 628ndash
666 (1989)[371] K Hepp EH Lieb On the superradiant phase transition for molecules in a quantized
radiation field The Dicke maser model Ann Phys (NY) 76 360ndash404 (1973)[372] K Hepp EH Lieb Equilibrium statistical mechanics of matter interacting with the
quantized radiation field Phys Rev A 8 2517ndash2525 (1973)[373] JA Hogan JD Lakey Extensions of the Heisenberg group by dilations and frames Appl
Comput Harmon Anal 2 174ndash199 (1995)[374] AL Hohoueacuteto K Thirulogasanthar ST Ali J-P Antoine Coherent states lattices and
square integrability of representations J Phys A Math Gen36 11817ndash11835 (2003)[375] M Holschneider On the wavelet transformation of fractal objects J Stat Phys 50 963ndash
993 (1988)[376] M Holschneider Wavelet analysis on the circle J Math Phys 31 39ndash44 (1990)[377] M Holschneider Inverse Radon transforms through inverse wavelet transforms Inv Probl
7 853ndash861 (1991)[378] M Holschneider Localization properties of wavelet transforms J Math Phys 34 3227ndash
3244 (1993)[379] M Holschneider General inversion formulas for wavelet transforms J Math Phys 34
4190ndash4198 (1993)[380] M Holschneider Wavelet analysis over abelian groups Applied Comput Harmon Anal
2 52ndash60 (1995)[381] M Holschneider Continuous wavelet transforms on the sphere J Math Phys 37 4156ndash
4165 (1996)[382] M Holschneider I Iglewska-Nowak Poisson wavelets on the sphere J Fourier Anal
Appl 13 405ndash419 (2007)
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[383] M Holschneider R Kronland-Martinet J Morlet P Tchamitchian A real-time algorithmfor signal analysis with the help of wavelet transform in Wavelets Time-FrequencyMethods and Phase Space (Proc Marseille 1987) ed by J-M Combes A Grossmann PTchamitchian 2nd edn (Springer Berlin 1990) pp 286ndash297
[384] M Holschneider P Tchamitchian Pointwise analysis of Riemannrsquos ldquonondifferentiablerdquofunction Invent Math 105 157ndash175 (1991)
[385] GR Honarasa MK Tavassoly M Hatami R Roknizadeh Nonclassical properties ofcoherent states and excited coherent states for continuous spectra J Phys A Math Theor44 085303 (2011)
[386] M Hongoh Coherent states associated with the continuous spectrum of noncompactgroups J Math Phys 18 2081ndash2085 (1977)
[387] A Horzela FH Szafraniec A measure free approach to coherent states J Phys A MathGen 45 244018 (2012)
[388] W-L Hwang S Mallat Characterization of self-similar multifractals with waveletmaxima Appl Comput Harmon Anal 1 316ndash328 (1994)
[389] W-L Hwang C-S Lu P-C Chung Shape from texture Estimation of planar surfaceorientation through the ridge surfaces of continuous wavelet transform IEEE Trans ImageProc 7 773ndash780 (1998)
[390] I Iglewska-Nowak M Holschneider Frames of Poisson wavelets on the sphere ApplComput Harmon Anal 28 227ndash248 (2010)
[391] E Inoumlnuuml EP Wigner On the contraction of groups and their representations Proc NatAcad Sci U S 39 510ndash524 (1953)
[392] S Iqbal F Saif Generalized coherent states and their statistical characteristics in power-law potentials J Math Phys 52 082105 (2011)
[393] CJ Isham JR Klauder Coherent states for n-dimensional Euclidean groups E(n) andtheir application J MathPhys 32 607ndash620 (1991)
[394] L Jacques J-P Antoine Multiselective pyramidal decomposition of images Wavelets withadaptive angular selectivity Int J Wavelets Multires Inform Proc 5 785ndash814 (2007)
[395] L Jacques L Duval C Chaux G Peyreacute A panorama on multiscale geometric rep-resentations intertwining spatial directional and frequency selectivity Signal Proc 912699ndash2730 (2011)
[396] HR Jalali M K Tavassoly On the ladder operators and nonclassicality of generalizedcoherent state associated with a particle in an infinite square well preprint (2013)arXiv13034100v1 [quant-ph]
[397] C Johnston On the pseudo-dilation representations of Flornes Grossmann Holschneiderand Torreacutesani Appl Comput Harmon Anal 3 377ndash385 (1997)
[398] G Kaiser Phase-space approach to relativistic quantum mechanics I Coherent staterepresentation for massive scalar particles J MathPhys 18 952ndash959 (1977)
[399] G Kaiser Phase-space approach to relativistic quantum mechanics II Geometrical aspectsJ MathPhys 19 502ndash507 (1978)
[400] C Kalisa B Torreacutesani N-dimensional affine Weyl-Heisenberg wavelets Ann Inst HPoincareacute 59 201ndash236 (1993)
[401] W Kaminski J Lewandowski T Pawłowski Quantum constraints Dirac observables andevolution group averaging versus the Schroumldinger picture in LQC Class Quant Grav 26245016 (2009)
[402] MR Karim ST Ali A relativistic windowed Fourier transform preprint ConcordiaUniversity Montreacuteal (1997) (unpublished)
[403] M R Karim ST Ali M Bodruzzaman A relativistic windowed Fourier transform inProceedings of IEEE SoutheastCon 2000 Nashville Tennessee pp 253ndash260 (2000)
[404] T Kawazoe Wavelet transforms associated to a principal series representation of semisim-ple Lie groups I II Proc Japan Acad Ser A ndash Math Sci 71 154ndash157 158ndash160 (1995)
[405] T Kawazoe Wavelet transform associated to an induced representation of SL(n+ 2R)Ann Inst H Poincareacute 65 1ndash13 (1996)
References 563
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[407] P Kittipoom G Kutyniok W-Q Lim Construction of compactly supported shearletframes Constr Approx 35 21ndash72 (2012)
[408] J Kiukas P Lahti K Ylinenc Phase space quantization and the operator moment problemJ Math Phys 47 072104 (2006)
[409] JR Klauder Continuous-representation theory I Postulates of continuous-representationtheory J Math Phys 4 1055ndash1058 (1963)
[410] JR Klauder Continuous-representation theory II Generalized relation between quantumand classical dynamics J Math Phys 4 1058ndash1073 (1963)
[411] JR Klauder Path integrals for affine variables in Functional Integration Theory andApplications ed by J-P Antoine E Tirapegui (Plenum Press New York and London1980) pp 101ndash119
[412] JR Klauder Are coherent states the natural language of quantum mechanics inFundamental Aspects of Quantum Theory ed by V Gorini A Frigerio NATO ASI Seriesvol B 144 (Plenum Press New York 1986) pp 1ndash12
[413] JR Klauder Quantization without quantization Ann Phys (NY) 237 147ndash160 (1995)[414] JR Klauder Coherent states for the hydrogen atom J Phys A Math Gen 29 L293ndash
L296 (1996)[415] JR Klauder An affinity for affine quantum gravity Proc Steklov Inst Math 272 169ndash176
(2011) and references therein[416] JR Klauder RF Streater A wavelet transform for the Poincareacute group J Math Phys 32
1609ndash1611 (1991)[417] JR Klauder RF Streater Wavelets and the Poincareacute half-plane J Math Phys 35 471ndash
478 (1994)[418] JR Klauder K Penson J-M Sixdeniers Constructing coherent states through solutions
of Stieltjes and Hausdorff moment problems Phys Rev A 64 013817 (2001)[419] A Kleppner RL Lipsman The Plancherel formula for group extensions Ann Ec Norm
Sup 5 459ndash516 (1972)[420] AB Klimov C Muntildeoz Coherent isotropic and squeezed states in a N-qubit system Phys
Scr 87 038110 (2013)[421] A Klyashko Dynamical symmetry approach to entanglement in Physics and Theoretical
Computer Science From Numbers and Languages to (Quantum) Cryptography - NATOSecurity through Science Series D - Information and Communication Security vol 7 edby J-P Gazeau J Nesetril B Rovan (IOS Press Washington DC 2007) pp 25ndash54
[422] S Kobayashi Irreducibility of certain unitary representations J Math Soc Japan 20 638ndash642 (1968)
[423] K Kowalski J Rembielinski LC Papaloucas Coherent states for a quantum particle ona circle J Phys A Math Gen 29 4149ndash4167 (1996)
[424] K Kowalski J Rembielinski Quantum mechanics on a sphere and coherent states J PhysA Math Gen 33 6035ndash6048 (2000)
[425] K Kowalski J Rembielinski The Bargmann representation for the quantum mechanicson a sphere J Math Phys 42 4138ndash4147 (2001)
[426] C Kristjansen J Plefka GW Semenoff M Staudacher A new double-scaling limit ofN = 4 super-Yang-Mills theory and pp-wave strings Nuclear Phys B 643 3ndash30 (2002)
[427] M Kulesh M Holschneider MS Diallo Geophysical wavelet library Applications ofthe continuous wavelet transform to the polarization and dispersion analysis of signalsComput Geosci 34 1732ndash1752 (2008)
[428] R Kunze On the Frobenius reciprocity theorem for square integrable representationsPacific J Math 53 465ndash471 (1974)
[429] Y Kuroda A Wada T Yamazaki K Nagayama Postacquisition data processing methodfor suppression of the solvent signal I J Magn Reson 84 604ndash610 (1989)
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[430] Y Kuroda A Wada T Yamazaki K Nagayama Postacquisition data processing methodfor suppression of the solvent signal II The weighted first derivative J Magn Reson 88141ndash145 (1990)
[431] G Kutyniok D Labate Resolution of the wavefront set using continuous shearlets TransAmer Math Soc 361 2719ndash2754 (2009)
[432] G Kutyniok W-Q Lim Compactly supported shearlets are optimally sparse J ApproxTheory 163 1564ndash1589 (2011)
[433] D Labate W-Q Lim G Kutyniok G Weiss Sparse multidimensional representationusing shearlets in Wavelets XI (San Diego CA 2005) ed by M Papadakis A Laine MUnser SPIE Proceedings vol 5914 (SPIE Bellingham WA 2005) pp 254ndash262
[434] P Lahti J-P Pellonpaumlauml Continuous variable tomographic measurements Phys Lett A373 3435ndash3438 (2009)
[435] Lambertrsquos projection see WikipediahttpenwikipediaorgwikiLambert_azimuthal_equal-area_projection
[436] J-P Leduc F Mujica R Murenzi MJT Smith Missile-tracking algorithm using target-adapted spatio-temporal wavelets in Automatic Object Recognition VII SPIE Proceedingsvol 5914 (SPIE Bellingham WA 1997) pp 400ndash411
[437] J-P Leduc F Mujica R Murenzi MJT Smith Spatio-temporal wavelet transforms formotion tracking in IEEE ICASSP 1997 vol 4 (1997) pp 3013ndash3016
[438] J-P Leduc F Mujica R Murenzi MJT Smith Spatio-temporal continuous waveletsapplied to missile warhead detection and tracking in SPIE VCIP rsquo97 vol 3024 ed byJ Biemond EJ Delp (1997) pp 787ndash798
[439] B Leistedt JD McEwen Exact wavelets on the ball IEEE Trans Signal Proc 60 1564ndash1589 (2012)
[440] PG Lemarieacute Y Meyer Ondelettes et bases hilbertiennes Rev Math Iberoamer 2 1ndash18(1986)
[441] C Lemke A Schuck Jr J-P Antoine D Sima Metabolite-sensitive analysis of magneticresonance spectroscopic signals using the continuous wavelet transform Meas SciTechnol 22 (2011) Art 114013
[442] J-M Leacutevy-Leblond Galilei group and non-relativistic quantum mechanics J Math Phys4 776-788 (1963)
[443] J-M Leacutevy-Leblond Galilei group and Galilean invariance in Group Theory and ItsApplications vol II ed by EM Loebl (Academic New York 1971) pp 221ndash299
[444] J-M Leacutevy-Leblond On the conceptual nature of the physical constants Riv Nuovo Cim7 187ndash214 (1977)
[445] EH Lieb The classical limit of quantum spin systems Commun Math Phys 31 327ndash340(1973)
[446] G Lindblad B Nagel Continuous bases for unitary irreducible representations of SU(11)Ann Inst H Poincareacute 13 27ndash56 (1970)
[447] W Lisiecki Kaumlhler coherent states orbits for representations of semisimple Lie groupsAnn Inst H Poincareacute 53 857ndash890 (1990)
[448] A Lisowska Moment-based fast wedgelet transform J Math Imaging Vis 39 180ndash192(2011)
[449] H Liu L Peng Admissible wavelets associated with the Heisenberg group Pacific JMath 180 101ndash123 (1997)
[450] E Livine S Speziale Physical boundary state for the quantum tetrahedron Class QuantGrav 25 085003 (2008)
[451] F Low Complete sets of wave packets in A Passion for Physics ndash Essay in Honor ofGeoffrey Chew ed by C DeTar (World Scientific Singapore 1985) pp 17ndash22
[452] G Mack All unitary ray representations of the conformal group SU(22) with positiveenergy Commun Math Phys 55 1ndash28 (1977)
[453] GW Mackey Imprimitivity for representations of locally compact groups I Proc NatAcad Sci 35 537ndash545 (1949)
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[454] S Majid M Rodriguez-Plaza Random walk and the heat equation on superspace andanyspace J Math Phys 35 3753ndash3760 (1994)
[455] M Mallalieu CR Stroud Jr Rydberg wave packets fractional revivals and classicalorbits in Coherent States Past Present and Future (Proc Oak Ridge 1993) ed by DHFeng JR Klauder M Strayer (World Scientific Singapore 1994) pp 301ndash314
[456] SG Mallat Multifrequency channel decompositions of images and wavelet models IEEETrans Acoust Speech Signal Proc 37 2091ndash2110 (1989)
[457] SG Mallat A theory for multiresolution signal decomposition The wavelet representa-tion IEEE Trans Pattern Anal Machine Intell 11 674ndash693 (1989)
[458] S Mallat W-L Hwang Singularity detection and processing with wavelets IEEE TransInform Theory 38 617ndash643 (1992)
[459] S Mallat Z Zhang Matching pursuits with time frequency dictionaries IEEE TransSignal Proc 41 3397ndash3415 (1993)
[460] S Mallat S Zhong Wavelet maxima representation in Wavelets and Applications (ProcMarseille 1989) ed by Y Meyer (Masson and Springer Paris and Berlin 1991) pp 207ndash284
[461] VI Manrsquoko G Marmo ECG Sudarshan F Zaccaria f -oscillators and non-linearcoherent states Phys Scr 55 528ndash541 (1997)
[462] D Marinucci D Pietrobon A Baldi P Baldi P Cabella G Kerkyacharian P Natoli DPicard N Vittorio Spherical needlets for CMB data analysis Mon Not R Astron Soc383 539ndash545 (2008)
[463] D Marion M Ikura A Bax Improved solvent suppression in one- and two-dimensionalNMR spectra by convolution of time-domain data J Magn Reson 84 425ndash430 (1989)
[464] Y Meyer Principe drsquoincertitude bases hilbertiennes et algegravebres drsquoopeacuterateurs SeacuteminaireBourbaki 662 (1985ndash1986)
[465] Y Meyer Principe drsquoincertitude bases hilbertiennes et algegravebres drsquoopeacuterateurs Asteacuterisque145ndash146 209ndash223 (1987)
[466] Y Meyer H Xu Wavelet analysis and chirps Appl Comput Harmon Anal 4 366ndash379(1997)
[467] L Michel Invariance in quantum mechanics and group extensions in Group TheoreticalConcepts and Methods in Elementary Particle Physics ed by F Guumlrsey (Gordon andBreach New York and London 1964) pp 135ndash200
[468] J Mickelsson J Niederle Contractions of representations of the de Sitter groupsCommun Math Phys 27 167ndash180 (1972)
[469] MM Miller Convergence of the Sudarshan expansion for the diagonal coherent-stateweight functional J Math Phys 9 1270ndash1274 (1968)
[470] V F Molchanov Harmonic analysis on homogeneous spaces in Representation Theoryand Noncommutative Harmonic Analysis II ed by AA Kirillov (Springer Berlin 1995)
[471] MI Monastyrsky AM Perelomov Coherent states and symmetric spaces II Ann InstH Poincareacute 23 23ndash48 (1975)
[472] B Moran S Howard D Cochran Positive-operator-valued measures A general settingfor frames in Excursions in Harmonic Analysis vol 1 2 ed by TD Andrews R BalanJJ Benedetto W Czaja KA Okoudjou (Birkhaumluser Boston 2013) pp 49ndash64
[473] H Moscovici Coherent states representations of nilpotent Lie groups Commun MathPhys 54 63ndash68 (1977)
[474] H Moscovici A Verona Coherent states and square integrable representations Ann InstH Poincareacute 29 139ndash156 (1978)
[475] F Mujica R Murenzi MJT Smith J-P Leduc Robust tracking in compressed imagesequences J Electr Imaging 7 746ndash754 (1998)
[476] R Murenzi Wavelet transforms associated to the n-dimensional Euclidean group withdilations Signals in more than one dimension in Wavelets Time-Frequency Methodsand Phase Space (Proc Marseille 1987) ed by J-M Combes A Grossmann PTchamitchian 2nd edn (Springer Berlin 1990) pp 239ndash246
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[477] MA Muschietti B Torreacutesani Pyramidal algorithms for LittlewoodndashPaley decomposi-tions SIAM J Math Anal 26 925ndash943 (1995)
[478] B Nagel Generalized eigenvectors in group representations in Studies in MathematicalPhysics (Proc Istanbul 1970) ed by AO Barut (Reidel Dordrecht and Boston 1970)pp 135ndash154
[479] MA Naımark Dokl Akad Nauk SSSR 41 359ndash361 (1943) see also B Sz-NagyExtensions of linear transformations in Hilbert space which extend beyond this spaceAppendix to F Riesz B Sz-Nagy Functional Analysis (Frederick Ungar New York 1960)
[480] FJ Narcowich P Petrushev JD Ward Localized tight frames on spheres SIAM J MathAnal 38 574ndash594 (2006)
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[486] MM Nieto LM Simmons Jr Coherent states for general potentials Phys Rev Lett 41207ndash210 (1987)
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[579] T Thiemann Gauge field theory coherent states (GCS) 1 General properties Class QuantGrav 18 2025ndash2064 (2001)
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4200 (1998) and references quoted there[616] AA Zakharova On the properties of generalized frames Math Notes 83 190ndash200 (2008)[617] W-M Zhang DH Feng R Gilmore Coherent states Theory and some applications Rev
Mod Phys 26 867ndash927 (1990)[618] I Zlatev W-M Zhang DH Feng Possibility that Schroumldingerrsquos conjecture for the
hydrogen atom coherent states is not attainable Phys Rev A 50 R1973ndashR1975 (1994)[619] WH Zurek Decoherence einselection and the quantum origins of the classical Rev Mod
Phys 75 715ndash775 (2003)[620] WH Zurek S Habib JP Paz Coherent states via decoherence Phys Rev Lett 70 1187ndash
1190 (1993)[621] K Zyczkowski Squeezed states in a quantum chaotic system J Phys A Math Theor 22
of SU(11) 81 296 297HilbertClowast-modules 164holomorphic 140nonholomorphic 151nonlinear 146of affine Galilei group 505of affine Poincareacute group 509of affine Weyl-Heisenberg group GaWH
497of compact semisimple Lie groups 174of Euclidean group E(n) 266of Galilei group G (11) 290of isochronous Galilei group 237of non-semisimple Lie groups 179of noncompact semisimple Lie groups 177of Poincareacute group Puarr
+(11) 283massless case 288
of Poincareacute group Puarr+(13) 279
of Schroumldinger group 508quasi-coherent states 186quaternionic 164
ST Ali et al Coherent States Wavelets and Their Generalizations Theoreticaland Mathematical Physics DOI 101007978-1-4614-8535-3copy Springer Science+Business Media New York 2014
573
574 Index
coherent states (CS) (cont)spin or SU(2) 175square integrable covariant 166 180 264vector (VCS) 73 108 112 170weighted 184 523
of affine Weyl-Heisenberg group GaWH497
of Poincareacute group Puarr+(11) 284
cohomology group 393 403coboundaries 403cochains 402cocycle 403
algebraic 387Cauchy 418Cauchy-Paul 354 419 425conical 418difference 417 462directional 416 440kinematical 499local 488metabolite-based 355 374minimal uncertainty 425multiselective 440on a graph 493on the sphere S
2 458on the sphere S
n 479on the torus T2 481steerable 439von Mises 440
wedgelet transform 455Wigner function 322Wigner-Ville transform 349Windowed Fourier or Gabor transform 349
ZZak transform 518
References
A Books and Theses
B Articles
Index
556 References
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[239] S De Biegravevre JA Gonzaacutelez Semiclassical behaviour of coherent states on the circle inQuantization and Coherent States Methods in Physics ed by A Odzijewicz et al (WorldScientific Singapore 1993)
[240] S De Biegravevre AE Gradechi Quantum mechanics and coherent states on the anti-de Sitterspace-time and their Poincareacute contraction Ann Inst H Poincareacute 57 403ndash428 (1992)
[241] J Deenen C Quesne Dynamical group of collective states I II III J Math Phys 23878ndash889 2004ndash2015 (1982)
[242] J Deenen C Quesne Dynamical group of collective states I II III J Math Phys 251638ndash1650 (1984)
[243] J Deenen C Quesne Partially coherent states of the real symplectic group J Math Phys25 2354ndash2366 (1984)
[244] J Deenen C Quesne Boson representations of the real symplectic group and theirapplication to the nuclear collective model J Math Phys 26 2705ndash2716 (1985)
[245] R Delbourgo Minimal uncertainty states for the rotation and allied groups J Phys AMath Gen 10 1837ndash1846 (1977)
[246] R Delbourgo J R Fox Maximum weight vectors possess minimal uncertainty J PhysA Math Gen 10 L233ndashL235 (1977)
[247] V Delouille J de Patoul J-F Hochedez L Jacques J-P Antoine Wavelet spectrumanalysis of EITSoHO images Solar Phys 228 301ndash321 (2005)
[248] N Delprat B Escudieacute P Guillemain R Kronland-Martinet P Tchamitchian B Tor-reacutesani Asymptotic wavelet and Gabor analysis Extraction of instantaneous frequenciesIEEE Trans Inform Theory 38 644ndash664 (1992)
[249] Th Deutsch L Genovese Wavelets for electronic structure calculations Collection SocFr Neut 12 33ndash76 (2011)
[250] B Dewitt Quantum theory of gravity I The canonical theory Phys Rev 160 1113ndash1148(1967)
[251] RH Dicke Coherence in spontaneous radiation processes Phys Rev 93 99ndash110 (1954)[252] AN Dinkelaker AL MacKinnon Wavelets intermittency and solar flare hard X-rays 1
Local intermittency measure in cascade and avalanche scenarios Solar Phys 282 471ndash481(2013)
[253] AN Dinkelaker AL MacKinnon Wavelets intermittency and solar flare hard X-rays 2LIM analysis of high time resolution BATSE data Solar Phys 282 483ndash501 (2013)
[254] MN Do M Vetterli Contourlets in Beyond Wavelets ed by GV Welland (AcademicSan Diego 2003) pp 83ndash105
[255] MN Do M Vetterli The contourlet transform An efficient directional multiresolutionimage representation IEEE Trans Image Process 14 2091ndash2106 (2005)
[256] VV Dodonov Nonclassical states in quantum optics A ldquosqueezedrdquo review of the first 75years J Opt B Quant Semiclass Opot 4 R1ndashR33 (2002)
[257] DL Donoho Nonlinear wavelet methods for recovery of signals densities and spectrafrom indirect and noisy data in Different Perspectives on Wavelets Proceedings ofSymposia in Applied Mathematics vol 38 ed by I Daubechies (American MathematicalSociety Providence RI 1993) pp 173ndash205
[258] DL Donoho Wedgelets Nearly minimax estimation of edges Ann Stat 27 859ndash897(1999)
[259] DL Donoho X Huo Beamlet pyramids A new form of multiresolution analysis suitedfor extracting lines curves and objects from very noisy image data in SPIE Proceedingsvol 5914 (SPIE Bellingham WA 2005) pp 1ndash12
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[268] M Duval-Destin M-A Muschietti B Torreacutesani Continuous wavelet decompositionsmultiresolution and contrast analysis SIAM J Math Anal 24 739ndash755 (1993)
[269] SJL van Eindhoven JLH Meyers New orthogonality relations for the Hermitepolynomials and related Hilbert spaces J Math Anal Appl 146 89ndash98 (1990)
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[278] HG Feichtinger KH Groumlchenig Banach spaces related to integrable group representa-tions and their atomic decompositions I J Funct Anal 86 307ndash340 (1989)
[279] HG Feichtinger KH Groumlchenig Banach spaces related to integrable group representa-tions and their atomic decompositions II Mh Math 108 129ndash148 (1989)
[280] M Flensted-Jensen Discrete series for semisimple symmetric spaces Ann of Math 111253ndash311 (1980)
[281] K Flornes A Grossmann M Holschneider B Torreacutesani Wavelets on discrete fieldsAppl Comput Harmon Anal 1 137ndash146 (1994)
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problem J Fourier Anal Appl 11 245ndash287 (2005)
558 References
[284] W Freeden M Schreiner Orthogonal and non-orthogonal multiresolution analysis scalediscrete and exact fully discrete wavelet transform on the sphere Constr Approx 14 493ndash515 (1997)
[285] W Freeden U Windheuser Combined spherical harmonic and wavelet expansion mdash Afuture concept in Earthrsquos gravitational determination Appl Comput Harmon Anal 4 1ndash37 (1997)
[286] W Freeden T Maier S Zimmermann A survey on wavelet methods for (geo)applicationsRevista Mathematica Complutense 16 (2003) 277ndash310
[287] W Freeden M Schreiner Biorthogonal locally supported wavelets on the sphere based onzonal kernel functions J Fourier Anal Appl 13 693ndash709 (2007)
[288] WT Freeman EH Adelson The design and use of steerable filters IEEE Trans PatternAnal Machine Intell 13 891ndash906 (1991)
[289] L Freidel ER Livine U(N) coherent states for loop quantum gravity J Math Phys 52052502 (2011)
[290] J Froment S Mallat Arbitrary low bit rate image compression using wavelets in Progressin Wavelet Analysis and Applications (Proc Toulouse 1992) ed by Y Meyer S Roques(Ed Frontiegraveres Gif-sur-Yvette 1993) pp 413ndash418 and references therein
[291] L Freidel S Speziale Twisted geometries A geometric parameterisation of SU(2) phasespace Phys Rev D 82 084040 (2010)
[292] H Fuumlhr Wavelet frames and admissibility in higher dimensions J Math Phys 37 6353ndash6366 (1996)
[293] H Fuumlhr M Mayer Continuous wavelet transforms from semidirect products Cyclicrepresentations and Plancherel measure J Fourier Anal Appl 8 375ndash396 (2002)
[294] D Gabor Theory of communication J Inst Electr Engrg(London) 93 429ndash457 (1946)[295] J-P Gabardo D Han Frames associated with measurable spaces Adv Comput Math 18
127ndash147 (2003)[296] E Galapon Paulirsquos theorem and quantum canonical pairs The consistency of a bounded
self-adjoint time operator canonically conjugate to a Hamiltonian with non-empty pointspectrum Proc R Soc Lond A 458 451ndash472 (2002)
[297] PL Garciacutea de Leacuteon J-P Gazeau Coherent state quantization and phase operator PhysLett A 361 301ndash304 (2007)
[298] L Garciacutea de Leoacuten J-P Gazeau J Queacuteva The infinite well revisited Coherent states andquantization Phys Lett A 372 3597ndash3607 (2008)
[299] T Garidi J-P Gazeau E Huguet M Lachiegraveze Rey J Renaud Fuzzy spheres frominequivalent coherent states quantization J Phys A Math Theor 40 10225ndash10249 (2007)
[300] J-P Gazeau Four Euclidean conformal group in atomic calculations Exact analyticalexpressions for the bound-bound two-photon transition matrix elements in the H atomJ Math Phys 19 1041ndash1048 (1978)
[301] J-P Gazeau On the four Euclidean conformal group structure of the sturmian operatorLett Math Phys 3 285ndash292 (1979)
[302] J-P Gazeau Technique Sturmienne pour le spectre discret de lrsquoeacutequation de SchroumldingerJ Phys A Math Gen 13 3605ndash3617 (1980)
[303] J-P Gazeau Four Euclidean conformal group approach to the multiphoton processes in theH atom J Math Phys 23 156ndash164 (1982)
[304] J-P Gazeau A remarkable duality in one particle quantum mechanics between someconfining potentials and (R+Linfin
ε ) potentials Phys Lett 75A 159ndash163 (1980)[305] J-P Gazeau SL(2R)-coherent states and integrable systems in classical and quantum
physics in Quantization Coherent States and Complex Structures ed by J-P AntoineST Ali W Lisiecki IM Mladenov A Odzijewicz (Plenum Press New York and London1995) pp 147ndash158
[306] J-P Gazeau S Graffi Quantum harmonic oscillator A relativistic and statistical point ofview Boll Unione Mat Ital 11-A 815ndash839 (1997)
[307] J-P Gazeau V Hussin Poincareacute contraction of SU(11) Fock-Bargmann structure J PhysA Math Gen 25 1549ndash1573 (1992)
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[309] J-P Gazeau JR Klauder Coherent states for systems with discrete and continuousspectrum J Phys A Math Gen 32 123ndash132 (1999)
[310] J-P Gazeau P Monceau Generalized coherent states for arbitrary quantum systems inColloquium M Flato (Dijon Sept 99) vol II (Kluumlwer Dordrecht 2000) pp 131ndash144
[311] J-P Gazeau M Novello The question of mass in (Anti-) de Sitter space-times J Phys AMath Theor 41 304008 (2008)
[312] J-P Gazeau M del Olmo q-coherent states quantization of the harmonic oscillator AnnPhys (NY) 330 220ndash245 (2013) arXiv12071200 [quant-ph]
[313] J-P Gazeau J Patera Tau-wavelets of Haar J Phys A Math Gen 29 4549ndash4559 (1996)[314] J-P Gazeau W Piechocki Coherent states quantization of a particle in de Sitter space
J Phys A Math Gen 37 6977ndash6986 (2004)[315] J-P Gazeau J Renaud Lie algorithm for an interacting SU(11) elementary system and its
contraction Ann Phys (NY) 222 89ndash121 (1993)[316] J-P Gazeau J Renaud Relativistic harmonic oscillator and space curvature Phys Lett A
179 67ndash71 (1993)[317] J-P Gazeau V Spiridonov Toward discrete wavelets with irrational scaling factor J Math
plane J Phys A Math Theor 44 495201 (2011)[319] J-P Gazeau J Patera E Pelantovaacute Tau-wavelets in the plane J Math Phys 39 4201ndash
4212 (1998)[320] J-P Gazeau M Andrle C Burdiacutek R Krejcar Wavelet multiresolutions for the Fibonacci
chain J Phys A Math Gen 33 L47ndashL51 (2000)[321] J-P Gazeau M Andrle C Burdiacutek Bernuau spline wavelets and sturmian sequences
J Fourier Anal Appl 10 269ndash300 (2004)[322] J-P Gazeau F-X Josse-Michaux P Monceau Finite dimensional quantizations of the
(q p) plane new space and momentum inequalities Int J Modern Phys B 20 1778ndash1791 (2006)
[323] J-P Gazeau J Mourad J Queacuteva Fuzzy de Sitter space-times via coherent statesquantization in Proceedings of the XXVIth Colloquium on Group Theoretical Methodsin Physics New York 2006 ed by J Birman S Catto B Nicolescu (Canopus PublishingLimited London 2009)
[324] D Geller A Mayeli Continuous wavelets on compact manifolds Math Z 262 895ndash927(2009)
[325] D Geller A Mayeli Nearly tight frames and space-frequency analysis on compactmanifolds Math Z 263 235ndash264 (2009)
[326] L Genovese B Videau M Ospici Th Deutsch S Goedecker J-F Mhaut Daubechieswavelets for high performance electronic structure calculations The BigDFT project CR Mecanique 339 149ndash164 (2011)
[327] G Gentili C Stoppato Power series and analyticity over the quaternions Math Ann 352113ndash131 (2012)
[328] G Gentili DC Struppa A new theory of regular functions of a quaternionic variable AdvMath 216 279ndash301 (2007)
[329] C Geyer K Daniilidis Catadioptric projective geometry Int J Comput Vision 45 223ndash243 (2001)
[330] R Gilmore Geometry of symmetrized states Ann Phys (NY) 74 391ndash463 (1972)[331] R Gilmore On properties of coherent states Rev Mex Fis 23 143ndash187 (1974)[332] J Ginibre Statistical ensembles of complex quaternion and real matrices J Math Phys
6 440ndash449 (1965)[333] RJ Glauber The quantum theory of optical coherence Phys Rev 130 2529ndash2539 (1963)
560 References
[334] RJ Glauber Coherent and incoherent states of radiation field Phys Rev 131 2766ndash2788(1963)
[335] J Glimm Locally compact transformation groups Trans Amer Math Soc 101 124ndash138(1961)
[336] R Godement Sur les relations drsquoorthogonaliteacute de V Bargmann C R Acad Sci Paris 255521ndash523 657ndash659 (1947)
[337] C Gonnet B Torreacutesani Local frequency analysis with two-dimensional wavelet trans-form Signal Proc 37 389ndash404 (1994)
[338] JA Gonzalez MA del Olmo Coherent states on the circle J Phys A Math Gen 318841ndash8857 (1998)
[339] XGonze B Amadon et al ABINIT First-principles approach to material and nanosystemproperties Computer Physics Comm 180 2582ndash2615 (2009)
[340] KM Gograverski E Hivon AJ Banday BD Wandelt FK Hansen M Reinecke MBartelmann HEALPix A framework for high-resolution discretization and fast analysisof data distributed on the sphere Astrophys J 622 759ndash771 (2005)
[341] P Goupillaud A Grossmann J Morlet Cycle-octave and related transforms in seismicsignal analysis Geoexploration 23 85ndash102 (1984)
[342] KH Groumlchenig A new approach to irregular sampling of band-limited functions in RecentAdvances in Fourier Analysis and Its applications ed by JS Byrnes JL Byrnes (KluwerDordrecht 1990) pp 251ndash260
[343] KH Groumlchenig Gabor analysis over LCA groups in Gabor Analysis and Algorithms ndashTheory and Applications ed by HG Feichtinger T Strohmer (Birkhaumluser Boston-Basel-Berlin 1998) pp 211ndash231
[344] HJ Groenewold On the principles of elementary quantum mechanics Physica 12 405ndash460 (1946)
[345] P Grohs Continuous shearlet tight frames J Fourier Anal Appl 17 506ndash518 (2011)[346] P Grohs G Kutyniok Parabolic molecules preprint TU Berlin (2012)[347] M Grosser A note on distribution spaces on manifolds Novi Sad J Math 38 121ndash128
(2008)[348] A Grossmann Parity operator and quantization of δ -functions Commun Math Phys 48
191ndash194 (1976)[349] A Grossmann J Morlet Decomposition of Hardy functions into square integrable
wavelets of constant shape SIAM J Math Anal 15 723ndash736 (1984)[350] A Grossmann J Morlet Decomposition of functions into wavelets of constant shape and
related transforms in Mathematics + Physics Lectures on recent results I ed by L Streit(World Scientific Singapore 1985) pp 135ndash166
[351] A Grossmann J Morlet T Paul Integral transforms associated to square integrablerepresentations I General results J Math Phys 26 2473ndash2479 (1985)
[352] A Grossmann J Morlet T Paul Integral transforms associated to square integrablerepresentations II Examples Ann Inst H Poincareacute 45 293ndash309 (1986)
[353] A Grossmann R Kronland-Martinet J Morlet Reading and understanding the contin-uous wavelet transform in Wavelets Time-Frequency Methods and Phase Space (ProcMarseille 1987) ed by J-M Combes A Grossmann P Tchamitchian 2nd edn (SpringerBerlin 1990) pp 2ndash20
[354] P Guillemain R Kronland-Martinet B Martens Estimation of spectral lines with helpof the wavelet transform Application in NMR spectroscopy in Wavelets and Applications(Proc Marseille 1989) ed by Y Meyer (Masson and Springer Paris and Berlin 1991) pp38ndash60
[355] H de Guise M Bertola Coherent state realizations of su(n+ 1) on the n-torus J MathPhys 43 3425ndash3444 (2002)
[356] K Guo D Labate Representation of Fourier Integral Operators using shearlets J FourierAnal Appl 14 327ndash371 (2008)
References 561
[357] K Guo G Kutyniok D Labate Sparse multidimensional representations usinganisotropic dilation and shear operators in Wavelets and Spines (Athens GA 2005)(Nashboro Press Nashville TN 2006) pp 189ndash201
[358] K Guo D Labate W-Q Lim G Weiss E Wilson Wavelets with composite dilationsand their MRA properties Appl Comput Harmon Anal 20 202ndash236 (2006)
[359] EA Gutkin Overcomplete subspace systems and operator symbols Funct Anal Appl 9260ndash261 (1975)
[360] G Gyoumlrgyi Integration of the dynamical symmetry groups for the 1r potential Acta PhysAcad Sci Hung 27 435ndash439 (1969)
[361] BC Hall The Segal-Bargmann ldquoCoherent Staterdquo transform for compact Lie groups JFunct Analysis 122 103ndash151 (1994)
[362] B Hall JJ Mitchell Coherent states on spheres J Math Phys 43 1211ndash1236 (2002)[363] DK Hammond P Vandergheynst R Gribonval Wavelets on graphs via spectral theory
Appl Comput Harmon Anal 30 129ndash150 (2011)[364] Y Hassouni EMF Curado MA Rego-Monteiro Construction of coherent states for
physical algebraic system Phys Rev A 71 022104 (2005)[365] J He H Liu Admissible wavelets associated with the affine automorphism group of the
Siegel upper half-plane J Math Anal Appl 208 58ndash70 (1997)[366] J He H Liu Admissible wavelets associated with the classical domain of type one
Approx Appl 14 (1998) 89ndash105[367] J He L Peng Wavelet transform on the symmetric matrix space preprint Beijing (1997)
(unpublished)[368] J He L Peng Admissible wavelets on the unit disk Complex Variables 35 109ndash119
(1998)[369] DM Healy Jr FE Schroeck Jr On informational completeness of covariant localization
observables and Wigner coefficients J Math Phys 36 453ndash507 (1995)[370] C Heil D Walnut Continuous and discrete wavelet transforms SIAM Review 31 628ndash
666 (1989)[371] K Hepp EH Lieb On the superradiant phase transition for molecules in a quantized
radiation field The Dicke maser model Ann Phys (NY) 76 360ndash404 (1973)[372] K Hepp EH Lieb Equilibrium statistical mechanics of matter interacting with the
quantized radiation field Phys Rev A 8 2517ndash2525 (1973)[373] JA Hogan JD Lakey Extensions of the Heisenberg group by dilations and frames Appl
Comput Harmon Anal 2 174ndash199 (1995)[374] AL Hohoueacuteto K Thirulogasanthar ST Ali J-P Antoine Coherent states lattices and
square integrability of representations J Phys A Math Gen36 11817ndash11835 (2003)[375] M Holschneider On the wavelet transformation of fractal objects J Stat Phys 50 963ndash
993 (1988)[376] M Holschneider Wavelet analysis on the circle J Math Phys 31 39ndash44 (1990)[377] M Holschneider Inverse Radon transforms through inverse wavelet transforms Inv Probl
7 853ndash861 (1991)[378] M Holschneider Localization properties of wavelet transforms J Math Phys 34 3227ndash
3244 (1993)[379] M Holschneider General inversion formulas for wavelet transforms J Math Phys 34
4190ndash4198 (1993)[380] M Holschneider Wavelet analysis over abelian groups Applied Comput Harmon Anal
2 52ndash60 (1995)[381] M Holschneider Continuous wavelet transforms on the sphere J Math Phys 37 4156ndash
4165 (1996)[382] M Holschneider I Iglewska-Nowak Poisson wavelets on the sphere J Fourier Anal
Appl 13 405ndash419 (2007)
562 References
[383] M Holschneider R Kronland-Martinet J Morlet P Tchamitchian A real-time algorithmfor signal analysis with the help of wavelet transform in Wavelets Time-FrequencyMethods and Phase Space (Proc Marseille 1987) ed by J-M Combes A Grossmann PTchamitchian 2nd edn (Springer Berlin 1990) pp 286ndash297
[384] M Holschneider P Tchamitchian Pointwise analysis of Riemannrsquos ldquonondifferentiablerdquofunction Invent Math 105 157ndash175 (1991)
[385] GR Honarasa MK Tavassoly M Hatami R Roknizadeh Nonclassical properties ofcoherent states and excited coherent states for continuous spectra J Phys A Math Theor44 085303 (2011)
[386] M Hongoh Coherent states associated with the continuous spectrum of noncompactgroups J Math Phys 18 2081ndash2085 (1977)
[387] A Horzela FH Szafraniec A measure free approach to coherent states J Phys A MathGen 45 244018 (2012)
[388] W-L Hwang S Mallat Characterization of self-similar multifractals with waveletmaxima Appl Comput Harmon Anal 1 316ndash328 (1994)
[389] W-L Hwang C-S Lu P-C Chung Shape from texture Estimation of planar surfaceorientation through the ridge surfaces of continuous wavelet transform IEEE Trans ImageProc 7 773ndash780 (1998)
[390] I Iglewska-Nowak M Holschneider Frames of Poisson wavelets on the sphere ApplComput Harmon Anal 28 227ndash248 (2010)
[391] E Inoumlnuuml EP Wigner On the contraction of groups and their representations Proc NatAcad Sci U S 39 510ndash524 (1953)
[392] S Iqbal F Saif Generalized coherent states and their statistical characteristics in power-law potentials J Math Phys 52 082105 (2011)
[393] CJ Isham JR Klauder Coherent states for n-dimensional Euclidean groups E(n) andtheir application J MathPhys 32 607ndash620 (1991)
[394] L Jacques J-P Antoine Multiselective pyramidal decomposition of images Wavelets withadaptive angular selectivity Int J Wavelets Multires Inform Proc 5 785ndash814 (2007)
[395] L Jacques L Duval C Chaux G Peyreacute A panorama on multiscale geometric rep-resentations intertwining spatial directional and frequency selectivity Signal Proc 912699ndash2730 (2011)
[396] HR Jalali M K Tavassoly On the ladder operators and nonclassicality of generalizedcoherent state associated with a particle in an infinite square well preprint (2013)arXiv13034100v1 [quant-ph]
[397] C Johnston On the pseudo-dilation representations of Flornes Grossmann Holschneiderand Torreacutesani Appl Comput Harmon Anal 3 377ndash385 (1997)
[398] G Kaiser Phase-space approach to relativistic quantum mechanics I Coherent staterepresentation for massive scalar particles J MathPhys 18 952ndash959 (1977)
[399] G Kaiser Phase-space approach to relativistic quantum mechanics II Geometrical aspectsJ MathPhys 19 502ndash507 (1978)
[400] C Kalisa B Torreacutesani N-dimensional affine Weyl-Heisenberg wavelets Ann Inst HPoincareacute 59 201ndash236 (1993)
[401] W Kaminski J Lewandowski T Pawłowski Quantum constraints Dirac observables andevolution group averaging versus the Schroumldinger picture in LQC Class Quant Grav 26245016 (2009)
[402] MR Karim ST Ali A relativistic windowed Fourier transform preprint ConcordiaUniversity Montreacuteal (1997) (unpublished)
[403] M R Karim ST Ali M Bodruzzaman A relativistic windowed Fourier transform inProceedings of IEEE SoutheastCon 2000 Nashville Tennessee pp 253ndash260 (2000)
[404] T Kawazoe Wavelet transforms associated to a principal series representation of semisim-ple Lie groups I II Proc Japan Acad Ser A ndash Math Sci 71 154ndash157 158ndash160 (1995)
[405] T Kawazoe Wavelet transform associated to an induced representation of SL(n+ 2R)Ann Inst H Poincareacute 65 1ndash13 (1996)
References 563
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[407] P Kittipoom G Kutyniok W-Q Lim Construction of compactly supported shearletframes Constr Approx 35 21ndash72 (2012)
[408] J Kiukas P Lahti K Ylinenc Phase space quantization and the operator moment problemJ Math Phys 47 072104 (2006)
[409] JR Klauder Continuous-representation theory I Postulates of continuous-representationtheory J Math Phys 4 1055ndash1058 (1963)
[410] JR Klauder Continuous-representation theory II Generalized relation between quantumand classical dynamics J Math Phys 4 1058ndash1073 (1963)
[411] JR Klauder Path integrals for affine variables in Functional Integration Theory andApplications ed by J-P Antoine E Tirapegui (Plenum Press New York and London1980) pp 101ndash119
[412] JR Klauder Are coherent states the natural language of quantum mechanics inFundamental Aspects of Quantum Theory ed by V Gorini A Frigerio NATO ASI Seriesvol B 144 (Plenum Press New York 1986) pp 1ndash12
[413] JR Klauder Quantization without quantization Ann Phys (NY) 237 147ndash160 (1995)[414] JR Klauder Coherent states for the hydrogen atom J Phys A Math Gen 29 L293ndash
L296 (1996)[415] JR Klauder An affinity for affine quantum gravity Proc Steklov Inst Math 272 169ndash176
(2011) and references therein[416] JR Klauder RF Streater A wavelet transform for the Poincareacute group J Math Phys 32
1609ndash1611 (1991)[417] JR Klauder RF Streater Wavelets and the Poincareacute half-plane J Math Phys 35 471ndash
478 (1994)[418] JR Klauder K Penson J-M Sixdeniers Constructing coherent states through solutions
of Stieltjes and Hausdorff moment problems Phys Rev A 64 013817 (2001)[419] A Kleppner RL Lipsman The Plancherel formula for group extensions Ann Ec Norm
Sup 5 459ndash516 (1972)[420] AB Klimov C Muntildeoz Coherent isotropic and squeezed states in a N-qubit system Phys
Scr 87 038110 (2013)[421] A Klyashko Dynamical symmetry approach to entanglement in Physics and Theoretical
Computer Science From Numbers and Languages to (Quantum) Cryptography - NATOSecurity through Science Series D - Information and Communication Security vol 7 edby J-P Gazeau J Nesetril B Rovan (IOS Press Washington DC 2007) pp 25ndash54
[422] S Kobayashi Irreducibility of certain unitary representations J Math Soc Japan 20 638ndash642 (1968)
[423] K Kowalski J Rembielinski LC Papaloucas Coherent states for a quantum particle ona circle J Phys A Math Gen 29 4149ndash4167 (1996)
[424] K Kowalski J Rembielinski Quantum mechanics on a sphere and coherent states J PhysA Math Gen 33 6035ndash6048 (2000)
[425] K Kowalski J Rembielinski The Bargmann representation for the quantum mechanicson a sphere J Math Phys 42 4138ndash4147 (2001)
[426] C Kristjansen J Plefka GW Semenoff M Staudacher A new double-scaling limit ofN = 4 super-Yang-Mills theory and pp-wave strings Nuclear Phys B 643 3ndash30 (2002)
[427] M Kulesh M Holschneider MS Diallo Geophysical wavelet library Applications ofthe continuous wavelet transform to the polarization and dispersion analysis of signalsComput Geosci 34 1732ndash1752 (2008)
[428] R Kunze On the Frobenius reciprocity theorem for square integrable representationsPacific J Math 53 465ndash471 (1974)
[429] Y Kuroda A Wada T Yamazaki K Nagayama Postacquisition data processing methodfor suppression of the solvent signal I J Magn Reson 84 604ndash610 (1989)
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[430] Y Kuroda A Wada T Yamazaki K Nagayama Postacquisition data processing methodfor suppression of the solvent signal II The weighted first derivative J Magn Reson 88141ndash145 (1990)
[431] G Kutyniok D Labate Resolution of the wavefront set using continuous shearlets TransAmer Math Soc 361 2719ndash2754 (2009)
[432] G Kutyniok W-Q Lim Compactly supported shearlets are optimally sparse J ApproxTheory 163 1564ndash1589 (2011)
[433] D Labate W-Q Lim G Kutyniok G Weiss Sparse multidimensional representationusing shearlets in Wavelets XI (San Diego CA 2005) ed by M Papadakis A Laine MUnser SPIE Proceedings vol 5914 (SPIE Bellingham WA 2005) pp 254ndash262
[434] P Lahti J-P Pellonpaumlauml Continuous variable tomographic measurements Phys Lett A373 3435ndash3438 (2009)
[435] Lambertrsquos projection see WikipediahttpenwikipediaorgwikiLambert_azimuthal_equal-area_projection
[436] J-P Leduc F Mujica R Murenzi MJT Smith Missile-tracking algorithm using target-adapted spatio-temporal wavelets in Automatic Object Recognition VII SPIE Proceedingsvol 5914 (SPIE Bellingham WA 1997) pp 400ndash411
[437] J-P Leduc F Mujica R Murenzi MJT Smith Spatio-temporal wavelet transforms formotion tracking in IEEE ICASSP 1997 vol 4 (1997) pp 3013ndash3016
[438] J-P Leduc F Mujica R Murenzi MJT Smith Spatio-temporal continuous waveletsapplied to missile warhead detection and tracking in SPIE VCIP rsquo97 vol 3024 ed byJ Biemond EJ Delp (1997) pp 787ndash798
[439] B Leistedt JD McEwen Exact wavelets on the ball IEEE Trans Signal Proc 60 1564ndash1589 (2012)
[440] PG Lemarieacute Y Meyer Ondelettes et bases hilbertiennes Rev Math Iberoamer 2 1ndash18(1986)
[441] C Lemke A Schuck Jr J-P Antoine D Sima Metabolite-sensitive analysis of magneticresonance spectroscopic signals using the continuous wavelet transform Meas SciTechnol 22 (2011) Art 114013
[442] J-M Leacutevy-Leblond Galilei group and non-relativistic quantum mechanics J Math Phys4 776-788 (1963)
[443] J-M Leacutevy-Leblond Galilei group and Galilean invariance in Group Theory and ItsApplications vol II ed by EM Loebl (Academic New York 1971) pp 221ndash299
[444] J-M Leacutevy-Leblond On the conceptual nature of the physical constants Riv Nuovo Cim7 187ndash214 (1977)
[445] EH Lieb The classical limit of quantum spin systems Commun Math Phys 31 327ndash340(1973)
[446] G Lindblad B Nagel Continuous bases for unitary irreducible representations of SU(11)Ann Inst H Poincareacute 13 27ndash56 (1970)
[447] W Lisiecki Kaumlhler coherent states orbits for representations of semisimple Lie groupsAnn Inst H Poincareacute 53 857ndash890 (1990)
[448] A Lisowska Moment-based fast wedgelet transform J Math Imaging Vis 39 180ndash192(2011)
[449] H Liu L Peng Admissible wavelets associated with the Heisenberg group Pacific JMath 180 101ndash123 (1997)
[450] E Livine S Speziale Physical boundary state for the quantum tetrahedron Class QuantGrav 25 085003 (2008)
[451] F Low Complete sets of wave packets in A Passion for Physics ndash Essay in Honor ofGeoffrey Chew ed by C DeTar (World Scientific Singapore 1985) pp 17ndash22
[452] G Mack All unitary ray representations of the conformal group SU(22) with positiveenergy Commun Math Phys 55 1ndash28 (1977)
[453] GW Mackey Imprimitivity for representations of locally compact groups I Proc NatAcad Sci 35 537ndash545 (1949)
References 565
[454] S Majid M Rodriguez-Plaza Random walk and the heat equation on superspace andanyspace J Math Phys 35 3753ndash3760 (1994)
[455] M Mallalieu CR Stroud Jr Rydberg wave packets fractional revivals and classicalorbits in Coherent States Past Present and Future (Proc Oak Ridge 1993) ed by DHFeng JR Klauder M Strayer (World Scientific Singapore 1994) pp 301ndash314
[456] SG Mallat Multifrequency channel decompositions of images and wavelet models IEEETrans Acoust Speech Signal Proc 37 2091ndash2110 (1989)
[457] SG Mallat A theory for multiresolution signal decomposition The wavelet representa-tion IEEE Trans Pattern Anal Machine Intell 11 674ndash693 (1989)
[458] S Mallat W-L Hwang Singularity detection and processing with wavelets IEEE TransInform Theory 38 617ndash643 (1992)
[459] S Mallat Z Zhang Matching pursuits with time frequency dictionaries IEEE TransSignal Proc 41 3397ndash3415 (1993)
[460] S Mallat S Zhong Wavelet maxima representation in Wavelets and Applications (ProcMarseille 1989) ed by Y Meyer (Masson and Springer Paris and Berlin 1991) pp 207ndash284
[461] VI Manrsquoko G Marmo ECG Sudarshan F Zaccaria f -oscillators and non-linearcoherent states Phys Scr 55 528ndash541 (1997)
[462] D Marinucci D Pietrobon A Baldi P Baldi P Cabella G Kerkyacharian P Natoli DPicard N Vittorio Spherical needlets for CMB data analysis Mon Not R Astron Soc383 539ndash545 (2008)
[463] D Marion M Ikura A Bax Improved solvent suppression in one- and two-dimensionalNMR spectra by convolution of time-domain data J Magn Reson 84 425ndash430 (1989)
[464] Y Meyer Principe drsquoincertitude bases hilbertiennes et algegravebres drsquoopeacuterateurs SeacuteminaireBourbaki 662 (1985ndash1986)
[465] Y Meyer Principe drsquoincertitude bases hilbertiennes et algegravebres drsquoopeacuterateurs Asteacuterisque145ndash146 209ndash223 (1987)
[466] Y Meyer H Xu Wavelet analysis and chirps Appl Comput Harmon Anal 4 366ndash379(1997)
[467] L Michel Invariance in quantum mechanics and group extensions in Group TheoreticalConcepts and Methods in Elementary Particle Physics ed by F Guumlrsey (Gordon andBreach New York and London 1964) pp 135ndash200
[468] J Mickelsson J Niederle Contractions of representations of the de Sitter groupsCommun Math Phys 27 167ndash180 (1972)
[469] MM Miller Convergence of the Sudarshan expansion for the diagonal coherent-stateweight functional J Math Phys 9 1270ndash1274 (1968)
[470] V F Molchanov Harmonic analysis on homogeneous spaces in Representation Theoryand Noncommutative Harmonic Analysis II ed by AA Kirillov (Springer Berlin 1995)
[471] MI Monastyrsky AM Perelomov Coherent states and symmetric spaces II Ann InstH Poincareacute 23 23ndash48 (1975)
[472] B Moran S Howard D Cochran Positive-operator-valued measures A general settingfor frames in Excursions in Harmonic Analysis vol 1 2 ed by TD Andrews R BalanJJ Benedetto W Czaja KA Okoudjou (Birkhaumluser Boston 2013) pp 49ndash64
[473] H Moscovici Coherent states representations of nilpotent Lie groups Commun MathPhys 54 63ndash68 (1977)
[474] H Moscovici A Verona Coherent states and square integrable representations Ann InstH Poincareacute 29 139ndash156 (1978)
[475] F Mujica R Murenzi MJT Smith J-P Leduc Robust tracking in compressed imagesequences J Electr Imaging 7 746ndash754 (1998)
[476] R Murenzi Wavelet transforms associated to the n-dimensional Euclidean group withdilations Signals in more than one dimension in Wavelets Time-Frequency Methodsand Phase Space (Proc Marseille 1987) ed by J-M Combes A Grossmann PTchamitchian 2nd edn (Springer Berlin 1990) pp 239ndash246
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[477] MA Muschietti B Torreacutesani Pyramidal algorithms for LittlewoodndashPaley decomposi-tions SIAM J Math Anal 26 925ndash943 (1995)
[478] B Nagel Generalized eigenvectors in group representations in Studies in MathematicalPhysics (Proc Istanbul 1970) ed by AO Barut (Reidel Dordrecht and Boston 1970)pp 135ndash154
[479] MA Naımark Dokl Akad Nauk SSSR 41 359ndash361 (1943) see also B Sz-NagyExtensions of linear transformations in Hilbert space which extend beyond this spaceAppendix to F Riesz B Sz-Nagy Functional Analysis (Frederick Ungar New York 1960)
[480] FJ Narcowich P Petrushev JD Ward Localized tight frames on spheres SIAM J MathAnal 38 574ndash594 (2006)
[481] M Nauenberg Quantum wave packets on Kepler elliptic orbits Phys Rev A 40 1133ndash1136 (1989)
[482] M Nauenberg C Stroud J Yeazell The classical limit of an atom Scient Amer 27024ndash29 (1994)
[483] H Neumann Transformation properties of observables Helv Phys Acta 45 811ndash819(1972)
[484] U Niederer The maximal kinematical invariance group of the free Schroumldinger equationHelv Phys Acta 45 802ndash881 (1972)
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[486] MM Nieto LM Simmons Jr Coherent states for general potentials Phys Rev Lett 41207ndash210 (1987)
[487] A Odzijewicz On reproducing kernels and quantization of states Commun Math Phys114 577ndash597 (1988)
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[579] T Thiemann Gauge field theory coherent states (GCS) 1 General properties Class QuantGrav 18 2025ndash2064 (2001)
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4200 (1998) and references quoted there[616] AA Zakharova On the properties of generalized frames Math Notes 83 190ndash200 (2008)[617] W-M Zhang DH Feng R Gilmore Coherent states Theory and some applications Rev
Mod Phys 26 867ndash927 (1990)[618] I Zlatev W-M Zhang DH Feng Possibility that Schroumldingerrsquos conjecture for the
hydrogen atom coherent states is not attainable Phys Rev A 50 R1973ndashR1975 (1994)[619] WH Zurek Decoherence einselection and the quantum origins of the classical Rev Mod
Phys 75 715ndash775 (2003)[620] WH Zurek S Habib JP Paz Coherent states via decoherence Phys Rev Lett 70 1187ndash
1190 (1993)[621] K Zyczkowski Squeezed states in a quantum chaotic system J Phys A Math Theor 22
of SU(11) 81 296 297HilbertClowast-modules 164holomorphic 140nonholomorphic 151nonlinear 146of affine Galilei group 505of affine Poincareacute group 509of affine Weyl-Heisenberg group GaWH
497of compact semisimple Lie groups 174of Euclidean group E(n) 266of Galilei group G (11) 290of isochronous Galilei group 237of non-semisimple Lie groups 179of noncompact semisimple Lie groups 177of Poincareacute group Puarr
+(11) 283massless case 288
of Poincareacute group Puarr+(13) 279
of Schroumldinger group 508quasi-coherent states 186quaternionic 164
ST Ali et al Coherent States Wavelets and Their Generalizations Theoreticaland Mathematical Physics DOI 101007978-1-4614-8535-3copy Springer Science+Business Media New York 2014
573
574 Index
coherent states (CS) (cont)spin or SU(2) 175square integrable covariant 166 180 264vector (VCS) 73 108 112 170weighted 184 523
of affine Weyl-Heisenberg group GaWH497
of Poincareacute group Puarr+(11) 284
cohomology group 393 403coboundaries 403cochains 402cocycle 403
algebraic 387Cauchy 418Cauchy-Paul 354 419 425conical 418difference 417 462directional 416 440kinematical 499local 488metabolite-based 355 374minimal uncertainty 425multiselective 440on a graph 493on the sphere S
2 458on the sphere S
n 479on the torus T2 481steerable 439von Mises 440
wedgelet transform 455Wigner function 322Wigner-Ville transform 349Windowed Fourier or Gabor transform 349
ZZak transform 518
References
A Books and Theses
B Articles
Index
References 557
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[262] AH Dooley JW Rice On contractions of semisimple Lie groups Trans Amer MathSoc 289 185ndash202 (1985)
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[268] M Duval-Destin M-A Muschietti B Torreacutesani Continuous wavelet decompositionsmultiresolution and contrast analysis SIAM J Math Anal 24 739ndash755 (1993)
[269] SJL van Eindhoven JLH Meyers New orthogonality relations for the Hermitepolynomials and related Hilbert spaces J Math Anal Appl 146 89ndash98 (1990)
[270] M ElBaz R Fresneda J-P Gazeau Y Hassouni Coherent state quantization of para-grassmann algebras J Phys A Math Theor 43 385202 (2010) Corrigendum J PhysA Math Theor 45 (2012)
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[273] M Fanuel S Zonetti Affine quantization and the initial cosmological singularity Euro-phys Lett 101 10001 (2013)
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[275] M Farge N Kevlahan V Perrier E Goirand Wavelets and turbulence Proc IEEE 84639ndash669 (1996)
[276] M Farge NK-R Kevlahan V Perrier K Schneider Turbulence analysis modellingand computing using wavelets in Wavelets in Physics Chap 4 ed by JC van den Berg(Cambridge University Press Cambridge 1999)
[277] HG Feichtinger Coherent frames and irregular sampling in Recent Advances in FourierAnalysis and Its applications ed by JS Byrnes JL Byrnes (Kluwer Dordrecht 1990)pp 427ndash440
[278] HG Feichtinger KH Groumlchenig Banach spaces related to integrable group representa-tions and their atomic decompositions I J Funct Anal 86 307ndash340 (1989)
[279] HG Feichtinger KH Groumlchenig Banach spaces related to integrable group representa-tions and their atomic decompositions II Mh Math 108 129ndash148 (1989)
[280] M Flensted-Jensen Discrete series for semisimple symmetric spaces Ann of Math 111253ndash311 (1980)
[281] K Flornes A Grossmann M Holschneider B Torreacutesani Wavelets on discrete fieldsAppl Comput Harmon Anal 1 137ndash146 (1994)
[282] V Fock Zur Theorie der Wasserstoffatoms Zs f Physik 98 145ndash54 (1936)[283] M Fornasier H Rauhut Continuous frames function spaces and the discretization
problem J Fourier Anal Appl 11 245ndash287 (2005)
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[285] W Freeden U Windheuser Combined spherical harmonic and wavelet expansion mdash Afuture concept in Earthrsquos gravitational determination Appl Comput Harmon Anal 4 1ndash37 (1997)
[286] W Freeden T Maier S Zimmermann A survey on wavelet methods for (geo)applicationsRevista Mathematica Complutense 16 (2003) 277ndash310
[287] W Freeden M Schreiner Biorthogonal locally supported wavelets on the sphere based onzonal kernel functions J Fourier Anal Appl 13 693ndash709 (2007)
[288] WT Freeman EH Adelson The design and use of steerable filters IEEE Trans PatternAnal Machine Intell 13 891ndash906 (1991)
[289] L Freidel ER Livine U(N) coherent states for loop quantum gravity J Math Phys 52052502 (2011)
[290] J Froment S Mallat Arbitrary low bit rate image compression using wavelets in Progressin Wavelet Analysis and Applications (Proc Toulouse 1992) ed by Y Meyer S Roques(Ed Frontiegraveres Gif-sur-Yvette 1993) pp 413ndash418 and references therein
[291] L Freidel S Speziale Twisted geometries A geometric parameterisation of SU(2) phasespace Phys Rev D 82 084040 (2010)
[292] H Fuumlhr Wavelet frames and admissibility in higher dimensions J Math Phys 37 6353ndash6366 (1996)
[293] H Fuumlhr M Mayer Continuous wavelet transforms from semidirect products Cyclicrepresentations and Plancherel measure J Fourier Anal Appl 8 375ndash396 (2002)
[294] D Gabor Theory of communication J Inst Electr Engrg(London) 93 429ndash457 (1946)[295] J-P Gabardo D Han Frames associated with measurable spaces Adv Comput Math 18
127ndash147 (2003)[296] E Galapon Paulirsquos theorem and quantum canonical pairs The consistency of a bounded
self-adjoint time operator canonically conjugate to a Hamiltonian with non-empty pointspectrum Proc R Soc Lond A 458 451ndash472 (2002)
[297] PL Garciacutea de Leacuteon J-P Gazeau Coherent state quantization and phase operator PhysLett A 361 301ndash304 (2007)
[298] L Garciacutea de Leoacuten J-P Gazeau J Queacuteva The infinite well revisited Coherent states andquantization Phys Lett A 372 3597ndash3607 (2008)
[299] T Garidi J-P Gazeau E Huguet M Lachiegraveze Rey J Renaud Fuzzy spheres frominequivalent coherent states quantization J Phys A Math Theor 40 10225ndash10249 (2007)
[300] J-P Gazeau Four Euclidean conformal group in atomic calculations Exact analyticalexpressions for the bound-bound two-photon transition matrix elements in the H atomJ Math Phys 19 1041ndash1048 (1978)
[301] J-P Gazeau On the four Euclidean conformal group structure of the sturmian operatorLett Math Phys 3 285ndash292 (1979)
[302] J-P Gazeau Technique Sturmienne pour le spectre discret de lrsquoeacutequation de SchroumldingerJ Phys A Math Gen 13 3605ndash3617 (1980)
[303] J-P Gazeau Four Euclidean conformal group approach to the multiphoton processes in theH atom J Math Phys 23 156ndash164 (1982)
[304] J-P Gazeau A remarkable duality in one particle quantum mechanics between someconfining potentials and (R+Linfin
ε ) potentials Phys Lett 75A 159ndash163 (1980)[305] J-P Gazeau SL(2R)-coherent states and integrable systems in classical and quantum
physics in Quantization Coherent States and Complex Structures ed by J-P AntoineST Ali W Lisiecki IM Mladenov A Odzijewicz (Plenum Press New York and London1995) pp 147ndash158
[306] J-P Gazeau S Graffi Quantum harmonic oscillator A relativistic and statistical point ofview Boll Unione Mat Ital 11-A 815ndash839 (1997)
[307] J-P Gazeau V Hussin Poincareacute contraction of SU(11) Fock-Bargmann structure J PhysA Math Gen 25 1549ndash1573 (1992)
References 559
[308] J-P Gazeau R Kanamoto Action-angle coherent states and related quantization inProceedings of QTS7 Colloquium Prague 2011 Journal of Physics Conference Seriesvol 343 (2012) p 012038-1-9
[309] J-P Gazeau JR Klauder Coherent states for systems with discrete and continuousspectrum J Phys A Math Gen 32 123ndash132 (1999)
[310] J-P Gazeau P Monceau Generalized coherent states for arbitrary quantum systems inColloquium M Flato (Dijon Sept 99) vol II (Kluumlwer Dordrecht 2000) pp 131ndash144
[311] J-P Gazeau M Novello The question of mass in (Anti-) de Sitter space-times J Phys AMath Theor 41 304008 (2008)
[312] J-P Gazeau M del Olmo q-coherent states quantization of the harmonic oscillator AnnPhys (NY) 330 220ndash245 (2013) arXiv12071200 [quant-ph]
[313] J-P Gazeau J Patera Tau-wavelets of Haar J Phys A Math Gen 29 4549ndash4559 (1996)[314] J-P Gazeau W Piechocki Coherent states quantization of a particle in de Sitter space
J Phys A Math Gen 37 6977ndash6986 (2004)[315] J-P Gazeau J Renaud Lie algorithm for an interacting SU(11) elementary system and its
contraction Ann Phys (NY) 222 89ndash121 (1993)[316] J-P Gazeau J Renaud Relativistic harmonic oscillator and space curvature Phys Lett A
179 67ndash71 (1993)[317] J-P Gazeau V Spiridonov Toward discrete wavelets with irrational scaling factor J Math
plane J Phys A Math Theor 44 495201 (2011)[319] J-P Gazeau J Patera E Pelantovaacute Tau-wavelets in the plane J Math Phys 39 4201ndash
4212 (1998)[320] J-P Gazeau M Andrle C Burdiacutek R Krejcar Wavelet multiresolutions for the Fibonacci
chain J Phys A Math Gen 33 L47ndashL51 (2000)[321] J-P Gazeau M Andrle C Burdiacutek Bernuau spline wavelets and sturmian sequences
J Fourier Anal Appl 10 269ndash300 (2004)[322] J-P Gazeau F-X Josse-Michaux P Monceau Finite dimensional quantizations of the
(q p) plane new space and momentum inequalities Int J Modern Phys B 20 1778ndash1791 (2006)
[323] J-P Gazeau J Mourad J Queacuteva Fuzzy de Sitter space-times via coherent statesquantization in Proceedings of the XXVIth Colloquium on Group Theoretical Methodsin Physics New York 2006 ed by J Birman S Catto B Nicolescu (Canopus PublishingLimited London 2009)
[324] D Geller A Mayeli Continuous wavelets on compact manifolds Math Z 262 895ndash927(2009)
[325] D Geller A Mayeli Nearly tight frames and space-frequency analysis on compactmanifolds Math Z 263 235ndash264 (2009)
[326] L Genovese B Videau M Ospici Th Deutsch S Goedecker J-F Mhaut Daubechieswavelets for high performance electronic structure calculations The BigDFT project CR Mecanique 339 149ndash164 (2011)
[327] G Gentili C Stoppato Power series and analyticity over the quaternions Math Ann 352113ndash131 (2012)
[328] G Gentili DC Struppa A new theory of regular functions of a quaternionic variable AdvMath 216 279ndash301 (2007)
[329] C Geyer K Daniilidis Catadioptric projective geometry Int J Comput Vision 45 223ndash243 (2001)
[330] R Gilmore Geometry of symmetrized states Ann Phys (NY) 74 391ndash463 (1972)[331] R Gilmore On properties of coherent states Rev Mex Fis 23 143ndash187 (1974)[332] J Ginibre Statistical ensembles of complex quaternion and real matrices J Math Phys
6 440ndash449 (1965)[333] RJ Glauber The quantum theory of optical coherence Phys Rev 130 2529ndash2539 (1963)
560 References
[334] RJ Glauber Coherent and incoherent states of radiation field Phys Rev 131 2766ndash2788(1963)
[335] J Glimm Locally compact transformation groups Trans Amer Math Soc 101 124ndash138(1961)
[336] R Godement Sur les relations drsquoorthogonaliteacute de V Bargmann C R Acad Sci Paris 255521ndash523 657ndash659 (1947)
[337] C Gonnet B Torreacutesani Local frequency analysis with two-dimensional wavelet trans-form Signal Proc 37 389ndash404 (1994)
[338] JA Gonzalez MA del Olmo Coherent states on the circle J Phys A Math Gen 318841ndash8857 (1998)
[339] XGonze B Amadon et al ABINIT First-principles approach to material and nanosystemproperties Computer Physics Comm 180 2582ndash2615 (2009)
[340] KM Gograverski E Hivon AJ Banday BD Wandelt FK Hansen M Reinecke MBartelmann HEALPix A framework for high-resolution discretization and fast analysisof data distributed on the sphere Astrophys J 622 759ndash771 (2005)
[341] P Goupillaud A Grossmann J Morlet Cycle-octave and related transforms in seismicsignal analysis Geoexploration 23 85ndash102 (1984)
[342] KH Groumlchenig A new approach to irregular sampling of band-limited functions in RecentAdvances in Fourier Analysis and Its applications ed by JS Byrnes JL Byrnes (KluwerDordrecht 1990) pp 251ndash260
[343] KH Groumlchenig Gabor analysis over LCA groups in Gabor Analysis and Algorithms ndashTheory and Applications ed by HG Feichtinger T Strohmer (Birkhaumluser Boston-Basel-Berlin 1998) pp 211ndash231
[344] HJ Groenewold On the principles of elementary quantum mechanics Physica 12 405ndash460 (1946)
[345] P Grohs Continuous shearlet tight frames J Fourier Anal Appl 17 506ndash518 (2011)[346] P Grohs G Kutyniok Parabolic molecules preprint TU Berlin (2012)[347] M Grosser A note on distribution spaces on manifolds Novi Sad J Math 38 121ndash128
(2008)[348] A Grossmann Parity operator and quantization of δ -functions Commun Math Phys 48
191ndash194 (1976)[349] A Grossmann J Morlet Decomposition of Hardy functions into square integrable
wavelets of constant shape SIAM J Math Anal 15 723ndash736 (1984)[350] A Grossmann J Morlet Decomposition of functions into wavelets of constant shape and
related transforms in Mathematics + Physics Lectures on recent results I ed by L Streit(World Scientific Singapore 1985) pp 135ndash166
[351] A Grossmann J Morlet T Paul Integral transforms associated to square integrablerepresentations I General results J Math Phys 26 2473ndash2479 (1985)
[352] A Grossmann J Morlet T Paul Integral transforms associated to square integrablerepresentations II Examples Ann Inst H Poincareacute 45 293ndash309 (1986)
[353] A Grossmann R Kronland-Martinet J Morlet Reading and understanding the contin-uous wavelet transform in Wavelets Time-Frequency Methods and Phase Space (ProcMarseille 1987) ed by J-M Combes A Grossmann P Tchamitchian 2nd edn (SpringerBerlin 1990) pp 2ndash20
[354] P Guillemain R Kronland-Martinet B Martens Estimation of spectral lines with helpof the wavelet transform Application in NMR spectroscopy in Wavelets and Applications(Proc Marseille 1989) ed by Y Meyer (Masson and Springer Paris and Berlin 1991) pp38ndash60
[355] H de Guise M Bertola Coherent state realizations of su(n+ 1) on the n-torus J MathPhys 43 3425ndash3444 (2002)
[356] K Guo D Labate Representation of Fourier Integral Operators using shearlets J FourierAnal Appl 14 327ndash371 (2008)
References 561
[357] K Guo G Kutyniok D Labate Sparse multidimensional representations usinganisotropic dilation and shear operators in Wavelets and Spines (Athens GA 2005)(Nashboro Press Nashville TN 2006) pp 189ndash201
[358] K Guo D Labate W-Q Lim G Weiss E Wilson Wavelets with composite dilationsand their MRA properties Appl Comput Harmon Anal 20 202ndash236 (2006)
[359] EA Gutkin Overcomplete subspace systems and operator symbols Funct Anal Appl 9260ndash261 (1975)
[360] G Gyoumlrgyi Integration of the dynamical symmetry groups for the 1r potential Acta PhysAcad Sci Hung 27 435ndash439 (1969)
[361] BC Hall The Segal-Bargmann ldquoCoherent Staterdquo transform for compact Lie groups JFunct Analysis 122 103ndash151 (1994)
[362] B Hall JJ Mitchell Coherent states on spheres J Math Phys 43 1211ndash1236 (2002)[363] DK Hammond P Vandergheynst R Gribonval Wavelets on graphs via spectral theory
Appl Comput Harmon Anal 30 129ndash150 (2011)[364] Y Hassouni EMF Curado MA Rego-Monteiro Construction of coherent states for
physical algebraic system Phys Rev A 71 022104 (2005)[365] J He H Liu Admissible wavelets associated with the affine automorphism group of the
Siegel upper half-plane J Math Anal Appl 208 58ndash70 (1997)[366] J He H Liu Admissible wavelets associated with the classical domain of type one
Approx Appl 14 (1998) 89ndash105[367] J He L Peng Wavelet transform on the symmetric matrix space preprint Beijing (1997)
(unpublished)[368] J He L Peng Admissible wavelets on the unit disk Complex Variables 35 109ndash119
(1998)[369] DM Healy Jr FE Schroeck Jr On informational completeness of covariant localization
observables and Wigner coefficients J Math Phys 36 453ndash507 (1995)[370] C Heil D Walnut Continuous and discrete wavelet transforms SIAM Review 31 628ndash
666 (1989)[371] K Hepp EH Lieb On the superradiant phase transition for molecules in a quantized
radiation field The Dicke maser model Ann Phys (NY) 76 360ndash404 (1973)[372] K Hepp EH Lieb Equilibrium statistical mechanics of matter interacting with the
quantized radiation field Phys Rev A 8 2517ndash2525 (1973)[373] JA Hogan JD Lakey Extensions of the Heisenberg group by dilations and frames Appl
Comput Harmon Anal 2 174ndash199 (1995)[374] AL Hohoueacuteto K Thirulogasanthar ST Ali J-P Antoine Coherent states lattices and
square integrability of representations J Phys A Math Gen36 11817ndash11835 (2003)[375] M Holschneider On the wavelet transformation of fractal objects J Stat Phys 50 963ndash
993 (1988)[376] M Holschneider Wavelet analysis on the circle J Math Phys 31 39ndash44 (1990)[377] M Holschneider Inverse Radon transforms through inverse wavelet transforms Inv Probl
7 853ndash861 (1991)[378] M Holschneider Localization properties of wavelet transforms J Math Phys 34 3227ndash
3244 (1993)[379] M Holschneider General inversion formulas for wavelet transforms J Math Phys 34
4190ndash4198 (1993)[380] M Holschneider Wavelet analysis over abelian groups Applied Comput Harmon Anal
2 52ndash60 (1995)[381] M Holschneider Continuous wavelet transforms on the sphere J Math Phys 37 4156ndash
4165 (1996)[382] M Holschneider I Iglewska-Nowak Poisson wavelets on the sphere J Fourier Anal
Appl 13 405ndash419 (2007)
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[383] M Holschneider R Kronland-Martinet J Morlet P Tchamitchian A real-time algorithmfor signal analysis with the help of wavelet transform in Wavelets Time-FrequencyMethods and Phase Space (Proc Marseille 1987) ed by J-M Combes A Grossmann PTchamitchian 2nd edn (Springer Berlin 1990) pp 286ndash297
[384] M Holschneider P Tchamitchian Pointwise analysis of Riemannrsquos ldquonondifferentiablerdquofunction Invent Math 105 157ndash175 (1991)
[385] GR Honarasa MK Tavassoly M Hatami R Roknizadeh Nonclassical properties ofcoherent states and excited coherent states for continuous spectra J Phys A Math Theor44 085303 (2011)
[386] M Hongoh Coherent states associated with the continuous spectrum of noncompactgroups J Math Phys 18 2081ndash2085 (1977)
[387] A Horzela FH Szafraniec A measure free approach to coherent states J Phys A MathGen 45 244018 (2012)
[388] W-L Hwang S Mallat Characterization of self-similar multifractals with waveletmaxima Appl Comput Harmon Anal 1 316ndash328 (1994)
[389] W-L Hwang C-S Lu P-C Chung Shape from texture Estimation of planar surfaceorientation through the ridge surfaces of continuous wavelet transform IEEE Trans ImageProc 7 773ndash780 (1998)
[390] I Iglewska-Nowak M Holschneider Frames of Poisson wavelets on the sphere ApplComput Harmon Anal 28 227ndash248 (2010)
[391] E Inoumlnuuml EP Wigner On the contraction of groups and their representations Proc NatAcad Sci U S 39 510ndash524 (1953)
[392] S Iqbal F Saif Generalized coherent states and their statistical characteristics in power-law potentials J Math Phys 52 082105 (2011)
[393] CJ Isham JR Klauder Coherent states for n-dimensional Euclidean groups E(n) andtheir application J MathPhys 32 607ndash620 (1991)
[394] L Jacques J-P Antoine Multiselective pyramidal decomposition of images Wavelets withadaptive angular selectivity Int J Wavelets Multires Inform Proc 5 785ndash814 (2007)
[395] L Jacques L Duval C Chaux G Peyreacute A panorama on multiscale geometric rep-resentations intertwining spatial directional and frequency selectivity Signal Proc 912699ndash2730 (2011)
[396] HR Jalali M K Tavassoly On the ladder operators and nonclassicality of generalizedcoherent state associated with a particle in an infinite square well preprint (2013)arXiv13034100v1 [quant-ph]
[397] C Johnston On the pseudo-dilation representations of Flornes Grossmann Holschneiderand Torreacutesani Appl Comput Harmon Anal 3 377ndash385 (1997)
[398] G Kaiser Phase-space approach to relativistic quantum mechanics I Coherent staterepresentation for massive scalar particles J MathPhys 18 952ndash959 (1977)
[399] G Kaiser Phase-space approach to relativistic quantum mechanics II Geometrical aspectsJ MathPhys 19 502ndash507 (1978)
[400] C Kalisa B Torreacutesani N-dimensional affine Weyl-Heisenberg wavelets Ann Inst HPoincareacute 59 201ndash236 (1993)
[401] W Kaminski J Lewandowski T Pawłowski Quantum constraints Dirac observables andevolution group averaging versus the Schroumldinger picture in LQC Class Quant Grav 26245016 (2009)
[402] MR Karim ST Ali A relativistic windowed Fourier transform preprint ConcordiaUniversity Montreacuteal (1997) (unpublished)
[403] M R Karim ST Ali M Bodruzzaman A relativistic windowed Fourier transform inProceedings of IEEE SoutheastCon 2000 Nashville Tennessee pp 253ndash260 (2000)
[404] T Kawazoe Wavelet transforms associated to a principal series representation of semisim-ple Lie groups I II Proc Japan Acad Ser A ndash Math Sci 71 154ndash157 158ndash160 (1995)
[405] T Kawazoe Wavelet transform associated to an induced representation of SL(n+ 2R)Ann Inst H Poincareacute 65 1ndash13 (1996)
References 563
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[407] P Kittipoom G Kutyniok W-Q Lim Construction of compactly supported shearletframes Constr Approx 35 21ndash72 (2012)
[408] J Kiukas P Lahti K Ylinenc Phase space quantization and the operator moment problemJ Math Phys 47 072104 (2006)
[409] JR Klauder Continuous-representation theory I Postulates of continuous-representationtheory J Math Phys 4 1055ndash1058 (1963)
[410] JR Klauder Continuous-representation theory II Generalized relation between quantumand classical dynamics J Math Phys 4 1058ndash1073 (1963)
[411] JR Klauder Path integrals for affine variables in Functional Integration Theory andApplications ed by J-P Antoine E Tirapegui (Plenum Press New York and London1980) pp 101ndash119
[412] JR Klauder Are coherent states the natural language of quantum mechanics inFundamental Aspects of Quantum Theory ed by V Gorini A Frigerio NATO ASI Seriesvol B 144 (Plenum Press New York 1986) pp 1ndash12
[413] JR Klauder Quantization without quantization Ann Phys (NY) 237 147ndash160 (1995)[414] JR Klauder Coherent states for the hydrogen atom J Phys A Math Gen 29 L293ndash
L296 (1996)[415] JR Klauder An affinity for affine quantum gravity Proc Steklov Inst Math 272 169ndash176
(2011) and references therein[416] JR Klauder RF Streater A wavelet transform for the Poincareacute group J Math Phys 32
1609ndash1611 (1991)[417] JR Klauder RF Streater Wavelets and the Poincareacute half-plane J Math Phys 35 471ndash
478 (1994)[418] JR Klauder K Penson J-M Sixdeniers Constructing coherent states through solutions
of Stieltjes and Hausdorff moment problems Phys Rev A 64 013817 (2001)[419] A Kleppner RL Lipsman The Plancherel formula for group extensions Ann Ec Norm
Sup 5 459ndash516 (1972)[420] AB Klimov C Muntildeoz Coherent isotropic and squeezed states in a N-qubit system Phys
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Computer Science From Numbers and Languages to (Quantum) Cryptography - NATOSecurity through Science Series D - Information and Communication Security vol 7 edby J-P Gazeau J Nesetril B Rovan (IOS Press Washington DC 2007) pp 25ndash54
[422] S Kobayashi Irreducibility of certain unitary representations J Math Soc Japan 20 638ndash642 (1968)
[423] K Kowalski J Rembielinski LC Papaloucas Coherent states for a quantum particle ona circle J Phys A Math Gen 29 4149ndash4167 (1996)
[424] K Kowalski J Rembielinski Quantum mechanics on a sphere and coherent states J PhysA Math Gen 33 6035ndash6048 (2000)
[425] K Kowalski J Rembielinski The Bargmann representation for the quantum mechanicson a sphere J Math Phys 42 4138ndash4147 (2001)
[426] C Kristjansen J Plefka GW Semenoff M Staudacher A new double-scaling limit ofN = 4 super-Yang-Mills theory and pp-wave strings Nuclear Phys B 643 3ndash30 (2002)
[427] M Kulesh M Holschneider MS Diallo Geophysical wavelet library Applications ofthe continuous wavelet transform to the polarization and dispersion analysis of signalsComput Geosci 34 1732ndash1752 (2008)
[428] R Kunze On the Frobenius reciprocity theorem for square integrable representationsPacific J Math 53 465ndash471 (1974)
[429] Y Kuroda A Wada T Yamazaki K Nagayama Postacquisition data processing methodfor suppression of the solvent signal I J Magn Reson 84 604ndash610 (1989)
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[431] G Kutyniok D Labate Resolution of the wavefront set using continuous shearlets TransAmer Math Soc 361 2719ndash2754 (2009)
[432] G Kutyniok W-Q Lim Compactly supported shearlets are optimally sparse J ApproxTheory 163 1564ndash1589 (2011)
[433] D Labate W-Q Lim G Kutyniok G Weiss Sparse multidimensional representationusing shearlets in Wavelets XI (San Diego CA 2005) ed by M Papadakis A Laine MUnser SPIE Proceedings vol 5914 (SPIE Bellingham WA 2005) pp 254ndash262
[434] P Lahti J-P Pellonpaumlauml Continuous variable tomographic measurements Phys Lett A373 3435ndash3438 (2009)
[435] Lambertrsquos projection see WikipediahttpenwikipediaorgwikiLambert_azimuthal_equal-area_projection
[436] J-P Leduc F Mujica R Murenzi MJT Smith Missile-tracking algorithm using target-adapted spatio-temporal wavelets in Automatic Object Recognition VII SPIE Proceedingsvol 5914 (SPIE Bellingham WA 1997) pp 400ndash411
[437] J-P Leduc F Mujica R Murenzi MJT Smith Spatio-temporal wavelet transforms formotion tracking in IEEE ICASSP 1997 vol 4 (1997) pp 3013ndash3016
[438] J-P Leduc F Mujica R Murenzi MJT Smith Spatio-temporal continuous waveletsapplied to missile warhead detection and tracking in SPIE VCIP rsquo97 vol 3024 ed byJ Biemond EJ Delp (1997) pp 787ndash798
[439] B Leistedt JD McEwen Exact wavelets on the ball IEEE Trans Signal Proc 60 1564ndash1589 (2012)
[440] PG Lemarieacute Y Meyer Ondelettes et bases hilbertiennes Rev Math Iberoamer 2 1ndash18(1986)
[441] C Lemke A Schuck Jr J-P Antoine D Sima Metabolite-sensitive analysis of magneticresonance spectroscopic signals using the continuous wavelet transform Meas SciTechnol 22 (2011) Art 114013
[442] J-M Leacutevy-Leblond Galilei group and non-relativistic quantum mechanics J Math Phys4 776-788 (1963)
[443] J-M Leacutevy-Leblond Galilei group and Galilean invariance in Group Theory and ItsApplications vol II ed by EM Loebl (Academic New York 1971) pp 221ndash299
[444] J-M Leacutevy-Leblond On the conceptual nature of the physical constants Riv Nuovo Cim7 187ndash214 (1977)
[445] EH Lieb The classical limit of quantum spin systems Commun Math Phys 31 327ndash340(1973)
[446] G Lindblad B Nagel Continuous bases for unitary irreducible representations of SU(11)Ann Inst H Poincareacute 13 27ndash56 (1970)
[447] W Lisiecki Kaumlhler coherent states orbits for representations of semisimple Lie groupsAnn Inst H Poincareacute 53 857ndash890 (1990)
[448] A Lisowska Moment-based fast wedgelet transform J Math Imaging Vis 39 180ndash192(2011)
[449] H Liu L Peng Admissible wavelets associated with the Heisenberg group Pacific JMath 180 101ndash123 (1997)
[450] E Livine S Speziale Physical boundary state for the quantum tetrahedron Class QuantGrav 25 085003 (2008)
[451] F Low Complete sets of wave packets in A Passion for Physics ndash Essay in Honor ofGeoffrey Chew ed by C DeTar (World Scientific Singapore 1985) pp 17ndash22
[452] G Mack All unitary ray representations of the conformal group SU(22) with positiveenergy Commun Math Phys 55 1ndash28 (1977)
[453] GW Mackey Imprimitivity for representations of locally compact groups I Proc NatAcad Sci 35 537ndash545 (1949)
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[456] SG Mallat Multifrequency channel decompositions of images and wavelet models IEEETrans Acoust Speech Signal Proc 37 2091ndash2110 (1989)
[457] SG Mallat A theory for multiresolution signal decomposition The wavelet representa-tion IEEE Trans Pattern Anal Machine Intell 11 674ndash693 (1989)
[458] S Mallat W-L Hwang Singularity detection and processing with wavelets IEEE TransInform Theory 38 617ndash643 (1992)
[459] S Mallat Z Zhang Matching pursuits with time frequency dictionaries IEEE TransSignal Proc 41 3397ndash3415 (1993)
[460] S Mallat S Zhong Wavelet maxima representation in Wavelets and Applications (ProcMarseille 1989) ed by Y Meyer (Masson and Springer Paris and Berlin 1991) pp 207ndash284
[461] VI Manrsquoko G Marmo ECG Sudarshan F Zaccaria f -oscillators and non-linearcoherent states Phys Scr 55 528ndash541 (1997)
[462] D Marinucci D Pietrobon A Baldi P Baldi P Cabella G Kerkyacharian P Natoli DPicard N Vittorio Spherical needlets for CMB data analysis Mon Not R Astron Soc383 539ndash545 (2008)
[463] D Marion M Ikura A Bax Improved solvent suppression in one- and two-dimensionalNMR spectra by convolution of time-domain data J Magn Reson 84 425ndash430 (1989)
[464] Y Meyer Principe drsquoincertitude bases hilbertiennes et algegravebres drsquoopeacuterateurs SeacuteminaireBourbaki 662 (1985ndash1986)
[465] Y Meyer Principe drsquoincertitude bases hilbertiennes et algegravebres drsquoopeacuterateurs Asteacuterisque145ndash146 209ndash223 (1987)
[466] Y Meyer H Xu Wavelet analysis and chirps Appl Comput Harmon Anal 4 366ndash379(1997)
[467] L Michel Invariance in quantum mechanics and group extensions in Group TheoreticalConcepts and Methods in Elementary Particle Physics ed by F Guumlrsey (Gordon andBreach New York and London 1964) pp 135ndash200
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[469] MM Miller Convergence of the Sudarshan expansion for the diagonal coherent-stateweight functional J Math Phys 9 1270ndash1274 (1968)
[470] V F Molchanov Harmonic analysis on homogeneous spaces in Representation Theoryand Noncommutative Harmonic Analysis II ed by AA Kirillov (Springer Berlin 1995)
[471] MI Monastyrsky AM Perelomov Coherent states and symmetric spaces II Ann InstH Poincareacute 23 23ndash48 (1975)
[472] B Moran S Howard D Cochran Positive-operator-valued measures A general settingfor frames in Excursions in Harmonic Analysis vol 1 2 ed by TD Andrews R BalanJJ Benedetto W Czaja KA Okoudjou (Birkhaumluser Boston 2013) pp 49ndash64
[473] H Moscovici Coherent states representations of nilpotent Lie groups Commun MathPhys 54 63ndash68 (1977)
[474] H Moscovici A Verona Coherent states and square integrable representations Ann InstH Poincareacute 29 139ndash156 (1978)
[475] F Mujica R Murenzi MJT Smith J-P Leduc Robust tracking in compressed imagesequences J Electr Imaging 7 746ndash754 (1998)
[476] R Murenzi Wavelet transforms associated to the n-dimensional Euclidean group withdilations Signals in more than one dimension in Wavelets Time-Frequency Methodsand Phase Space (Proc Marseille 1987) ed by J-M Combes A Grossmann PTchamitchian 2nd edn (Springer Berlin 1990) pp 239ndash246
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[479] MA Naımark Dokl Akad Nauk SSSR 41 359ndash361 (1943) see also B Sz-NagyExtensions of linear transformations in Hilbert space which extend beyond this spaceAppendix to F Riesz B Sz-Nagy Functional Analysis (Frederick Ungar New York 1960)
[480] FJ Narcowich P Petrushev JD Ward Localized tight frames on spheres SIAM J MathAnal 38 574ndash594 (2006)
[481] M Nauenberg Quantum wave packets on Kepler elliptic orbits Phys Rev A 40 1133ndash1136 (1989)
[482] M Nauenberg C Stroud J Yeazell The classical limit of an atom Scient Amer 27024ndash29 (1994)
[483] H Neumann Transformation properties of observables Helv Phys Acta 45 811ndash819(1972)
[484] U Niederer The maximal kinematical invariance group of the free Schroumldinger equationHelv Phys Acta 45 802ndash881 (1972)
[485] MM Nieto LM Simmons Jr Coherent states for general potentials I Formalism IIConfining one-dimensional examples III Nonconfining one-dimensional examples PhysRev D 20 1321ndash1331 1332ndash1341 1342ndash1350 (1979)
[486] MM Nieto LM Simmons Jr Coherent states for general potentials Phys Rev Lett 41207ndash210 (1987)
[487] A Odzijewicz On reproducing kernels and quantization of states Commun Math Phys114 577ndash597 (1988)
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[491] G Oacutelafsson B Oslashrsted The holomorphic discrete series for affine symmetric spaces JFunct Anal 81 126ndash159 (1988)
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[494] E Onofri Dynamical quantization of the Kepler manifold J Math Phys 17 401ndash408(1976)
[495] D Oriti R Pereira L Sindoni Coherent states in quantum gravity A construction basedon the flux representation of loop quantum gravity J Phys A Math Theor 45 244004(2012)
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[498] Z Pasternak-Winiarski On reproducing kernels for holomorphic vector bundles inQuantization and Infinite Dimensional Systems (Proc Białowieza Poland 1993) ed by J-P Antoine ST Ali W Lisiecki IM Mladenov A Odzijewicz (Plenum Press New Yorkand London 1994) pp 109ndash112
[499] T Paul Affine coherent states and the radial Schroumldinger equation I preprint CPT-84P1710 (1984) (unpublished)
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[501] AM Perelomov On the completeness of a system of coherent states Theor Math Phys6 156ndash164 (1971)
[502] AM Perelomov Coherent states for arbitrary Lie group Commun Math Phys 26 222ndash236 (1972)
[503] AM Perelomov Coherent states and symmetric spaces Commun Math Phys 44 197ndash210 (1975)
[504] M Perroud Projective representations of the Schroumldinger group Helv Phys Acta 50 233ndash252 (1977)
[505] J Phillips A note on square-integrable representations J Funct Anal 20 83ndash92 (1975)[506] D Pietrobon P Baldi D Marinucci Integrated Sachs-Wolfe effect from the cross
correlation of WMAP3 year and the NRAO VLA sky survey data New results andconstraints on dark energy Phys Rev D 74 043524 (2006)
[507] WWF Pijnappel A van den Boogaart R de Beer D van Ormondt SVD-basedquantification of magnetic resonance signals J Magn Reson 97 122ndash134 (1992)
[508] V Pop D Rosca Generalized piecewise constant orthogonal wavelet bases on 2D-domains Appl Anal 90 715ndash723 (2011)
[509] G Poumlschl E Teller Bemerkungen zur Quantenmechanik des anharmonischen OszillatorsZ Physik 83 143ndash151 (1933)
[510] D Potts G Steidl M Tasche Kernels of spherical harmonics and spherical frames inAdvanced Topics in Multivariate Approximation ed by F Fontanella K Jetter PJ Laurent(World Scientific Singapore 1996) pp 287ndash301
[511] E Prugovecki Consistent formulation of relativistic dynamics for massive spin-zeroparticles in external fields Phys Rev D 18 3655ndash3673 (1978) (Appendix C)
[512] E Prugovecki Relativistic quantum kinematics on stochastic phase space for massiveparticles J MathPhys 19 2261ndash2270 (1978)
[513] C Quesne Coherent states of the real symplectic group in a complex analytic parametriza-tion I II J Math Phys 27 428ndash441 869ndash878 (1986)
[514] C Quesne Generalized vector coherent states of sp(2NR) vector operators and ofsp(2NR) sup u(N) reduced Wigner coefficients J Phys A Math Gen 24 2697ndash2714(1991)
[515] JM Radcliffe Some properties of spin coherent states J Phys A Math Gen 4 313ndash323(1971)
[516] A Rahimi A Najati YN Dehghan Continuous frames in Hilbert spaces Methods FunctAnal Topol 12 170ndash182 (2006)
[517] H Rauhut M Roumlsler Radial multiresolution in dimension three Constr Approx 22 193ndash218 (2005)
[518] JH Rawnsley Coherent states and Kaumlhler manifolds Quart J Math Oxford 28(2) 403ndash415 (1977)
[519] J Renaud The contraction of the SU(11) discrete series of representations by means ofcoherent states J Math Phys 37 3168ndash3179 (1996)
[520] A Reacutenyi Representations for real numbers and their ergodic properties Acta Math AcadSci Hungary 8(3ndash4) 477ndash493 (1957)
[521] D Robert La coheacuterence dans tous ses eacutetats SMF Gazette 132 (2012)[522] JE Roberts The Dirac bra and ket formalism J Math Phys 7 1097ndash1104 (1966)[523] JE Roberts Rigged Hilbert spaces in quantum mechanics Commun Math Phys 3 98ndash
119 (1966)[524] S Roques F Bourzeix K Bouyoucef Soft-thresholding technique and restoration of
3C273 jet Astrophys Space Sci Nr 239 297ndash304 (1996)[525] D Rosca Haar wavelets on spherical triangulations in Advances in Multiresolution for
Geometric Modelling ed by NA Dogson MS Floater MA Sabin (Springer Berlin2005) pp 407ndash419
568 References
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[527] D Rosca Wavelets defined on closed surfaces J Comput Anal Appl 8 121ndash132 (2006)[528] D Rosca Weighted Haar wavelets on the sphere Int J Wavelets Multiresol Inf Proc 5
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Wavelets Multiresolut Inf Process 6 209ndash222 (2008)[531] D Rosca On a norm equivalence on L2(S2) Results Math 53 399ndash405 (2009)[532] D Rosca New uniform grids on the sphere Astron Astrophys 520 (2010) Art A63[533] D Rosca Uniform and refinable grids on elliptic domains and on some surfaces of
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stereographic projection Math Probl Eng 2009 124904 (2009)[536] D Rosca J-P Antoine Constructing wavelet frames and orthogonal wavelet bases on the
sphere in Recent Advances in Signal Processing ed by S Miron (IN-TECH ViennaAustria and Rijeka Croatia 2010) pp 59ndash76
[537] D Rosca G Plonka Uniform spherical grids via area preserving projection from the cubeto the sphere J Comput Appl Math 236 1033ndash1041 (2011)
[538] D Rosca G Plonka An area preserving projection from the regular octahedron to thesphere Results Math 63 429ndash444 (2012)
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[541] C Rovelli Zakopane lectures on loop gravity in Proceedings of 3rd Quantum Gravityand Quantum Geometry School 28 Febndash13 March 2011 (Zakopane Poland 2011)arXiv11023660v5
[542] C Rovelli S Speziale A semiclassical tetrahedron Class Quant Grav 23 5861ndash5870(2006)
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[579] T Thiemann Gauge field theory coherent states (GCS) 1 General properties Class QuantGrav 18 2025ndash2064 (2001)
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simulation of an impact test using wavelets analytical and finite element models Int JSolids Struct 38 5481ndash5508 (2001)
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Mod Phys 26 867ndash927 (1990)[618] I Zlatev W-M Zhang DH Feng Possibility that Schroumldingerrsquos conjecture for the
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Phys 75 715ndash775 (2003)[620] WH Zurek S Habib JP Paz Coherent states via decoherence Phys Rev Lett 70 1187ndash
1190 (1993)[621] K Zyczkowski Squeezed states in a quantum chaotic system J Phys A Math Theor 22
of SU(11) 81 296 297HilbertClowast-modules 164holomorphic 140nonholomorphic 151nonlinear 146of affine Galilei group 505of affine Poincareacute group 509of affine Weyl-Heisenberg group GaWH
497of compact semisimple Lie groups 174of Euclidean group E(n) 266of Galilei group G (11) 290of isochronous Galilei group 237of non-semisimple Lie groups 179of noncompact semisimple Lie groups 177of Poincareacute group Puarr
+(11) 283massless case 288
of Poincareacute group Puarr+(13) 279
of Schroumldinger group 508quasi-coherent states 186quaternionic 164
ST Ali et al Coherent States Wavelets and Their Generalizations Theoreticaland Mathematical Physics DOI 101007978-1-4614-8535-3copy Springer Science+Business Media New York 2014
573
574 Index
coherent states (CS) (cont)spin or SU(2) 175square integrable covariant 166 180 264vector (VCS) 73 108 112 170weighted 184 523
of affine Weyl-Heisenberg group GaWH497
of Poincareacute group Puarr+(11) 284
cohomology group 393 403coboundaries 403cochains 402cocycle 403
algebraic 387Cauchy 418Cauchy-Paul 354 419 425conical 418difference 417 462directional 416 440kinematical 499local 488metabolite-based 355 374minimal uncertainty 425multiselective 440on a graph 493on the sphere S
2 458on the sphere S
n 479on the torus T2 481steerable 439von Mises 440
wedgelet transform 455Wigner function 322Wigner-Ville transform 349Windowed Fourier or Gabor transform 349
ZZak transform 518
References
A Books and Theses
B Articles
Index
558 References
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[286] W Freeden T Maier S Zimmermann A survey on wavelet methods for (geo)applicationsRevista Mathematica Complutense 16 (2003) 277ndash310
[287] W Freeden M Schreiner Biorthogonal locally supported wavelets on the sphere based onzonal kernel functions J Fourier Anal Appl 13 693ndash709 (2007)
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[289] L Freidel ER Livine U(N) coherent states for loop quantum gravity J Math Phys 52052502 (2011)
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[292] H Fuumlhr Wavelet frames and admissibility in higher dimensions J Math Phys 37 6353ndash6366 (1996)
[293] H Fuumlhr M Mayer Continuous wavelet transforms from semidirect products Cyclicrepresentations and Plancherel measure J Fourier Anal Appl 8 375ndash396 (2002)
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127ndash147 (2003)[296] E Galapon Paulirsquos theorem and quantum canonical pairs The consistency of a bounded
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ε ) potentials Phys Lett 75A 159ndash163 (1980)[305] J-P Gazeau SL(2R)-coherent states and integrable systems in classical and quantum
physics in Quantization Coherent States and Complex Structures ed by J-P AntoineST Ali W Lisiecki IM Mladenov A Odzijewicz (Plenum Press New York and London1995) pp 147ndash158
[306] J-P Gazeau S Graffi Quantum harmonic oscillator A relativistic and statistical point ofview Boll Unione Mat Ital 11-A 815ndash839 (1997)
[307] J-P Gazeau V Hussin Poincareacute contraction of SU(11) Fock-Bargmann structure J PhysA Math Gen 25 1549ndash1573 (1992)
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J Phys A Math Gen 37 6977ndash6986 (2004)[315] J-P Gazeau J Renaud Lie algorithm for an interacting SU(11) elementary system and its
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179 67ndash71 (1993)[317] J-P Gazeau V Spiridonov Toward discrete wavelets with irrational scaling factor J Math
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4212 (1998)[320] J-P Gazeau M Andrle C Burdiacutek R Krejcar Wavelet multiresolutions for the Fibonacci
chain J Phys A Math Gen 33 L47ndashL51 (2000)[321] J-P Gazeau M Andrle C Burdiacutek Bernuau spline wavelets and sturmian sequences
J Fourier Anal Appl 10 269ndash300 (2004)[322] J-P Gazeau F-X Josse-Michaux P Monceau Finite dimensional quantizations of the
(q p) plane new space and momentum inequalities Int J Modern Phys B 20 1778ndash1791 (2006)
[323] J-P Gazeau J Mourad J Queacuteva Fuzzy de Sitter space-times via coherent statesquantization in Proceedings of the XXVIth Colloquium on Group Theoretical Methodsin Physics New York 2006 ed by J Birman S Catto B Nicolescu (Canopus PublishingLimited London 2009)
[324] D Geller A Mayeli Continuous wavelets on compact manifolds Math Z 262 895ndash927(2009)
[325] D Geller A Mayeli Nearly tight frames and space-frequency analysis on compactmanifolds Math Z 263 235ndash264 (2009)
[326] L Genovese B Videau M Ospici Th Deutsch S Goedecker J-F Mhaut Daubechieswavelets for high performance electronic structure calculations The BigDFT project CR Mecanique 339 149ndash164 (2011)
[327] G Gentili C Stoppato Power series and analyticity over the quaternions Math Ann 352113ndash131 (2012)
[328] G Gentili DC Struppa A new theory of regular functions of a quaternionic variable AdvMath 216 279ndash301 (2007)
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6 440ndash449 (1965)[333] RJ Glauber The quantum theory of optical coherence Phys Rev 130 2529ndash2539 (1963)
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[336] R Godement Sur les relations drsquoorthogonaliteacute de V Bargmann C R Acad Sci Paris 255521ndash523 657ndash659 (1947)
[337] C Gonnet B Torreacutesani Local frequency analysis with two-dimensional wavelet trans-form Signal Proc 37 389ndash404 (1994)
[338] JA Gonzalez MA del Olmo Coherent states on the circle J Phys A Math Gen 318841ndash8857 (1998)
[339] XGonze B Amadon et al ABINIT First-principles approach to material and nanosystemproperties Computer Physics Comm 180 2582ndash2615 (2009)
[340] KM Gograverski E Hivon AJ Banday BD Wandelt FK Hansen M Reinecke MBartelmann HEALPix A framework for high-resolution discretization and fast analysisof data distributed on the sphere Astrophys J 622 759ndash771 (2005)
[341] P Goupillaud A Grossmann J Morlet Cycle-octave and related transforms in seismicsignal analysis Geoexploration 23 85ndash102 (1984)
[342] KH Groumlchenig A new approach to irregular sampling of band-limited functions in RecentAdvances in Fourier Analysis and Its applications ed by JS Byrnes JL Byrnes (KluwerDordrecht 1990) pp 251ndash260
[343] KH Groumlchenig Gabor analysis over LCA groups in Gabor Analysis and Algorithms ndashTheory and Applications ed by HG Feichtinger T Strohmer (Birkhaumluser Boston-Basel-Berlin 1998) pp 211ndash231
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[345] P Grohs Continuous shearlet tight frames J Fourier Anal Appl 17 506ndash518 (2011)[346] P Grohs G Kutyniok Parabolic molecules preprint TU Berlin (2012)[347] M Grosser A note on distribution spaces on manifolds Novi Sad J Math 38 121ndash128
(2008)[348] A Grossmann Parity operator and quantization of δ -functions Commun Math Phys 48
191ndash194 (1976)[349] A Grossmann J Morlet Decomposition of Hardy functions into square integrable
wavelets of constant shape SIAM J Math Anal 15 723ndash736 (1984)[350] A Grossmann J Morlet Decomposition of functions into wavelets of constant shape and
related transforms in Mathematics + Physics Lectures on recent results I ed by L Streit(World Scientific Singapore 1985) pp 135ndash166
[351] A Grossmann J Morlet T Paul Integral transforms associated to square integrablerepresentations I General results J Math Phys 26 2473ndash2479 (1985)
[352] A Grossmann J Morlet T Paul Integral transforms associated to square integrablerepresentations II Examples Ann Inst H Poincareacute 45 293ndash309 (1986)
[353] A Grossmann R Kronland-Martinet J Morlet Reading and understanding the contin-uous wavelet transform in Wavelets Time-Frequency Methods and Phase Space (ProcMarseille 1987) ed by J-M Combes A Grossmann P Tchamitchian 2nd edn (SpringerBerlin 1990) pp 2ndash20
[354] P Guillemain R Kronland-Martinet B Martens Estimation of spectral lines with helpof the wavelet transform Application in NMR spectroscopy in Wavelets and Applications(Proc Marseille 1989) ed by Y Meyer (Masson and Springer Paris and Berlin 1991) pp38ndash60
[355] H de Guise M Bertola Coherent state realizations of su(n+ 1) on the n-torus J MathPhys 43 3425ndash3444 (2002)
[356] K Guo D Labate Representation of Fourier Integral Operators using shearlets J FourierAnal Appl 14 327ndash371 (2008)
References 561
[357] K Guo G Kutyniok D Labate Sparse multidimensional representations usinganisotropic dilation and shear operators in Wavelets and Spines (Athens GA 2005)(Nashboro Press Nashville TN 2006) pp 189ndash201
[358] K Guo D Labate W-Q Lim G Weiss E Wilson Wavelets with composite dilationsand their MRA properties Appl Comput Harmon Anal 20 202ndash236 (2006)
[359] EA Gutkin Overcomplete subspace systems and operator symbols Funct Anal Appl 9260ndash261 (1975)
[360] G Gyoumlrgyi Integration of the dynamical symmetry groups for the 1r potential Acta PhysAcad Sci Hung 27 435ndash439 (1969)
[361] BC Hall The Segal-Bargmann ldquoCoherent Staterdquo transform for compact Lie groups JFunct Analysis 122 103ndash151 (1994)
[362] B Hall JJ Mitchell Coherent states on spheres J Math Phys 43 1211ndash1236 (2002)[363] DK Hammond P Vandergheynst R Gribonval Wavelets on graphs via spectral theory
Appl Comput Harmon Anal 30 129ndash150 (2011)[364] Y Hassouni EMF Curado MA Rego-Monteiro Construction of coherent states for
physical algebraic system Phys Rev A 71 022104 (2005)[365] J He H Liu Admissible wavelets associated with the affine automorphism group of the
Siegel upper half-plane J Math Anal Appl 208 58ndash70 (1997)[366] J He H Liu Admissible wavelets associated with the classical domain of type one
Approx Appl 14 (1998) 89ndash105[367] J He L Peng Wavelet transform on the symmetric matrix space preprint Beijing (1997)
(unpublished)[368] J He L Peng Admissible wavelets on the unit disk Complex Variables 35 109ndash119
(1998)[369] DM Healy Jr FE Schroeck Jr On informational completeness of covariant localization
observables and Wigner coefficients J Math Phys 36 453ndash507 (1995)[370] C Heil D Walnut Continuous and discrete wavelet transforms SIAM Review 31 628ndash
666 (1989)[371] K Hepp EH Lieb On the superradiant phase transition for molecules in a quantized
radiation field The Dicke maser model Ann Phys (NY) 76 360ndash404 (1973)[372] K Hepp EH Lieb Equilibrium statistical mechanics of matter interacting with the
quantized radiation field Phys Rev A 8 2517ndash2525 (1973)[373] JA Hogan JD Lakey Extensions of the Heisenberg group by dilations and frames Appl
Comput Harmon Anal 2 174ndash199 (1995)[374] AL Hohoueacuteto K Thirulogasanthar ST Ali J-P Antoine Coherent states lattices and
square integrability of representations J Phys A Math Gen36 11817ndash11835 (2003)[375] M Holschneider On the wavelet transformation of fractal objects J Stat Phys 50 963ndash
993 (1988)[376] M Holschneider Wavelet analysis on the circle J Math Phys 31 39ndash44 (1990)[377] M Holschneider Inverse Radon transforms through inverse wavelet transforms Inv Probl
7 853ndash861 (1991)[378] M Holschneider Localization properties of wavelet transforms J Math Phys 34 3227ndash
3244 (1993)[379] M Holschneider General inversion formulas for wavelet transforms J Math Phys 34
4190ndash4198 (1993)[380] M Holschneider Wavelet analysis over abelian groups Applied Comput Harmon Anal
2 52ndash60 (1995)[381] M Holschneider Continuous wavelet transforms on the sphere J Math Phys 37 4156ndash
4165 (1996)[382] M Holschneider I Iglewska-Nowak Poisson wavelets on the sphere J Fourier Anal
Appl 13 405ndash419 (2007)
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[383] M Holschneider R Kronland-Martinet J Morlet P Tchamitchian A real-time algorithmfor signal analysis with the help of wavelet transform in Wavelets Time-FrequencyMethods and Phase Space (Proc Marseille 1987) ed by J-M Combes A Grossmann PTchamitchian 2nd edn (Springer Berlin 1990) pp 286ndash297
[384] M Holschneider P Tchamitchian Pointwise analysis of Riemannrsquos ldquonondifferentiablerdquofunction Invent Math 105 157ndash175 (1991)
[385] GR Honarasa MK Tavassoly M Hatami R Roknizadeh Nonclassical properties ofcoherent states and excited coherent states for continuous spectra J Phys A Math Theor44 085303 (2011)
[386] M Hongoh Coherent states associated with the continuous spectrum of noncompactgroups J Math Phys 18 2081ndash2085 (1977)
[387] A Horzela FH Szafraniec A measure free approach to coherent states J Phys A MathGen 45 244018 (2012)
[388] W-L Hwang S Mallat Characterization of self-similar multifractals with waveletmaxima Appl Comput Harmon Anal 1 316ndash328 (1994)
[389] W-L Hwang C-S Lu P-C Chung Shape from texture Estimation of planar surfaceorientation through the ridge surfaces of continuous wavelet transform IEEE Trans ImageProc 7 773ndash780 (1998)
[390] I Iglewska-Nowak M Holschneider Frames of Poisson wavelets on the sphere ApplComput Harmon Anal 28 227ndash248 (2010)
[391] E Inoumlnuuml EP Wigner On the contraction of groups and their representations Proc NatAcad Sci U S 39 510ndash524 (1953)
[392] S Iqbal F Saif Generalized coherent states and their statistical characteristics in power-law potentials J Math Phys 52 082105 (2011)
[393] CJ Isham JR Klauder Coherent states for n-dimensional Euclidean groups E(n) andtheir application J MathPhys 32 607ndash620 (1991)
[394] L Jacques J-P Antoine Multiselective pyramidal decomposition of images Wavelets withadaptive angular selectivity Int J Wavelets Multires Inform Proc 5 785ndash814 (2007)
[395] L Jacques L Duval C Chaux G Peyreacute A panorama on multiscale geometric rep-resentations intertwining spatial directional and frequency selectivity Signal Proc 912699ndash2730 (2011)
[396] HR Jalali M K Tavassoly On the ladder operators and nonclassicality of generalizedcoherent state associated with a particle in an infinite square well preprint (2013)arXiv13034100v1 [quant-ph]
[397] C Johnston On the pseudo-dilation representations of Flornes Grossmann Holschneiderand Torreacutesani Appl Comput Harmon Anal 3 377ndash385 (1997)
[398] G Kaiser Phase-space approach to relativistic quantum mechanics I Coherent staterepresentation for massive scalar particles J MathPhys 18 952ndash959 (1977)
[399] G Kaiser Phase-space approach to relativistic quantum mechanics II Geometrical aspectsJ MathPhys 19 502ndash507 (1978)
[400] C Kalisa B Torreacutesani N-dimensional affine Weyl-Heisenberg wavelets Ann Inst HPoincareacute 59 201ndash236 (1993)
[401] W Kaminski J Lewandowski T Pawłowski Quantum constraints Dirac observables andevolution group averaging versus the Schroumldinger picture in LQC Class Quant Grav 26245016 (2009)
[402] MR Karim ST Ali A relativistic windowed Fourier transform preprint ConcordiaUniversity Montreacuteal (1997) (unpublished)
[403] M R Karim ST Ali M Bodruzzaman A relativistic windowed Fourier transform inProceedings of IEEE SoutheastCon 2000 Nashville Tennessee pp 253ndash260 (2000)
[404] T Kawazoe Wavelet transforms associated to a principal series representation of semisim-ple Lie groups I II Proc Japan Acad Ser A ndash Math Sci 71 154ndash157 158ndash160 (1995)
[405] T Kawazoe Wavelet transform associated to an induced representation of SL(n+ 2R)Ann Inst H Poincareacute 65 1ndash13 (1996)
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[407] P Kittipoom G Kutyniok W-Q Lim Construction of compactly supported shearletframes Constr Approx 35 21ndash72 (2012)
[408] J Kiukas P Lahti K Ylinenc Phase space quantization and the operator moment problemJ Math Phys 47 072104 (2006)
[409] JR Klauder Continuous-representation theory I Postulates of continuous-representationtheory J Math Phys 4 1055ndash1058 (1963)
[410] JR Klauder Continuous-representation theory II Generalized relation between quantumand classical dynamics J Math Phys 4 1058ndash1073 (1963)
[411] JR Klauder Path integrals for affine variables in Functional Integration Theory andApplications ed by J-P Antoine E Tirapegui (Plenum Press New York and London1980) pp 101ndash119
[412] JR Klauder Are coherent states the natural language of quantum mechanics inFundamental Aspects of Quantum Theory ed by V Gorini A Frigerio NATO ASI Seriesvol B 144 (Plenum Press New York 1986) pp 1ndash12
[413] JR Klauder Quantization without quantization Ann Phys (NY) 237 147ndash160 (1995)[414] JR Klauder Coherent states for the hydrogen atom J Phys A Math Gen 29 L293ndash
L296 (1996)[415] JR Klauder An affinity for affine quantum gravity Proc Steklov Inst Math 272 169ndash176
(2011) and references therein[416] JR Klauder RF Streater A wavelet transform for the Poincareacute group J Math Phys 32
1609ndash1611 (1991)[417] JR Klauder RF Streater Wavelets and the Poincareacute half-plane J Math Phys 35 471ndash
478 (1994)[418] JR Klauder K Penson J-M Sixdeniers Constructing coherent states through solutions
of Stieltjes and Hausdorff moment problems Phys Rev A 64 013817 (2001)[419] A Kleppner RL Lipsman The Plancherel formula for group extensions Ann Ec Norm
Sup 5 459ndash516 (1972)[420] AB Klimov C Muntildeoz Coherent isotropic and squeezed states in a N-qubit system Phys
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[422] S Kobayashi Irreducibility of certain unitary representations J Math Soc Japan 20 638ndash642 (1968)
[423] K Kowalski J Rembielinski LC Papaloucas Coherent states for a quantum particle ona circle J Phys A Math Gen 29 4149ndash4167 (1996)
[424] K Kowalski J Rembielinski Quantum mechanics on a sphere and coherent states J PhysA Math Gen 33 6035ndash6048 (2000)
[425] K Kowalski J Rembielinski The Bargmann representation for the quantum mechanicson a sphere J Math Phys 42 4138ndash4147 (2001)
[426] C Kristjansen J Plefka GW Semenoff M Staudacher A new double-scaling limit ofN = 4 super-Yang-Mills theory and pp-wave strings Nuclear Phys B 643 3ndash30 (2002)
[427] M Kulesh M Holschneider MS Diallo Geophysical wavelet library Applications ofthe continuous wavelet transform to the polarization and dispersion analysis of signalsComput Geosci 34 1732ndash1752 (2008)
[428] R Kunze On the Frobenius reciprocity theorem for square integrable representationsPacific J Math 53 465ndash471 (1974)
[429] Y Kuroda A Wada T Yamazaki K Nagayama Postacquisition data processing methodfor suppression of the solvent signal I J Magn Reson 84 604ndash610 (1989)
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[431] G Kutyniok D Labate Resolution of the wavefront set using continuous shearlets TransAmer Math Soc 361 2719ndash2754 (2009)
[432] G Kutyniok W-Q Lim Compactly supported shearlets are optimally sparse J ApproxTheory 163 1564ndash1589 (2011)
[433] D Labate W-Q Lim G Kutyniok G Weiss Sparse multidimensional representationusing shearlets in Wavelets XI (San Diego CA 2005) ed by M Papadakis A Laine MUnser SPIE Proceedings vol 5914 (SPIE Bellingham WA 2005) pp 254ndash262
[434] P Lahti J-P Pellonpaumlauml Continuous variable tomographic measurements Phys Lett A373 3435ndash3438 (2009)
[435] Lambertrsquos projection see WikipediahttpenwikipediaorgwikiLambert_azimuthal_equal-area_projection
[436] J-P Leduc F Mujica R Murenzi MJT Smith Missile-tracking algorithm using target-adapted spatio-temporal wavelets in Automatic Object Recognition VII SPIE Proceedingsvol 5914 (SPIE Bellingham WA 1997) pp 400ndash411
[437] J-P Leduc F Mujica R Murenzi MJT Smith Spatio-temporal wavelet transforms formotion tracking in IEEE ICASSP 1997 vol 4 (1997) pp 3013ndash3016
[438] J-P Leduc F Mujica R Murenzi MJT Smith Spatio-temporal continuous waveletsapplied to missile warhead detection and tracking in SPIE VCIP rsquo97 vol 3024 ed byJ Biemond EJ Delp (1997) pp 787ndash798
[439] B Leistedt JD McEwen Exact wavelets on the ball IEEE Trans Signal Proc 60 1564ndash1589 (2012)
[440] PG Lemarieacute Y Meyer Ondelettes et bases hilbertiennes Rev Math Iberoamer 2 1ndash18(1986)
[441] C Lemke A Schuck Jr J-P Antoine D Sima Metabolite-sensitive analysis of magneticresonance spectroscopic signals using the continuous wavelet transform Meas SciTechnol 22 (2011) Art 114013
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[443] J-M Leacutevy-Leblond Galilei group and Galilean invariance in Group Theory and ItsApplications vol II ed by EM Loebl (Academic New York 1971) pp 221ndash299
[444] J-M Leacutevy-Leblond On the conceptual nature of the physical constants Riv Nuovo Cim7 187ndash214 (1977)
[445] EH Lieb The classical limit of quantum spin systems Commun Math Phys 31 327ndash340(1973)
[446] G Lindblad B Nagel Continuous bases for unitary irreducible representations of SU(11)Ann Inst H Poincareacute 13 27ndash56 (1970)
[447] W Lisiecki Kaumlhler coherent states orbits for representations of semisimple Lie groupsAnn Inst H Poincareacute 53 857ndash890 (1990)
[448] A Lisowska Moment-based fast wedgelet transform J Math Imaging Vis 39 180ndash192(2011)
[449] H Liu L Peng Admissible wavelets associated with the Heisenberg group Pacific JMath 180 101ndash123 (1997)
[450] E Livine S Speziale Physical boundary state for the quantum tetrahedron Class QuantGrav 25 085003 (2008)
[451] F Low Complete sets of wave packets in A Passion for Physics ndash Essay in Honor ofGeoffrey Chew ed by C DeTar (World Scientific Singapore 1985) pp 17ndash22
[452] G Mack All unitary ray representations of the conformal group SU(22) with positiveenergy Commun Math Phys 55 1ndash28 (1977)
[453] GW Mackey Imprimitivity for representations of locally compact groups I Proc NatAcad Sci 35 537ndash545 (1949)
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[457] SG Mallat A theory for multiresolution signal decomposition The wavelet representa-tion IEEE Trans Pattern Anal Machine Intell 11 674ndash693 (1989)
[458] S Mallat W-L Hwang Singularity detection and processing with wavelets IEEE TransInform Theory 38 617ndash643 (1992)
[459] S Mallat Z Zhang Matching pursuits with time frequency dictionaries IEEE TransSignal Proc 41 3397ndash3415 (1993)
[460] S Mallat S Zhong Wavelet maxima representation in Wavelets and Applications (ProcMarseille 1989) ed by Y Meyer (Masson and Springer Paris and Berlin 1991) pp 207ndash284
[461] VI Manrsquoko G Marmo ECG Sudarshan F Zaccaria f -oscillators and non-linearcoherent states Phys Scr 55 528ndash541 (1997)
[462] D Marinucci D Pietrobon A Baldi P Baldi P Cabella G Kerkyacharian P Natoli DPicard N Vittorio Spherical needlets for CMB data analysis Mon Not R Astron Soc383 539ndash545 (2008)
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[464] Y Meyer Principe drsquoincertitude bases hilbertiennes et algegravebres drsquoopeacuterateurs SeacuteminaireBourbaki 662 (1985ndash1986)
[465] Y Meyer Principe drsquoincertitude bases hilbertiennes et algegravebres drsquoopeacuterateurs Asteacuterisque145ndash146 209ndash223 (1987)
[466] Y Meyer H Xu Wavelet analysis and chirps Appl Comput Harmon Anal 4 366ndash379(1997)
[467] L Michel Invariance in quantum mechanics and group extensions in Group TheoreticalConcepts and Methods in Elementary Particle Physics ed by F Guumlrsey (Gordon andBreach New York and London 1964) pp 135ndash200
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[470] V F Molchanov Harmonic analysis on homogeneous spaces in Representation Theoryand Noncommutative Harmonic Analysis II ed by AA Kirillov (Springer Berlin 1995)
[471] MI Monastyrsky AM Perelomov Coherent states and symmetric spaces II Ann InstH Poincareacute 23 23ndash48 (1975)
[472] B Moran S Howard D Cochran Positive-operator-valued measures A general settingfor frames in Excursions in Harmonic Analysis vol 1 2 ed by TD Andrews R BalanJJ Benedetto W Czaja KA Okoudjou (Birkhaumluser Boston 2013) pp 49ndash64
[473] H Moscovici Coherent states representations of nilpotent Lie groups Commun MathPhys 54 63ndash68 (1977)
[474] H Moscovici A Verona Coherent states and square integrable representations Ann InstH Poincareacute 29 139ndash156 (1978)
[475] F Mujica R Murenzi MJT Smith J-P Leduc Robust tracking in compressed imagesequences J Electr Imaging 7 746ndash754 (1998)
[476] R Murenzi Wavelet transforms associated to the n-dimensional Euclidean group withdilations Signals in more than one dimension in Wavelets Time-Frequency Methodsand Phase Space (Proc Marseille 1987) ed by J-M Combes A Grossmann PTchamitchian 2nd edn (Springer Berlin 1990) pp 239ndash246
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[479] MA Naımark Dokl Akad Nauk SSSR 41 359ndash361 (1943) see also B Sz-NagyExtensions of linear transformations in Hilbert space which extend beyond this spaceAppendix to F Riesz B Sz-Nagy Functional Analysis (Frederick Ungar New York 1960)
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[481] M Nauenberg Quantum wave packets on Kepler elliptic orbits Phys Rev A 40 1133ndash1136 (1989)
[482] M Nauenberg C Stroud J Yeazell The classical limit of an atom Scient Amer 27024ndash29 (1994)
[483] H Neumann Transformation properties of observables Helv Phys Acta 45 811ndash819(1972)
[484] U Niederer The maximal kinematical invariance group of the free Schroumldinger equationHelv Phys Acta 45 802ndash881 (1972)
[485] MM Nieto LM Simmons Jr Coherent states for general potentials I Formalism IIConfining one-dimensional examples III Nonconfining one-dimensional examples PhysRev D 20 1321ndash1331 1332ndash1341 1342ndash1350 (1979)
[486] MM Nieto LM Simmons Jr Coherent states for general potentials Phys Rev Lett 41207ndash210 (1987)
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[491] G Oacutelafsson B Oslashrsted The holomorphic discrete series for affine symmetric spaces JFunct Anal 81 126ndash159 (1988)
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[499] T Paul Affine coherent states and the radial Schroumldinger equation I preprint CPT-84P1710 (1984) (unpublished)
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[501] AM Perelomov On the completeness of a system of coherent states Theor Math Phys6 156ndash164 (1971)
[502] AM Perelomov Coherent states for arbitrary Lie group Commun Math Phys 26 222ndash236 (1972)
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[504] M Perroud Projective representations of the Schroumldinger group Helv Phys Acta 50 233ndash252 (1977)
[505] J Phillips A note on square-integrable representations J Funct Anal 20 83ndash92 (1975)[506] D Pietrobon P Baldi D Marinucci Integrated Sachs-Wolfe effect from the cross
correlation of WMAP3 year and the NRAO VLA sky survey data New results andconstraints on dark energy Phys Rev D 74 043524 (2006)
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[508] V Pop D Rosca Generalized piecewise constant orthogonal wavelet bases on 2D-domains Appl Anal 90 715ndash723 (2011)
[509] G Poumlschl E Teller Bemerkungen zur Quantenmechanik des anharmonischen OszillatorsZ Physik 83 143ndash151 (1933)
[510] D Potts G Steidl M Tasche Kernels of spherical harmonics and spherical frames inAdvanced Topics in Multivariate Approximation ed by F Fontanella K Jetter PJ Laurent(World Scientific Singapore 1996) pp 287ndash301
[511] E Prugovecki Consistent formulation of relativistic dynamics for massive spin-zeroparticles in external fields Phys Rev D 18 3655ndash3673 (1978) (Appendix C)
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[513] C Quesne Coherent states of the real symplectic group in a complex analytic parametriza-tion I II J Math Phys 27 428ndash441 869ndash878 (1986)
[514] C Quesne Generalized vector coherent states of sp(2NR) vector operators and ofsp(2NR) sup u(N) reduced Wigner coefficients J Phys A Math Gen 24 2697ndash2714(1991)
[515] JM Radcliffe Some properties of spin coherent states J Phys A Math Gen 4 313ndash323(1971)
[516] A Rahimi A Najati YN Dehghan Continuous frames in Hilbert spaces Methods FunctAnal Topol 12 170ndash182 (2006)
[517] H Rauhut M Roumlsler Radial multiresolution in dimension three Constr Approx 22 193ndash218 (2005)
[518] JH Rawnsley Coherent states and Kaumlhler manifolds Quart J Math Oxford 28(2) 403ndash415 (1977)
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[520] A Reacutenyi Representations for real numbers and their ergodic properties Acta Math AcadSci Hungary 8(3ndash4) 477ndash493 (1957)
[521] D Robert La coheacuterence dans tous ses eacutetats SMF Gazette 132 (2012)[522] JE Roberts The Dirac bra and ket formalism J Math Phys 7 1097ndash1104 (1966)[523] JE Roberts Rigged Hilbert spaces in quantum mechanics Commun Math Phys 3 98ndash
119 (1966)[524] S Roques F Bourzeix K Bouyoucef Soft-thresholding technique and restoration of
3C273 jet Astrophys Space Sci Nr 239 297ndash304 (1996)[525] D Rosca Haar wavelets on spherical triangulations in Advances in Multiresolution for
Geometric Modelling ed by NA Dogson MS Floater MA Sabin (Springer Berlin2005) pp 407ndash419
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501ndash511 (2007)[529] D Rosca Wavelet bases on the sphere obtained by radial projection J Fourier Anal Appl
13 421ndash434 (2007)[530] D Rosca Piecewise constant wavelets on triangulations obtained by 1ndash3 splitting Int J
Wavelets Multiresolut Inf Process 6 209ndash222 (2008)[531] D Rosca On a norm equivalence on L2(S2) Results Math 53 399ndash405 (2009)[532] D Rosca New uniform grids on the sphere Astron Astrophys 520 (2010) Art A63[533] D Rosca Uniform and refinable grids on elliptic domains and on some surfaces of
revolution Appl Math Comput 217 7812ndash7817 (2011)[534] D Rosca Wavelet analysis on some surfaces of revolution via area preserving projection
Appl Comput Harmon Anal 30 262ndash272 (2011)[535] D Rosca J-P Antoine Locally supported orthogonal wavelet bases on the sphere via
stereographic projection Math Probl Eng 2009 124904 (2009)[536] D Rosca J-P Antoine Constructing wavelet frames and orthogonal wavelet bases on the
sphere in Recent Advances in Signal Processing ed by S Miron (IN-TECH ViennaAustria and Rijeka Croatia 2010) pp 59ndash76
[537] D Rosca G Plonka Uniform spherical grids via area preserving projection from the cubeto the sphere J Comput Appl Math 236 1033ndash1041 (2011)
[538] D Rosca G Plonka An area preserving projection from the regular octahedron to thesphere Results Math 63 429ndash444 (2012)
[539] H Rossi M Vergne Analytic continuation of the holomorphic discrete series for a semi-simple Lie group Acta Math 136 1ndash59 (1976)
[540] DJ Rotenberg Application of Sturmian functions to the Schroedinger three-body prob-lem Elastic e+ndashH scattering Ann Phys (NY) 19 262ndash278 (1962)
[541] C Rovelli Zakopane lectures on loop gravity in Proceedings of 3rd Quantum Gravityand Quantum Geometry School 28 Febndash13 March 2011 (Zakopane Poland 2011)arXiv11023660v5
[542] C Rovelli S Speziale A semiclassical tetrahedron Class Quant Grav 23 5861ndash5870(2006)
[543] DJ Rowe Coherent state theory of the noncompact symplectic group J Math Phys 252662ndash2271 (1984)
[544] DJ Rowe Microscopic theory of the nuclear collective model Rep Prog Phys 48 1419ndash1480 (1985)
[545] DJ Rowe Vector coherent state representations and their inner products J Phys A MathGen 45 244003 (2012) (This paper belongs to the special issue [38])
[546] DJ Rowe J Repka Vector-coherent-state theory as a theory of induced representationsJ Math Phys 32 2614ndash2634 (1991)
[547] DJ Rowe G Rosensteel R Gilmore Vector coherent state representation theory J MathPhys 26 2787ndash2791 (1985)
[548] A Royer Phase states and phase operators for the quantum harmonic oscillator Phys RevA 53 70ndash108 (1996)
[549] J Saletan Contraction of Lie groups J Math Phys 2 1ndash21 (1961)[550] G Saracco A Grossmann P Tchamitchian Use of wavelet transforms in the study of
propagation of transient acoustic signals across a plane interface between two homoge-neous media in Wavelets Time-Frequency Methods and Phase Space (Proc Marseille1987) ed by J-M Combes A Grossmann P Tchamitchian 2nd edn (Springer Berlin1990) pp 139ndash146
[551] P Schroumlder W Sweldens Spherical wavelets Efficiently representing functions on thesphere in Computer Graphics Proceedings (SIGGRAPH95) (ACM Siggraph Los Angeles1995) pp 161ndash175
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[553] S Scodeller Oslash Rudjord FK Hansen D Marinucci D Geller A Mayeli IntroducingMexican needlets for CMB analysis Issues for practical applications and comparison withstandard needlets Astrophys J 733 (2011) Art 121
[554] H Scutaru Coherent states and induced representations Lett Math Phys 2 101ndash107(1977)
[555] B Simon Distributions and their Hermite expansions J Math Phys 12 140ndash148 (1971)[556] B Simon The classical moment problem as a self-adjoint finite difference operator Adv
Math 137 82ndash203 (1998)[557] R Simon ECG Sudarshan N Mukunda Gaussian pure states in quantum mechanics
and the symplectic group Phys Rev A37 3028ndash3038 (1988)[558] S Sivakumar Studies on nonlinear coherent states J Opt B Quant Semiclass Opt 2
R61ndashR75 (2000)[559] E Slezak A Bijaoui G Mars Identification of structures from galaxy counts Use of the
wavelet transform Astron Astroph 227 301ndash316 (1990)[560] A Solomon A characteristic functional for deformed photon phenomenology Phys Lett
A 196 29ndash34 (1994)[561] SB Sontz Paragrassmann algebras as quantum spaces Part I Reproducing kernels in
Geometric Methods in Physics XXXI Workshop 2012 (Trends in Mathematics ed byP Kielanowski et al Birkhaumluser Verlag Basel 2013) pp 47ndash63
[562] SB Sontz Paragrassmann algebras as quantum spaces Part II Toeplitz operators J OperTh (2013 to appear) arXiv12055493
[563] SB Sontz A reproducing kernel and Toeplitz operators in the quantum plane Preprint(2013) arXiv13056986 [math-ph]
[564] SB Sontz Toeplitz quantization of an algebra with conjugation Preprint (2013)arXiv13085454 [math-ph]
[565] M Spera On a generalized Uncertainty Principle coherent states and the moment mapJ Geom Phys 12 165ndash182 (1993)
[566] J-L Starck EJ Candegraves DL Donoho The curvelet transform for image denoising IEEETrans Image Proc 11 670ndash684 (2002)
[567] J-L Starck DL Donoho E J Candegraves Astronomical image representation by the curvelettransform Astron Astroph 398 785ndash800 (2003)
[568] J-L Starck Y Moudden P Abrial M Nguyen Wavelets ridgelets and curvelets on thesphere Astron Astroph 446 1191ndash1204 (2006)
[569] MB Stenzel The Segal-Bargmann transform on a symmetric space of compact type JFunct Analysis 165 44ndash58 (1994)
[570] ECG Sudarshan Equivalence of semiclassical and quantum mechanical descriptions ofstatistical light beams Phys Rev Lett 10 277ndash279 (1963)
[571] A Suvichakorn H Ratiney A Bucur S Cavassila J-P Antoine Toward a quantitativeanalysis of in vivo magnetic resonance proton spectroscopic signals using the continuousMorlet wavelet transform Meas Sci Technol 20 (2009) Art 104029
[572] W Sweldens The lifting scheme A custom-design construction of biorthogonal waveletsApplied Comput Harmon Anal 3 1186ndash1200 (1996)
[573] W Sweldens The lifting scheme A construction of second generation wavelets SIAM JMath Anal 29 511ndash546 (1998)
[574] FH Szafraniec The reproducing kernel Hilbert space and its multiplication operatorsin Complex Analysis and Related Topics ed by E Ramirez de Arellano et al OperatorTheory Advances and Applications vol 114 (Birkhaumluser Basel 2000) pp 254ndash263
[575] FH Szafraniec Multipliers in the reproducing kernel Hilbert space subnormality andnoncommutative complex analysis in Reproducing Kernel Spaces and Applications edby D Alpay Operator Theory Advances and Applications vol 143 (Birkhaumluser Basel2003) pp 313ndash331
570 References
[576] R Takahashi Sur les repreacutesentations unitaires des groupes de Lorentz geacuteneacuteraliseacutes BullSoc Math France 91 289ndash433 (1963)
[577] MC Teich BEA Saleh Squeezed states of light Quantum Opt 1 152ndash191 (1989)[578] R Terrier L Demanet IA Grenier J-P Antoine Wavelet analysis of EGRET data in
Proceedings of the 27th International Cosmic Ray Conference (ICRC 2001) (CopernicusGesellschaft DE 2001) pp 2923ndash2926
[579] T Thiemann Gauge field theory coherent states (GCS) 1 General properties Class QuantGrav 18 2025ndash2064 (2001)
[580] T Thiemann O Winkler Gauge field theory coherent states (GCS) 2 Peakednessproperties Class Quant Grav 18 2561ndash2636 (2001)
[581] T Thiemann O Winkler Gauge field theory coherent states (GCS) 3 Ehrenfest theoremsClass Quant Grav 18 4629ndash4682 (2001)
[582] T Thiemann O Winkler Gauge field theory coherent states (GCS) 4 Infinite tensorproduct and thermodynamical limit Class Quant Grav 18 4997ndash5054 (2001)
[583] K Thirulagasanthar ST Ali Regular subspaces of a quaternionic Hilbert space fromquaternionic Hermite polynomials and associated coherent states J Math Phys 54013506 (2013)
[584] K Thirulogasanthar G Honnouvo A Krzyzak Coherent states and Hermite polynomialson quaternionic Hilbert spaces J Phys A Math Theor 43 385205 (2010)
[585] Tokamak see Wikipedia httpenwikipediaorgwikiTokamak[586] B Torreacutesani Wavelets associated with representations of the affine Weyl-Heisenberg
group J Math Phys 32 1273ndash1279 (1991)[587] B Torreacutesani Time-frequency representation Wavelet packets and optimal decomposition
Ann Inst H Poincareacute 56 215ndash234 (1992)[588] B Torreacutesani Position-frequency analysis for signals defined on spheres Signal Proc 43
341ndash346 (2005)[589] DA Trifonov Generalized intelligent states and squeezing J Math Phys 35 2297ndash2308
(1994)[590] AS Trushechkin IV Volovich Localization properties of squeezed quantum states in
nanoscale space domains preprint (2013) arXiv13046277v1 [quant-ph][591] M Unser N Chenouard A unifying parametric framework for 2D steerable wavelet
transforms SIAM J Imaging Sci 6 102ndash135 (2013)[592] P Vandergheynst J-F Gobbers Directional dyadic wavelet transforms Design and
algorithms IEEE Trans Image Proc 11 363ndash372 (2002)[593] P Vandergheynst J-P Antoine E Van Vyve A Goldberg I Doghri Modelling and
simulation of an impact test using wavelets analytical and finite element models Int JSolids Struct 38 5481ndash5508 (2001)
[594] L Vanhamme RD Fierro S Van Huffel R de Beer Fast removal of residual water inproton spectra J Magn Reson 132 197ndash203 (1998)
[595] J Ville Theacuteorie et applications de la notion de signal analytique Cacircbles et Trans 2 61ndash74(1948)
[596] J Voisin On some unitary representations of the Galilei group I Irreducible representa-tions J Math Phys 6 1519ndash1529 (1965)
[597] A Vourdas Analytic representations in quantum mechanics J Phys A Math Gen 39R65ndashR141 (2006)
[598] DF Walls Squeezed states of light Nature 306 141ndash146 (1983)[599] YK Wang FT Hioe Phase transition in the Dicke maser model Phys Rev A 7 831ndash836
(1973)[600] PSP Wang J Yang A review of wavelet-based edge detection methods Int J Patt
Recogn Artif Intell 26 1255011 (2012)[601] I Weinreich A construction of C1-wavelets on the two-dimensional sphere Appl Comput
Harmon Anal 10 1ndash26 (2001)[602] H Weyl Quantenmechanik und Gruppentheorie Z Phys 46 1ndash46 (1927)
References 571
[603] Y Wiaux L Jacques P Vandergheynst Correspondence principle between spherical andEuclidean wavelets Astrophys J 632 15ndash28 (2005)
[604] Y Wiaux L Jacques P Vielva P Vandergheynst Fast directional correlation on the spherewith steerable filters Astrophys J 652 820ndash832 (2006)
[605] Y Wiaux JD McEwen P Vandergheynst O Blanc Exact reconstruction with directionalwavelets on the sphere Mon Not R Astron Soc 388 770ndash788 (2008)
[606] WM Wieland Complex Ashtekar variables and reality conditions for Holstrsquos action AnnHenri Poincareacute 13 425ndash448 (2012)
[607] EP Wigner On the quantum correction for thermodynamic equilibrium Phys Rev 40749ndash759 (1932)
[608] RM Willette RD Nowak Platelets A multiscale approach for recovering edges andsurfaces in photon-limited medical imaging IEEE Trans Med Imaging 22 332ndash350(2003)
[609] W Wisnoe P Gajan A Strzelecki C Lempereur J-M Matheacute The use of the two-dimensional wavelet transform in flow visualization processing in Progress in WaveletAnalysis and Applications (Proc Toulouse 1992) ed by Y Meyer S Roques (EdFrontiegraveres Gif-sur-Yvette 1993) pp 455ndash458
[610] K Woacutedkiewicz On the quantum mechanics of squeezed states J Modern Optics 34 941ndash948(1987)
[611] JA Yeazell M Mallalieu CR Stroud Jr Observation of the collapse and revival of aRydberg electronic wave packet Phys Rev Lett 64 2007ndash2010 (1990)
[612] JA Yeazell CR Stroud Jr Observation of fractional revivals in the evolution of aRydberg atomic wave packet Phys Rev A 43 5153ndash5156 (1991)
[613] HP Yuen Two-photon coherent states of the radiation field Phys Rev A 13 2226ndash2243(1976)
[614] J Zak Balian-Low theorem for Landau levels Phys Rev Lett 79 533ndash536 (1997)[615] J Zak Orthonormal sets of localized functions for a Landau level J Math Phys 39 4195ndash
4200 (1998) and references quoted there[616] AA Zakharova On the properties of generalized frames Math Notes 83 190ndash200 (2008)[617] W-M Zhang DH Feng R Gilmore Coherent states Theory and some applications Rev
Mod Phys 26 867ndash927 (1990)[618] I Zlatev W-M Zhang DH Feng Possibility that Schroumldingerrsquos conjecture for the
hydrogen atom coherent states is not attainable Phys Rev A 50 R1973ndashR1975 (1994)[619] WH Zurek Decoherence einselection and the quantum origins of the classical Rev Mod
Phys 75 715ndash775 (2003)[620] WH Zurek S Habib JP Paz Coherent states via decoherence Phys Rev Lett 70 1187ndash
1190 (1993)[621] K Zyczkowski Squeezed states in a quantum chaotic system J Phys A Math Theor 22
of SU(11) 81 296 297HilbertClowast-modules 164holomorphic 140nonholomorphic 151nonlinear 146of affine Galilei group 505of affine Poincareacute group 509of affine Weyl-Heisenberg group GaWH
497of compact semisimple Lie groups 174of Euclidean group E(n) 266of Galilei group G (11) 290of isochronous Galilei group 237of non-semisimple Lie groups 179of noncompact semisimple Lie groups 177of Poincareacute group Puarr
+(11) 283massless case 288
of Poincareacute group Puarr+(13) 279
of Schroumldinger group 508quasi-coherent states 186quaternionic 164
ST Ali et al Coherent States Wavelets and Their Generalizations Theoreticaland Mathematical Physics DOI 101007978-1-4614-8535-3copy Springer Science+Business Media New York 2014
573
574 Index
coherent states (CS) (cont)spin or SU(2) 175square integrable covariant 166 180 264vector (VCS) 73 108 112 170weighted 184 523
of affine Weyl-Heisenberg group GaWH497
of Poincareacute group Puarr+(11) 284
cohomology group 393 403coboundaries 403cochains 402cocycle 403
algebraic 387Cauchy 418Cauchy-Paul 354 419 425conical 418difference 417 462directional 416 440kinematical 499local 488metabolite-based 355 374minimal uncertainty 425multiselective 440on a graph 493on the sphere S
2 458on the sphere S
n 479on the torus T2 481steerable 439von Mises 440
wedgelet transform 455Wigner function 322Wigner-Ville transform 349Windowed Fourier or Gabor transform 349
ZZak transform 518
References
A Books and Theses
B Articles
Index
References 559
[308] J-P Gazeau R Kanamoto Action-angle coherent states and related quantization inProceedings of QTS7 Colloquium Prague 2011 Journal of Physics Conference Seriesvol 343 (2012) p 012038-1-9
[309] J-P Gazeau JR Klauder Coherent states for systems with discrete and continuousspectrum J Phys A Math Gen 32 123ndash132 (1999)
[310] J-P Gazeau P Monceau Generalized coherent states for arbitrary quantum systems inColloquium M Flato (Dijon Sept 99) vol II (Kluumlwer Dordrecht 2000) pp 131ndash144
[311] J-P Gazeau M Novello The question of mass in (Anti-) de Sitter space-times J Phys AMath Theor 41 304008 (2008)
[312] J-P Gazeau M del Olmo q-coherent states quantization of the harmonic oscillator AnnPhys (NY) 330 220ndash245 (2013) arXiv12071200 [quant-ph]
[313] J-P Gazeau J Patera Tau-wavelets of Haar J Phys A Math Gen 29 4549ndash4559 (1996)[314] J-P Gazeau W Piechocki Coherent states quantization of a particle in de Sitter space
J Phys A Math Gen 37 6977ndash6986 (2004)[315] J-P Gazeau J Renaud Lie algorithm for an interacting SU(11) elementary system and its
contraction Ann Phys (NY) 222 89ndash121 (1993)[316] J-P Gazeau J Renaud Relativistic harmonic oscillator and space curvature Phys Lett A
179 67ndash71 (1993)[317] J-P Gazeau V Spiridonov Toward discrete wavelets with irrational scaling factor J Math
plane J Phys A Math Theor 44 495201 (2011)[319] J-P Gazeau J Patera E Pelantovaacute Tau-wavelets in the plane J Math Phys 39 4201ndash
4212 (1998)[320] J-P Gazeau M Andrle C Burdiacutek R Krejcar Wavelet multiresolutions for the Fibonacci
chain J Phys A Math Gen 33 L47ndashL51 (2000)[321] J-P Gazeau M Andrle C Burdiacutek Bernuau spline wavelets and sturmian sequences
J Fourier Anal Appl 10 269ndash300 (2004)[322] J-P Gazeau F-X Josse-Michaux P Monceau Finite dimensional quantizations of the
(q p) plane new space and momentum inequalities Int J Modern Phys B 20 1778ndash1791 (2006)
[323] J-P Gazeau J Mourad J Queacuteva Fuzzy de Sitter space-times via coherent statesquantization in Proceedings of the XXVIth Colloquium on Group Theoretical Methodsin Physics New York 2006 ed by J Birman S Catto B Nicolescu (Canopus PublishingLimited London 2009)
[324] D Geller A Mayeli Continuous wavelets on compact manifolds Math Z 262 895ndash927(2009)
[325] D Geller A Mayeli Nearly tight frames and space-frequency analysis on compactmanifolds Math Z 263 235ndash264 (2009)
[326] L Genovese B Videau M Ospici Th Deutsch S Goedecker J-F Mhaut Daubechieswavelets for high performance electronic structure calculations The BigDFT project CR Mecanique 339 149ndash164 (2011)
[327] G Gentili C Stoppato Power series and analyticity over the quaternions Math Ann 352113ndash131 (2012)
[328] G Gentili DC Struppa A new theory of regular functions of a quaternionic variable AdvMath 216 279ndash301 (2007)
[329] C Geyer K Daniilidis Catadioptric projective geometry Int J Comput Vision 45 223ndash243 (2001)
[330] R Gilmore Geometry of symmetrized states Ann Phys (NY) 74 391ndash463 (1972)[331] R Gilmore On properties of coherent states Rev Mex Fis 23 143ndash187 (1974)[332] J Ginibre Statistical ensembles of complex quaternion and real matrices J Math Phys
6 440ndash449 (1965)[333] RJ Glauber The quantum theory of optical coherence Phys Rev 130 2529ndash2539 (1963)
560 References
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[335] J Glimm Locally compact transformation groups Trans Amer Math Soc 101 124ndash138(1961)
[336] R Godement Sur les relations drsquoorthogonaliteacute de V Bargmann C R Acad Sci Paris 255521ndash523 657ndash659 (1947)
[337] C Gonnet B Torreacutesani Local frequency analysis with two-dimensional wavelet trans-form Signal Proc 37 389ndash404 (1994)
[338] JA Gonzalez MA del Olmo Coherent states on the circle J Phys A Math Gen 318841ndash8857 (1998)
[339] XGonze B Amadon et al ABINIT First-principles approach to material and nanosystemproperties Computer Physics Comm 180 2582ndash2615 (2009)
[340] KM Gograverski E Hivon AJ Banday BD Wandelt FK Hansen M Reinecke MBartelmann HEALPix A framework for high-resolution discretization and fast analysisof data distributed on the sphere Astrophys J 622 759ndash771 (2005)
[341] P Goupillaud A Grossmann J Morlet Cycle-octave and related transforms in seismicsignal analysis Geoexploration 23 85ndash102 (1984)
[342] KH Groumlchenig A new approach to irregular sampling of band-limited functions in RecentAdvances in Fourier Analysis and Its applications ed by JS Byrnes JL Byrnes (KluwerDordrecht 1990) pp 251ndash260
[343] KH Groumlchenig Gabor analysis over LCA groups in Gabor Analysis and Algorithms ndashTheory and Applications ed by HG Feichtinger T Strohmer (Birkhaumluser Boston-Basel-Berlin 1998) pp 211ndash231
[344] HJ Groenewold On the principles of elementary quantum mechanics Physica 12 405ndash460 (1946)
[345] P Grohs Continuous shearlet tight frames J Fourier Anal Appl 17 506ndash518 (2011)[346] P Grohs G Kutyniok Parabolic molecules preprint TU Berlin (2012)[347] M Grosser A note on distribution spaces on manifolds Novi Sad J Math 38 121ndash128
(2008)[348] A Grossmann Parity operator and quantization of δ -functions Commun Math Phys 48
191ndash194 (1976)[349] A Grossmann J Morlet Decomposition of Hardy functions into square integrable
wavelets of constant shape SIAM J Math Anal 15 723ndash736 (1984)[350] A Grossmann J Morlet Decomposition of functions into wavelets of constant shape and
related transforms in Mathematics + Physics Lectures on recent results I ed by L Streit(World Scientific Singapore 1985) pp 135ndash166
[351] A Grossmann J Morlet T Paul Integral transforms associated to square integrablerepresentations I General results J Math Phys 26 2473ndash2479 (1985)
[352] A Grossmann J Morlet T Paul Integral transforms associated to square integrablerepresentations II Examples Ann Inst H Poincareacute 45 293ndash309 (1986)
[353] A Grossmann R Kronland-Martinet J Morlet Reading and understanding the contin-uous wavelet transform in Wavelets Time-Frequency Methods and Phase Space (ProcMarseille 1987) ed by J-M Combes A Grossmann P Tchamitchian 2nd edn (SpringerBerlin 1990) pp 2ndash20
[354] P Guillemain R Kronland-Martinet B Martens Estimation of spectral lines with helpof the wavelet transform Application in NMR spectroscopy in Wavelets and Applications(Proc Marseille 1989) ed by Y Meyer (Masson and Springer Paris and Berlin 1991) pp38ndash60
[355] H de Guise M Bertola Coherent state realizations of su(n+ 1) on the n-torus J MathPhys 43 3425ndash3444 (2002)
[356] K Guo D Labate Representation of Fourier Integral Operators using shearlets J FourierAnal Appl 14 327ndash371 (2008)
References 561
[357] K Guo G Kutyniok D Labate Sparse multidimensional representations usinganisotropic dilation and shear operators in Wavelets and Spines (Athens GA 2005)(Nashboro Press Nashville TN 2006) pp 189ndash201
[358] K Guo D Labate W-Q Lim G Weiss E Wilson Wavelets with composite dilationsand their MRA properties Appl Comput Harmon Anal 20 202ndash236 (2006)
[359] EA Gutkin Overcomplete subspace systems and operator symbols Funct Anal Appl 9260ndash261 (1975)
[360] G Gyoumlrgyi Integration of the dynamical symmetry groups for the 1r potential Acta PhysAcad Sci Hung 27 435ndash439 (1969)
[361] BC Hall The Segal-Bargmann ldquoCoherent Staterdquo transform for compact Lie groups JFunct Analysis 122 103ndash151 (1994)
[362] B Hall JJ Mitchell Coherent states on spheres J Math Phys 43 1211ndash1236 (2002)[363] DK Hammond P Vandergheynst R Gribonval Wavelets on graphs via spectral theory
Appl Comput Harmon Anal 30 129ndash150 (2011)[364] Y Hassouni EMF Curado MA Rego-Monteiro Construction of coherent states for
physical algebraic system Phys Rev A 71 022104 (2005)[365] J He H Liu Admissible wavelets associated with the affine automorphism group of the
Siegel upper half-plane J Math Anal Appl 208 58ndash70 (1997)[366] J He H Liu Admissible wavelets associated with the classical domain of type one
Approx Appl 14 (1998) 89ndash105[367] J He L Peng Wavelet transform on the symmetric matrix space preprint Beijing (1997)
(unpublished)[368] J He L Peng Admissible wavelets on the unit disk Complex Variables 35 109ndash119
(1998)[369] DM Healy Jr FE Schroeck Jr On informational completeness of covariant localization
observables and Wigner coefficients J Math Phys 36 453ndash507 (1995)[370] C Heil D Walnut Continuous and discrete wavelet transforms SIAM Review 31 628ndash
666 (1989)[371] K Hepp EH Lieb On the superradiant phase transition for molecules in a quantized
radiation field The Dicke maser model Ann Phys (NY) 76 360ndash404 (1973)[372] K Hepp EH Lieb Equilibrium statistical mechanics of matter interacting with the
quantized radiation field Phys Rev A 8 2517ndash2525 (1973)[373] JA Hogan JD Lakey Extensions of the Heisenberg group by dilations and frames Appl
Comput Harmon Anal 2 174ndash199 (1995)[374] AL Hohoueacuteto K Thirulogasanthar ST Ali J-P Antoine Coherent states lattices and
square integrability of representations J Phys A Math Gen36 11817ndash11835 (2003)[375] M Holschneider On the wavelet transformation of fractal objects J Stat Phys 50 963ndash
993 (1988)[376] M Holschneider Wavelet analysis on the circle J Math Phys 31 39ndash44 (1990)[377] M Holschneider Inverse Radon transforms through inverse wavelet transforms Inv Probl
7 853ndash861 (1991)[378] M Holschneider Localization properties of wavelet transforms J Math Phys 34 3227ndash
3244 (1993)[379] M Holschneider General inversion formulas for wavelet transforms J Math Phys 34
4190ndash4198 (1993)[380] M Holschneider Wavelet analysis over abelian groups Applied Comput Harmon Anal
2 52ndash60 (1995)[381] M Holschneider Continuous wavelet transforms on the sphere J Math Phys 37 4156ndash
4165 (1996)[382] M Holschneider I Iglewska-Nowak Poisson wavelets on the sphere J Fourier Anal
Appl 13 405ndash419 (2007)
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[383] M Holschneider R Kronland-Martinet J Morlet P Tchamitchian A real-time algorithmfor signal analysis with the help of wavelet transform in Wavelets Time-FrequencyMethods and Phase Space (Proc Marseille 1987) ed by J-M Combes A Grossmann PTchamitchian 2nd edn (Springer Berlin 1990) pp 286ndash297
[384] M Holschneider P Tchamitchian Pointwise analysis of Riemannrsquos ldquonondifferentiablerdquofunction Invent Math 105 157ndash175 (1991)
[385] GR Honarasa MK Tavassoly M Hatami R Roknizadeh Nonclassical properties ofcoherent states and excited coherent states for continuous spectra J Phys A Math Theor44 085303 (2011)
[386] M Hongoh Coherent states associated with the continuous spectrum of noncompactgroups J Math Phys 18 2081ndash2085 (1977)
[387] A Horzela FH Szafraniec A measure free approach to coherent states J Phys A MathGen 45 244018 (2012)
[388] W-L Hwang S Mallat Characterization of self-similar multifractals with waveletmaxima Appl Comput Harmon Anal 1 316ndash328 (1994)
[389] W-L Hwang C-S Lu P-C Chung Shape from texture Estimation of planar surfaceorientation through the ridge surfaces of continuous wavelet transform IEEE Trans ImageProc 7 773ndash780 (1998)
[390] I Iglewska-Nowak M Holschneider Frames of Poisson wavelets on the sphere ApplComput Harmon Anal 28 227ndash248 (2010)
[391] E Inoumlnuuml EP Wigner On the contraction of groups and their representations Proc NatAcad Sci U S 39 510ndash524 (1953)
[392] S Iqbal F Saif Generalized coherent states and their statistical characteristics in power-law potentials J Math Phys 52 082105 (2011)
[393] CJ Isham JR Klauder Coherent states for n-dimensional Euclidean groups E(n) andtheir application J MathPhys 32 607ndash620 (1991)
[394] L Jacques J-P Antoine Multiselective pyramidal decomposition of images Wavelets withadaptive angular selectivity Int J Wavelets Multires Inform Proc 5 785ndash814 (2007)
[395] L Jacques L Duval C Chaux G Peyreacute A panorama on multiscale geometric rep-resentations intertwining spatial directional and frequency selectivity Signal Proc 912699ndash2730 (2011)
[396] HR Jalali M K Tavassoly On the ladder operators and nonclassicality of generalizedcoherent state associated with a particle in an infinite square well preprint (2013)arXiv13034100v1 [quant-ph]
[397] C Johnston On the pseudo-dilation representations of Flornes Grossmann Holschneiderand Torreacutesani Appl Comput Harmon Anal 3 377ndash385 (1997)
[398] G Kaiser Phase-space approach to relativistic quantum mechanics I Coherent staterepresentation for massive scalar particles J MathPhys 18 952ndash959 (1977)
[399] G Kaiser Phase-space approach to relativistic quantum mechanics II Geometrical aspectsJ MathPhys 19 502ndash507 (1978)
[400] C Kalisa B Torreacutesani N-dimensional affine Weyl-Heisenberg wavelets Ann Inst HPoincareacute 59 201ndash236 (1993)
[401] W Kaminski J Lewandowski T Pawłowski Quantum constraints Dirac observables andevolution group averaging versus the Schroumldinger picture in LQC Class Quant Grav 26245016 (2009)
[402] MR Karim ST Ali A relativistic windowed Fourier transform preprint ConcordiaUniversity Montreacuteal (1997) (unpublished)
[403] M R Karim ST Ali M Bodruzzaman A relativistic windowed Fourier transform inProceedings of IEEE SoutheastCon 2000 Nashville Tennessee pp 253ndash260 (2000)
[404] T Kawazoe Wavelet transforms associated to a principal series representation of semisim-ple Lie groups I II Proc Japan Acad Ser A ndash Math Sci 71 154ndash157 158ndash160 (1995)
[405] T Kawazoe Wavelet transform associated to an induced representation of SL(n+ 2R)Ann Inst H Poincareacute 65 1ndash13 (1996)
References 563
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[407] P Kittipoom G Kutyniok W-Q Lim Construction of compactly supported shearletframes Constr Approx 35 21ndash72 (2012)
[408] J Kiukas P Lahti K Ylinenc Phase space quantization and the operator moment problemJ Math Phys 47 072104 (2006)
[409] JR Klauder Continuous-representation theory I Postulates of continuous-representationtheory J Math Phys 4 1055ndash1058 (1963)
[410] JR Klauder Continuous-representation theory II Generalized relation between quantumand classical dynamics J Math Phys 4 1058ndash1073 (1963)
[411] JR Klauder Path integrals for affine variables in Functional Integration Theory andApplications ed by J-P Antoine E Tirapegui (Plenum Press New York and London1980) pp 101ndash119
[412] JR Klauder Are coherent states the natural language of quantum mechanics inFundamental Aspects of Quantum Theory ed by V Gorini A Frigerio NATO ASI Seriesvol B 144 (Plenum Press New York 1986) pp 1ndash12
[413] JR Klauder Quantization without quantization Ann Phys (NY) 237 147ndash160 (1995)[414] JR Klauder Coherent states for the hydrogen atom J Phys A Math Gen 29 L293ndash
L296 (1996)[415] JR Klauder An affinity for affine quantum gravity Proc Steklov Inst Math 272 169ndash176
(2011) and references therein[416] JR Klauder RF Streater A wavelet transform for the Poincareacute group J Math Phys 32
1609ndash1611 (1991)[417] JR Klauder RF Streater Wavelets and the Poincareacute half-plane J Math Phys 35 471ndash
478 (1994)[418] JR Klauder K Penson J-M Sixdeniers Constructing coherent states through solutions
of Stieltjes and Hausdorff moment problems Phys Rev A 64 013817 (2001)[419] A Kleppner RL Lipsman The Plancherel formula for group extensions Ann Ec Norm
Sup 5 459ndash516 (1972)[420] AB Klimov C Muntildeoz Coherent isotropic and squeezed states in a N-qubit system Phys
Scr 87 038110 (2013)[421] A Klyashko Dynamical symmetry approach to entanglement in Physics and Theoretical
Computer Science From Numbers and Languages to (Quantum) Cryptography - NATOSecurity through Science Series D - Information and Communication Security vol 7 edby J-P Gazeau J Nesetril B Rovan (IOS Press Washington DC 2007) pp 25ndash54
[422] S Kobayashi Irreducibility of certain unitary representations J Math Soc Japan 20 638ndash642 (1968)
[423] K Kowalski J Rembielinski LC Papaloucas Coherent states for a quantum particle ona circle J Phys A Math Gen 29 4149ndash4167 (1996)
[424] K Kowalski J Rembielinski Quantum mechanics on a sphere and coherent states J PhysA Math Gen 33 6035ndash6048 (2000)
[425] K Kowalski J Rembielinski The Bargmann representation for the quantum mechanicson a sphere J Math Phys 42 4138ndash4147 (2001)
[426] C Kristjansen J Plefka GW Semenoff M Staudacher A new double-scaling limit ofN = 4 super-Yang-Mills theory and pp-wave strings Nuclear Phys B 643 3ndash30 (2002)
[427] M Kulesh M Holschneider MS Diallo Geophysical wavelet library Applications ofthe continuous wavelet transform to the polarization and dispersion analysis of signalsComput Geosci 34 1732ndash1752 (2008)
[428] R Kunze On the Frobenius reciprocity theorem for square integrable representationsPacific J Math 53 465ndash471 (1974)
[429] Y Kuroda A Wada T Yamazaki K Nagayama Postacquisition data processing methodfor suppression of the solvent signal I J Magn Reson 84 604ndash610 (1989)
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[431] G Kutyniok D Labate Resolution of the wavefront set using continuous shearlets TransAmer Math Soc 361 2719ndash2754 (2009)
[432] G Kutyniok W-Q Lim Compactly supported shearlets are optimally sparse J ApproxTheory 163 1564ndash1589 (2011)
[433] D Labate W-Q Lim G Kutyniok G Weiss Sparse multidimensional representationusing shearlets in Wavelets XI (San Diego CA 2005) ed by M Papadakis A Laine MUnser SPIE Proceedings vol 5914 (SPIE Bellingham WA 2005) pp 254ndash262
[434] P Lahti J-P Pellonpaumlauml Continuous variable tomographic measurements Phys Lett A373 3435ndash3438 (2009)
[435] Lambertrsquos projection see WikipediahttpenwikipediaorgwikiLambert_azimuthal_equal-area_projection
[436] J-P Leduc F Mujica R Murenzi MJT Smith Missile-tracking algorithm using target-adapted spatio-temporal wavelets in Automatic Object Recognition VII SPIE Proceedingsvol 5914 (SPIE Bellingham WA 1997) pp 400ndash411
[437] J-P Leduc F Mujica R Murenzi MJT Smith Spatio-temporal wavelet transforms formotion tracking in IEEE ICASSP 1997 vol 4 (1997) pp 3013ndash3016
[438] J-P Leduc F Mujica R Murenzi MJT Smith Spatio-temporal continuous waveletsapplied to missile warhead detection and tracking in SPIE VCIP rsquo97 vol 3024 ed byJ Biemond EJ Delp (1997) pp 787ndash798
[439] B Leistedt JD McEwen Exact wavelets on the ball IEEE Trans Signal Proc 60 1564ndash1589 (2012)
[440] PG Lemarieacute Y Meyer Ondelettes et bases hilbertiennes Rev Math Iberoamer 2 1ndash18(1986)
[441] C Lemke A Schuck Jr J-P Antoine D Sima Metabolite-sensitive analysis of magneticresonance spectroscopic signals using the continuous wavelet transform Meas SciTechnol 22 (2011) Art 114013
[442] J-M Leacutevy-Leblond Galilei group and non-relativistic quantum mechanics J Math Phys4 776-788 (1963)
[443] J-M Leacutevy-Leblond Galilei group and Galilean invariance in Group Theory and ItsApplications vol II ed by EM Loebl (Academic New York 1971) pp 221ndash299
[444] J-M Leacutevy-Leblond On the conceptual nature of the physical constants Riv Nuovo Cim7 187ndash214 (1977)
[445] EH Lieb The classical limit of quantum spin systems Commun Math Phys 31 327ndash340(1973)
[446] G Lindblad B Nagel Continuous bases for unitary irreducible representations of SU(11)Ann Inst H Poincareacute 13 27ndash56 (1970)
[447] W Lisiecki Kaumlhler coherent states orbits for representations of semisimple Lie groupsAnn Inst H Poincareacute 53 857ndash890 (1990)
[448] A Lisowska Moment-based fast wedgelet transform J Math Imaging Vis 39 180ndash192(2011)
[449] H Liu L Peng Admissible wavelets associated with the Heisenberg group Pacific JMath 180 101ndash123 (1997)
[450] E Livine S Speziale Physical boundary state for the quantum tetrahedron Class QuantGrav 25 085003 (2008)
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[452] G Mack All unitary ray representations of the conformal group SU(22) with positiveenergy Commun Math Phys 55 1ndash28 (1977)
[453] GW Mackey Imprimitivity for representations of locally compact groups I Proc NatAcad Sci 35 537ndash545 (1949)
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[457] SG Mallat A theory for multiresolution signal decomposition The wavelet representa-tion IEEE Trans Pattern Anal Machine Intell 11 674ndash693 (1989)
[458] S Mallat W-L Hwang Singularity detection and processing with wavelets IEEE TransInform Theory 38 617ndash643 (1992)
[459] S Mallat Z Zhang Matching pursuits with time frequency dictionaries IEEE TransSignal Proc 41 3397ndash3415 (1993)
[460] S Mallat S Zhong Wavelet maxima representation in Wavelets and Applications (ProcMarseille 1989) ed by Y Meyer (Masson and Springer Paris and Berlin 1991) pp 207ndash284
[461] VI Manrsquoko G Marmo ECG Sudarshan F Zaccaria f -oscillators and non-linearcoherent states Phys Scr 55 528ndash541 (1997)
[462] D Marinucci D Pietrobon A Baldi P Baldi P Cabella G Kerkyacharian P Natoli DPicard N Vittorio Spherical needlets for CMB data analysis Mon Not R Astron Soc383 539ndash545 (2008)
[463] D Marion M Ikura A Bax Improved solvent suppression in one- and two-dimensionalNMR spectra by convolution of time-domain data J Magn Reson 84 425ndash430 (1989)
[464] Y Meyer Principe drsquoincertitude bases hilbertiennes et algegravebres drsquoopeacuterateurs SeacuteminaireBourbaki 662 (1985ndash1986)
[465] Y Meyer Principe drsquoincertitude bases hilbertiennes et algegravebres drsquoopeacuterateurs Asteacuterisque145ndash146 209ndash223 (1987)
[466] Y Meyer H Xu Wavelet analysis and chirps Appl Comput Harmon Anal 4 366ndash379(1997)
[467] L Michel Invariance in quantum mechanics and group extensions in Group TheoreticalConcepts and Methods in Elementary Particle Physics ed by F Guumlrsey (Gordon andBreach New York and London 1964) pp 135ndash200
[468] J Mickelsson J Niederle Contractions of representations of the de Sitter groupsCommun Math Phys 27 167ndash180 (1972)
[469] MM Miller Convergence of the Sudarshan expansion for the diagonal coherent-stateweight functional J Math Phys 9 1270ndash1274 (1968)
[470] V F Molchanov Harmonic analysis on homogeneous spaces in Representation Theoryand Noncommutative Harmonic Analysis II ed by AA Kirillov (Springer Berlin 1995)
[471] MI Monastyrsky AM Perelomov Coherent states and symmetric spaces II Ann InstH Poincareacute 23 23ndash48 (1975)
[472] B Moran S Howard D Cochran Positive-operator-valued measures A general settingfor frames in Excursions in Harmonic Analysis vol 1 2 ed by TD Andrews R BalanJJ Benedetto W Czaja KA Okoudjou (Birkhaumluser Boston 2013) pp 49ndash64
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[474] H Moscovici A Verona Coherent states and square integrable representations Ann InstH Poincareacute 29 139ndash156 (1978)
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[476] R Murenzi Wavelet transforms associated to the n-dimensional Euclidean group withdilations Signals in more than one dimension in Wavelets Time-Frequency Methodsand Phase Space (Proc Marseille 1987) ed by J-M Combes A Grossmann PTchamitchian 2nd edn (Springer Berlin 1990) pp 239ndash246
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[480] FJ Narcowich P Petrushev JD Ward Localized tight frames on spheres SIAM J MathAnal 38 574ndash594 (2006)
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Wavelets Multiresolut Inf Process 6 209ndash222 (2008)[531] D Rosca On a norm equivalence on L2(S2) Results Math 53 399ndash405 (2009)[532] D Rosca New uniform grids on the sphere Astron Astrophys 520 (2010) Art A63[533] D Rosca Uniform and refinable grids on elliptic domains and on some surfaces of
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[579] T Thiemann Gauge field theory coherent states (GCS) 1 General properties Class QuantGrav 18 2025ndash2064 (2001)
[580] T Thiemann O Winkler Gauge field theory coherent states (GCS) 2 Peakednessproperties Class Quant Grav 18 2561ndash2636 (2001)
[581] T Thiemann O Winkler Gauge field theory coherent states (GCS) 3 Ehrenfest theoremsClass Quant Grav 18 4629ndash4682 (2001)
[582] T Thiemann O Winkler Gauge field theory coherent states (GCS) 4 Infinite tensorproduct and thermodynamical limit Class Quant Grav 18 4997ndash5054 (2001)
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simulation of an impact test using wavelets analytical and finite element models Int JSolids Struct 38 5481ndash5508 (2001)
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Recogn Artif Intell 26 1255011 (2012)[601] I Weinreich A construction of C1-wavelets on the two-dimensional sphere Appl Comput
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[610] K Woacutedkiewicz On the quantum mechanics of squeezed states J Modern Optics 34 941ndash948(1987)
[611] JA Yeazell M Mallalieu CR Stroud Jr Observation of the collapse and revival of aRydberg electronic wave packet Phys Rev Lett 64 2007ndash2010 (1990)
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[613] HP Yuen Two-photon coherent states of the radiation field Phys Rev A 13 2226ndash2243(1976)
[614] J Zak Balian-Low theorem for Landau levels Phys Rev Lett 79 533ndash536 (1997)[615] J Zak Orthonormal sets of localized functions for a Landau level J Math Phys 39 4195ndash
4200 (1998) and references quoted there[616] AA Zakharova On the properties of generalized frames Math Notes 83 190ndash200 (2008)[617] W-M Zhang DH Feng R Gilmore Coherent states Theory and some applications Rev
Mod Phys 26 867ndash927 (1990)[618] I Zlatev W-M Zhang DH Feng Possibility that Schroumldingerrsquos conjecture for the
hydrogen atom coherent states is not attainable Phys Rev A 50 R1973ndashR1975 (1994)[619] WH Zurek Decoherence einselection and the quantum origins of the classical Rev Mod
Phys 75 715ndash775 (2003)[620] WH Zurek S Habib JP Paz Coherent states via decoherence Phys Rev Lett 70 1187ndash
1190 (1993)[621] K Zyczkowski Squeezed states in a quantum chaotic system J Phys A Math Theor 22
of SU(11) 81 296 297HilbertClowast-modules 164holomorphic 140nonholomorphic 151nonlinear 146of affine Galilei group 505of affine Poincareacute group 509of affine Weyl-Heisenberg group GaWH
497of compact semisimple Lie groups 174of Euclidean group E(n) 266of Galilei group G (11) 290of isochronous Galilei group 237of non-semisimple Lie groups 179of noncompact semisimple Lie groups 177of Poincareacute group Puarr
+(11) 283massless case 288
of Poincareacute group Puarr+(13) 279
of Schroumldinger group 508quasi-coherent states 186quaternionic 164
ST Ali et al Coherent States Wavelets and Their Generalizations Theoreticaland Mathematical Physics DOI 101007978-1-4614-8535-3copy Springer Science+Business Media New York 2014
573
574 Index
coherent states (CS) (cont)spin or SU(2) 175square integrable covariant 166 180 264vector (VCS) 73 108 112 170weighted 184 523
of affine Weyl-Heisenberg group GaWH497
of Poincareacute group Puarr+(11) 284
cohomology group 393 403coboundaries 403cochains 402cocycle 403
algebraic 387Cauchy 418Cauchy-Paul 354 419 425conical 418difference 417 462directional 416 440kinematical 499local 488metabolite-based 355 374minimal uncertainty 425multiselective 440on a graph 493on the sphere S
2 458on the sphere S
n 479on the torus T2 481steerable 439von Mises 440
wedgelet transform 455Wigner function 322Wigner-Ville transform 349Windowed Fourier or Gabor transform 349
ZZak transform 518
References
A Books and Theses
B Articles
Index
560 References
[334] RJ Glauber Coherent and incoherent states of radiation field Phys Rev 131 2766ndash2788(1963)
[335] J Glimm Locally compact transformation groups Trans Amer Math Soc 101 124ndash138(1961)
[336] R Godement Sur les relations drsquoorthogonaliteacute de V Bargmann C R Acad Sci Paris 255521ndash523 657ndash659 (1947)
[337] C Gonnet B Torreacutesani Local frequency analysis with two-dimensional wavelet trans-form Signal Proc 37 389ndash404 (1994)
[338] JA Gonzalez MA del Olmo Coherent states on the circle J Phys A Math Gen 318841ndash8857 (1998)
[339] XGonze B Amadon et al ABINIT First-principles approach to material and nanosystemproperties Computer Physics Comm 180 2582ndash2615 (2009)
[340] KM Gograverski E Hivon AJ Banday BD Wandelt FK Hansen M Reinecke MBartelmann HEALPix A framework for high-resolution discretization and fast analysisof data distributed on the sphere Astrophys J 622 759ndash771 (2005)
[341] P Goupillaud A Grossmann J Morlet Cycle-octave and related transforms in seismicsignal analysis Geoexploration 23 85ndash102 (1984)
[342] KH Groumlchenig A new approach to irregular sampling of band-limited functions in RecentAdvances in Fourier Analysis and Its applications ed by JS Byrnes JL Byrnes (KluwerDordrecht 1990) pp 251ndash260
[343] KH Groumlchenig Gabor analysis over LCA groups in Gabor Analysis and Algorithms ndashTheory and Applications ed by HG Feichtinger T Strohmer (Birkhaumluser Boston-Basel-Berlin 1998) pp 211ndash231
[344] HJ Groenewold On the principles of elementary quantum mechanics Physica 12 405ndash460 (1946)
[345] P Grohs Continuous shearlet tight frames J Fourier Anal Appl 17 506ndash518 (2011)[346] P Grohs G Kutyniok Parabolic molecules preprint TU Berlin (2012)[347] M Grosser A note on distribution spaces on manifolds Novi Sad J Math 38 121ndash128
(2008)[348] A Grossmann Parity operator and quantization of δ -functions Commun Math Phys 48
191ndash194 (1976)[349] A Grossmann J Morlet Decomposition of Hardy functions into square integrable
wavelets of constant shape SIAM J Math Anal 15 723ndash736 (1984)[350] A Grossmann J Morlet Decomposition of functions into wavelets of constant shape and
related transforms in Mathematics + Physics Lectures on recent results I ed by L Streit(World Scientific Singapore 1985) pp 135ndash166
[351] A Grossmann J Morlet T Paul Integral transforms associated to square integrablerepresentations I General results J Math Phys 26 2473ndash2479 (1985)
[352] A Grossmann J Morlet T Paul Integral transforms associated to square integrablerepresentations II Examples Ann Inst H Poincareacute 45 293ndash309 (1986)
[353] A Grossmann R Kronland-Martinet J Morlet Reading and understanding the contin-uous wavelet transform in Wavelets Time-Frequency Methods and Phase Space (ProcMarseille 1987) ed by J-M Combes A Grossmann P Tchamitchian 2nd edn (SpringerBerlin 1990) pp 2ndash20
[354] P Guillemain R Kronland-Martinet B Martens Estimation of spectral lines with helpof the wavelet transform Application in NMR spectroscopy in Wavelets and Applications(Proc Marseille 1989) ed by Y Meyer (Masson and Springer Paris and Berlin 1991) pp38ndash60
[355] H de Guise M Bertola Coherent state realizations of su(n+ 1) on the n-torus J MathPhys 43 3425ndash3444 (2002)
[356] K Guo D Labate Representation of Fourier Integral Operators using shearlets J FourierAnal Appl 14 327ndash371 (2008)
References 561
[357] K Guo G Kutyniok D Labate Sparse multidimensional representations usinganisotropic dilation and shear operators in Wavelets and Spines (Athens GA 2005)(Nashboro Press Nashville TN 2006) pp 189ndash201
[358] K Guo D Labate W-Q Lim G Weiss E Wilson Wavelets with composite dilationsand their MRA properties Appl Comput Harmon Anal 20 202ndash236 (2006)
[359] EA Gutkin Overcomplete subspace systems and operator symbols Funct Anal Appl 9260ndash261 (1975)
[360] G Gyoumlrgyi Integration of the dynamical symmetry groups for the 1r potential Acta PhysAcad Sci Hung 27 435ndash439 (1969)
[361] BC Hall The Segal-Bargmann ldquoCoherent Staterdquo transform for compact Lie groups JFunct Analysis 122 103ndash151 (1994)
[362] B Hall JJ Mitchell Coherent states on spheres J Math Phys 43 1211ndash1236 (2002)[363] DK Hammond P Vandergheynst R Gribonval Wavelets on graphs via spectral theory
Appl Comput Harmon Anal 30 129ndash150 (2011)[364] Y Hassouni EMF Curado MA Rego-Monteiro Construction of coherent states for
physical algebraic system Phys Rev A 71 022104 (2005)[365] J He H Liu Admissible wavelets associated with the affine automorphism group of the
Siegel upper half-plane J Math Anal Appl 208 58ndash70 (1997)[366] J He H Liu Admissible wavelets associated with the classical domain of type one
Approx Appl 14 (1998) 89ndash105[367] J He L Peng Wavelet transform on the symmetric matrix space preprint Beijing (1997)
(unpublished)[368] J He L Peng Admissible wavelets on the unit disk Complex Variables 35 109ndash119
(1998)[369] DM Healy Jr FE Schroeck Jr On informational completeness of covariant localization
observables and Wigner coefficients J Math Phys 36 453ndash507 (1995)[370] C Heil D Walnut Continuous and discrete wavelet transforms SIAM Review 31 628ndash
666 (1989)[371] K Hepp EH Lieb On the superradiant phase transition for molecules in a quantized
radiation field The Dicke maser model Ann Phys (NY) 76 360ndash404 (1973)[372] K Hepp EH Lieb Equilibrium statistical mechanics of matter interacting with the
quantized radiation field Phys Rev A 8 2517ndash2525 (1973)[373] JA Hogan JD Lakey Extensions of the Heisenberg group by dilations and frames Appl
Comput Harmon Anal 2 174ndash199 (1995)[374] AL Hohoueacuteto K Thirulogasanthar ST Ali J-P Antoine Coherent states lattices and
square integrability of representations J Phys A Math Gen36 11817ndash11835 (2003)[375] M Holschneider On the wavelet transformation of fractal objects J Stat Phys 50 963ndash
993 (1988)[376] M Holschneider Wavelet analysis on the circle J Math Phys 31 39ndash44 (1990)[377] M Holschneider Inverse Radon transforms through inverse wavelet transforms Inv Probl
7 853ndash861 (1991)[378] M Holschneider Localization properties of wavelet transforms J Math Phys 34 3227ndash
3244 (1993)[379] M Holschneider General inversion formulas for wavelet transforms J Math Phys 34
4190ndash4198 (1993)[380] M Holschneider Wavelet analysis over abelian groups Applied Comput Harmon Anal
2 52ndash60 (1995)[381] M Holschneider Continuous wavelet transforms on the sphere J Math Phys 37 4156ndash
4165 (1996)[382] M Holschneider I Iglewska-Nowak Poisson wavelets on the sphere J Fourier Anal
Appl 13 405ndash419 (2007)
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[383] M Holschneider R Kronland-Martinet J Morlet P Tchamitchian A real-time algorithmfor signal analysis with the help of wavelet transform in Wavelets Time-FrequencyMethods and Phase Space (Proc Marseille 1987) ed by J-M Combes A Grossmann PTchamitchian 2nd edn (Springer Berlin 1990) pp 286ndash297
[384] M Holschneider P Tchamitchian Pointwise analysis of Riemannrsquos ldquonondifferentiablerdquofunction Invent Math 105 157ndash175 (1991)
[385] GR Honarasa MK Tavassoly M Hatami R Roknizadeh Nonclassical properties ofcoherent states and excited coherent states for continuous spectra J Phys A Math Theor44 085303 (2011)
[386] M Hongoh Coherent states associated with the continuous spectrum of noncompactgroups J Math Phys 18 2081ndash2085 (1977)
[387] A Horzela FH Szafraniec A measure free approach to coherent states J Phys A MathGen 45 244018 (2012)
[388] W-L Hwang S Mallat Characterization of self-similar multifractals with waveletmaxima Appl Comput Harmon Anal 1 316ndash328 (1994)
[389] W-L Hwang C-S Lu P-C Chung Shape from texture Estimation of planar surfaceorientation through the ridge surfaces of continuous wavelet transform IEEE Trans ImageProc 7 773ndash780 (1998)
[390] I Iglewska-Nowak M Holschneider Frames of Poisson wavelets on the sphere ApplComput Harmon Anal 28 227ndash248 (2010)
[391] E Inoumlnuuml EP Wigner On the contraction of groups and their representations Proc NatAcad Sci U S 39 510ndash524 (1953)
[392] S Iqbal F Saif Generalized coherent states and their statistical characteristics in power-law potentials J Math Phys 52 082105 (2011)
[393] CJ Isham JR Klauder Coherent states for n-dimensional Euclidean groups E(n) andtheir application J MathPhys 32 607ndash620 (1991)
[394] L Jacques J-P Antoine Multiselective pyramidal decomposition of images Wavelets withadaptive angular selectivity Int J Wavelets Multires Inform Proc 5 785ndash814 (2007)
[395] L Jacques L Duval C Chaux G Peyreacute A panorama on multiscale geometric rep-resentations intertwining spatial directional and frequency selectivity Signal Proc 912699ndash2730 (2011)
[396] HR Jalali M K Tavassoly On the ladder operators and nonclassicality of generalizedcoherent state associated with a particle in an infinite square well preprint (2013)arXiv13034100v1 [quant-ph]
[397] C Johnston On the pseudo-dilation representations of Flornes Grossmann Holschneiderand Torreacutesani Appl Comput Harmon Anal 3 377ndash385 (1997)
[398] G Kaiser Phase-space approach to relativistic quantum mechanics I Coherent staterepresentation for massive scalar particles J MathPhys 18 952ndash959 (1977)
[399] G Kaiser Phase-space approach to relativistic quantum mechanics II Geometrical aspectsJ MathPhys 19 502ndash507 (1978)
[400] C Kalisa B Torreacutesani N-dimensional affine Weyl-Heisenberg wavelets Ann Inst HPoincareacute 59 201ndash236 (1993)
[401] W Kaminski J Lewandowski T Pawłowski Quantum constraints Dirac observables andevolution group averaging versus the Schroumldinger picture in LQC Class Quant Grav 26245016 (2009)
[402] MR Karim ST Ali A relativistic windowed Fourier transform preprint ConcordiaUniversity Montreacuteal (1997) (unpublished)
[403] M R Karim ST Ali M Bodruzzaman A relativistic windowed Fourier transform inProceedings of IEEE SoutheastCon 2000 Nashville Tennessee pp 253ndash260 (2000)
[404] T Kawazoe Wavelet transforms associated to a principal series representation of semisim-ple Lie groups I II Proc Japan Acad Ser A ndash Math Sci 71 154ndash157 158ndash160 (1995)
[405] T Kawazoe Wavelet transform associated to an induced representation of SL(n+ 2R)Ann Inst H Poincareacute 65 1ndash13 (1996)
References 563
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[407] P Kittipoom G Kutyniok W-Q Lim Construction of compactly supported shearletframes Constr Approx 35 21ndash72 (2012)
[408] J Kiukas P Lahti K Ylinenc Phase space quantization and the operator moment problemJ Math Phys 47 072104 (2006)
[409] JR Klauder Continuous-representation theory I Postulates of continuous-representationtheory J Math Phys 4 1055ndash1058 (1963)
[410] JR Klauder Continuous-representation theory II Generalized relation between quantumand classical dynamics J Math Phys 4 1058ndash1073 (1963)
[411] JR Klauder Path integrals for affine variables in Functional Integration Theory andApplications ed by J-P Antoine E Tirapegui (Plenum Press New York and London1980) pp 101ndash119
[412] JR Klauder Are coherent states the natural language of quantum mechanics inFundamental Aspects of Quantum Theory ed by V Gorini A Frigerio NATO ASI Seriesvol B 144 (Plenum Press New York 1986) pp 1ndash12
[413] JR Klauder Quantization without quantization Ann Phys (NY) 237 147ndash160 (1995)[414] JR Klauder Coherent states for the hydrogen atom J Phys A Math Gen 29 L293ndash
L296 (1996)[415] JR Klauder An affinity for affine quantum gravity Proc Steklov Inst Math 272 169ndash176
(2011) and references therein[416] JR Klauder RF Streater A wavelet transform for the Poincareacute group J Math Phys 32
1609ndash1611 (1991)[417] JR Klauder RF Streater Wavelets and the Poincareacute half-plane J Math Phys 35 471ndash
478 (1994)[418] JR Klauder K Penson J-M Sixdeniers Constructing coherent states through solutions
of Stieltjes and Hausdorff moment problems Phys Rev A 64 013817 (2001)[419] A Kleppner RL Lipsman The Plancherel formula for group extensions Ann Ec Norm
Sup 5 459ndash516 (1972)[420] AB Klimov C Muntildeoz Coherent isotropic and squeezed states in a N-qubit system Phys
Scr 87 038110 (2013)[421] A Klyashko Dynamical symmetry approach to entanglement in Physics and Theoretical
Computer Science From Numbers and Languages to (Quantum) Cryptography - NATOSecurity through Science Series D - Information and Communication Security vol 7 edby J-P Gazeau J Nesetril B Rovan (IOS Press Washington DC 2007) pp 25ndash54
[422] S Kobayashi Irreducibility of certain unitary representations J Math Soc Japan 20 638ndash642 (1968)
[423] K Kowalski J Rembielinski LC Papaloucas Coherent states for a quantum particle ona circle J Phys A Math Gen 29 4149ndash4167 (1996)
[424] K Kowalski J Rembielinski Quantum mechanics on a sphere and coherent states J PhysA Math Gen 33 6035ndash6048 (2000)
[425] K Kowalski J Rembielinski The Bargmann representation for the quantum mechanicson a sphere J Math Phys 42 4138ndash4147 (2001)
[426] C Kristjansen J Plefka GW Semenoff M Staudacher A new double-scaling limit ofN = 4 super-Yang-Mills theory and pp-wave strings Nuclear Phys B 643 3ndash30 (2002)
[427] M Kulesh M Holschneider MS Diallo Geophysical wavelet library Applications ofthe continuous wavelet transform to the polarization and dispersion analysis of signalsComput Geosci 34 1732ndash1752 (2008)
[428] R Kunze On the Frobenius reciprocity theorem for square integrable representationsPacific J Math 53 465ndash471 (1974)
[429] Y Kuroda A Wada T Yamazaki K Nagayama Postacquisition data processing methodfor suppression of the solvent signal I J Magn Reson 84 604ndash610 (1989)
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[431] G Kutyniok D Labate Resolution of the wavefront set using continuous shearlets TransAmer Math Soc 361 2719ndash2754 (2009)
[432] G Kutyniok W-Q Lim Compactly supported shearlets are optimally sparse J ApproxTheory 163 1564ndash1589 (2011)
[433] D Labate W-Q Lim G Kutyniok G Weiss Sparse multidimensional representationusing shearlets in Wavelets XI (San Diego CA 2005) ed by M Papadakis A Laine MUnser SPIE Proceedings vol 5914 (SPIE Bellingham WA 2005) pp 254ndash262
[434] P Lahti J-P Pellonpaumlauml Continuous variable tomographic measurements Phys Lett A373 3435ndash3438 (2009)
[435] Lambertrsquos projection see WikipediahttpenwikipediaorgwikiLambert_azimuthal_equal-area_projection
[436] J-P Leduc F Mujica R Murenzi MJT Smith Missile-tracking algorithm using target-adapted spatio-temporal wavelets in Automatic Object Recognition VII SPIE Proceedingsvol 5914 (SPIE Bellingham WA 1997) pp 400ndash411
[437] J-P Leduc F Mujica R Murenzi MJT Smith Spatio-temporal wavelet transforms formotion tracking in IEEE ICASSP 1997 vol 4 (1997) pp 3013ndash3016
[438] J-P Leduc F Mujica R Murenzi MJT Smith Spatio-temporal continuous waveletsapplied to missile warhead detection and tracking in SPIE VCIP rsquo97 vol 3024 ed byJ Biemond EJ Delp (1997) pp 787ndash798
[439] B Leistedt JD McEwen Exact wavelets on the ball IEEE Trans Signal Proc 60 1564ndash1589 (2012)
[440] PG Lemarieacute Y Meyer Ondelettes et bases hilbertiennes Rev Math Iberoamer 2 1ndash18(1986)
[441] C Lemke A Schuck Jr J-P Antoine D Sima Metabolite-sensitive analysis of magneticresonance spectroscopic signals using the continuous wavelet transform Meas SciTechnol 22 (2011) Art 114013
[442] J-M Leacutevy-Leblond Galilei group and non-relativistic quantum mechanics J Math Phys4 776-788 (1963)
[443] J-M Leacutevy-Leblond Galilei group and Galilean invariance in Group Theory and ItsApplications vol II ed by EM Loebl (Academic New York 1971) pp 221ndash299
[444] J-M Leacutevy-Leblond On the conceptual nature of the physical constants Riv Nuovo Cim7 187ndash214 (1977)
[445] EH Lieb The classical limit of quantum spin systems Commun Math Phys 31 327ndash340(1973)
[446] G Lindblad B Nagel Continuous bases for unitary irreducible representations of SU(11)Ann Inst H Poincareacute 13 27ndash56 (1970)
[447] W Lisiecki Kaumlhler coherent states orbits for representations of semisimple Lie groupsAnn Inst H Poincareacute 53 857ndash890 (1990)
[448] A Lisowska Moment-based fast wedgelet transform J Math Imaging Vis 39 180ndash192(2011)
[449] H Liu L Peng Admissible wavelets associated with the Heisenberg group Pacific JMath 180 101ndash123 (1997)
[450] E Livine S Speziale Physical boundary state for the quantum tetrahedron Class QuantGrav 25 085003 (2008)
[451] F Low Complete sets of wave packets in A Passion for Physics ndash Essay in Honor ofGeoffrey Chew ed by C DeTar (World Scientific Singapore 1985) pp 17ndash22
[452] G Mack All unitary ray representations of the conformal group SU(22) with positiveenergy Commun Math Phys 55 1ndash28 (1977)
[453] GW Mackey Imprimitivity for representations of locally compact groups I Proc NatAcad Sci 35 537ndash545 (1949)
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[456] SG Mallat Multifrequency channel decompositions of images and wavelet models IEEETrans Acoust Speech Signal Proc 37 2091ndash2110 (1989)
[457] SG Mallat A theory for multiresolution signal decomposition The wavelet representa-tion IEEE Trans Pattern Anal Machine Intell 11 674ndash693 (1989)
[458] S Mallat W-L Hwang Singularity detection and processing with wavelets IEEE TransInform Theory 38 617ndash643 (1992)
[459] S Mallat Z Zhang Matching pursuits with time frequency dictionaries IEEE TransSignal Proc 41 3397ndash3415 (1993)
[460] S Mallat S Zhong Wavelet maxima representation in Wavelets and Applications (ProcMarseille 1989) ed by Y Meyer (Masson and Springer Paris and Berlin 1991) pp 207ndash284
[461] VI Manrsquoko G Marmo ECG Sudarshan F Zaccaria f -oscillators and non-linearcoherent states Phys Scr 55 528ndash541 (1997)
[462] D Marinucci D Pietrobon A Baldi P Baldi P Cabella G Kerkyacharian P Natoli DPicard N Vittorio Spherical needlets for CMB data analysis Mon Not R Astron Soc383 539ndash545 (2008)
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[464] Y Meyer Principe drsquoincertitude bases hilbertiennes et algegravebres drsquoopeacuterateurs SeacuteminaireBourbaki 662 (1985ndash1986)
[465] Y Meyer Principe drsquoincertitude bases hilbertiennes et algegravebres drsquoopeacuterateurs Asteacuterisque145ndash146 209ndash223 (1987)
[466] Y Meyer H Xu Wavelet analysis and chirps Appl Comput Harmon Anal 4 366ndash379(1997)
[467] L Michel Invariance in quantum mechanics and group extensions in Group TheoreticalConcepts and Methods in Elementary Particle Physics ed by F Guumlrsey (Gordon andBreach New York and London 1964) pp 135ndash200
[468] J Mickelsson J Niederle Contractions of representations of the de Sitter groupsCommun Math Phys 27 167ndash180 (1972)
[469] MM Miller Convergence of the Sudarshan expansion for the diagonal coherent-stateweight functional J Math Phys 9 1270ndash1274 (1968)
[470] V F Molchanov Harmonic analysis on homogeneous spaces in Representation Theoryand Noncommutative Harmonic Analysis II ed by AA Kirillov (Springer Berlin 1995)
[471] MI Monastyrsky AM Perelomov Coherent states and symmetric spaces II Ann InstH Poincareacute 23 23ndash48 (1975)
[472] B Moran S Howard D Cochran Positive-operator-valued measures A general settingfor frames in Excursions in Harmonic Analysis vol 1 2 ed by TD Andrews R BalanJJ Benedetto W Czaja KA Okoudjou (Birkhaumluser Boston 2013) pp 49ndash64
[473] H Moscovici Coherent states representations of nilpotent Lie groups Commun MathPhys 54 63ndash68 (1977)
[474] H Moscovici A Verona Coherent states and square integrable representations Ann InstH Poincareacute 29 139ndash156 (1978)
[475] F Mujica R Murenzi MJT Smith J-P Leduc Robust tracking in compressed imagesequences J Electr Imaging 7 746ndash754 (1998)
[476] R Murenzi Wavelet transforms associated to the n-dimensional Euclidean group withdilations Signals in more than one dimension in Wavelets Time-Frequency Methodsand Phase Space (Proc Marseille 1987) ed by J-M Combes A Grossmann PTchamitchian 2nd edn (Springer Berlin 1990) pp 239ndash246
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[479] MA Naımark Dokl Akad Nauk SSSR 41 359ndash361 (1943) see also B Sz-NagyExtensions of linear transformations in Hilbert space which extend beyond this spaceAppendix to F Riesz B Sz-Nagy Functional Analysis (Frederick Ungar New York 1960)
[480] FJ Narcowich P Petrushev JD Ward Localized tight frames on spheres SIAM J MathAnal 38 574ndash594 (2006)
[481] M Nauenberg Quantum wave packets on Kepler elliptic orbits Phys Rev A 40 1133ndash1136 (1989)
[482] M Nauenberg C Stroud J Yeazell The classical limit of an atom Scient Amer 27024ndash29 (1994)
[483] H Neumann Transformation properties of observables Helv Phys Acta 45 811ndash819(1972)
[484] U Niederer The maximal kinematical invariance group of the free Schroumldinger equationHelv Phys Acta 45 802ndash881 (1972)
[485] MM Nieto LM Simmons Jr Coherent states for general potentials I Formalism IIConfining one-dimensional examples III Nonconfining one-dimensional examples PhysRev D 20 1321ndash1331 1332ndash1341 1342ndash1350 (1979)
[486] MM Nieto LM Simmons Jr Coherent states for general potentials Phys Rev Lett 41207ndash210 (1987)
[487] A Odzijewicz On reproducing kernels and quantization of states Commun Math Phys114 577ndash597 (1988)
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[490] A Odzijewicz M Horowski A Tereszkiewicz Integrable multi-boson systems andorthogonal polynomials J Phys A Math Gen 34 4353ndash4376 (2001)
[491] G Oacutelafsson B Oslashrsted The holomorphic discrete series for affine symmetric spaces JFunct Anal 81 126ndash159 (1988)
[492] G Oacutelafsson H Schlichtkrull Representation theory Radon transform and the heatequation on a Riemannian symmetric space Contemp Math 449 315ndash344 (2008)
[493] E Onofri A note on coherent state representations of Lie groups J Math Phys 16 1087ndash1089 (1975)
[494] E Onofri Dynamical quantization of the Kepler manifold J Math Phys 17 401ndash408(1976)
[495] D Oriti R Pereira L Sindoni Coherent states in quantum gravity A construction basedon the flux representation of loop quantum gravity J Phys A Math Theor 45 244004(2012)
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[497] Z Pasternak-Winiarski On the dependence of the reproducing kernel on the weight ofintegration J Funct Anal 94 110ndash134 (1990)
[498] Z Pasternak-Winiarski On reproducing kernels for holomorphic vector bundles inQuantization and Infinite Dimensional Systems (Proc Białowieza Poland 1993) ed by J-P Antoine ST Ali W Lisiecki IM Mladenov A Odzijewicz (Plenum Press New Yorkand London 1994) pp 109ndash112
[499] T Paul Affine coherent states and the radial Schroumldinger equation I preprint CPT-84P1710 (1984) (unpublished)
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[501] AM Perelomov On the completeness of a system of coherent states Theor Math Phys6 156ndash164 (1971)
[502] AM Perelomov Coherent states for arbitrary Lie group Commun Math Phys 26 222ndash236 (1972)
[503] AM Perelomov Coherent states and symmetric spaces Commun Math Phys 44 197ndash210 (1975)
[504] M Perroud Projective representations of the Schroumldinger group Helv Phys Acta 50 233ndash252 (1977)
[505] J Phillips A note on square-integrable representations J Funct Anal 20 83ndash92 (1975)[506] D Pietrobon P Baldi D Marinucci Integrated Sachs-Wolfe effect from the cross
correlation of WMAP3 year and the NRAO VLA sky survey data New results andconstraints on dark energy Phys Rev D 74 043524 (2006)
[507] WWF Pijnappel A van den Boogaart R de Beer D van Ormondt SVD-basedquantification of magnetic resonance signals J Magn Reson 97 122ndash134 (1992)
[508] V Pop D Rosca Generalized piecewise constant orthogonal wavelet bases on 2D-domains Appl Anal 90 715ndash723 (2011)
[509] G Poumlschl E Teller Bemerkungen zur Quantenmechanik des anharmonischen OszillatorsZ Physik 83 143ndash151 (1933)
[510] D Potts G Steidl M Tasche Kernels of spherical harmonics and spherical frames inAdvanced Topics in Multivariate Approximation ed by F Fontanella K Jetter PJ Laurent(World Scientific Singapore 1996) pp 287ndash301
[511] E Prugovecki Consistent formulation of relativistic dynamics for massive spin-zeroparticles in external fields Phys Rev D 18 3655ndash3673 (1978) (Appendix C)
[512] E Prugovecki Relativistic quantum kinematics on stochastic phase space for massiveparticles J MathPhys 19 2261ndash2270 (1978)
[513] C Quesne Coherent states of the real symplectic group in a complex analytic parametriza-tion I II J Math Phys 27 428ndash441 869ndash878 (1986)
[514] C Quesne Generalized vector coherent states of sp(2NR) vector operators and ofsp(2NR) sup u(N) reduced Wigner coefficients J Phys A Math Gen 24 2697ndash2714(1991)
[515] JM Radcliffe Some properties of spin coherent states J Phys A Math Gen 4 313ndash323(1971)
[516] A Rahimi A Najati YN Dehghan Continuous frames in Hilbert spaces Methods FunctAnal Topol 12 170ndash182 (2006)
[517] H Rauhut M Roumlsler Radial multiresolution in dimension three Constr Approx 22 193ndash218 (2005)
[518] JH Rawnsley Coherent states and Kaumlhler manifolds Quart J Math Oxford 28(2) 403ndash415 (1977)
[519] J Renaud The contraction of the SU(11) discrete series of representations by means ofcoherent states J Math Phys 37 3168ndash3179 (1996)
[520] A Reacutenyi Representations for real numbers and their ergodic properties Acta Math AcadSci Hungary 8(3ndash4) 477ndash493 (1957)
[521] D Robert La coheacuterence dans tous ses eacutetats SMF Gazette 132 (2012)[522] JE Roberts The Dirac bra and ket formalism J Math Phys 7 1097ndash1104 (1966)[523] JE Roberts Rigged Hilbert spaces in quantum mechanics Commun Math Phys 3 98ndash
119 (1966)[524] S Roques F Bourzeix K Bouyoucef Soft-thresholding technique and restoration of
3C273 jet Astrophys Space Sci Nr 239 297ndash304 (1996)[525] D Rosca Haar wavelets on spherical triangulations in Advances in Multiresolution for
Geometric Modelling ed by NA Dogson MS Floater MA Sabin (Springer Berlin2005) pp 407ndash419
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[527] D Rosca Wavelets defined on closed surfaces J Comput Anal Appl 8 121ndash132 (2006)[528] D Rosca Weighted Haar wavelets on the sphere Int J Wavelets Multiresol Inf Proc 5
501ndash511 (2007)[529] D Rosca Wavelet bases on the sphere obtained by radial projection J Fourier Anal Appl
13 421ndash434 (2007)[530] D Rosca Piecewise constant wavelets on triangulations obtained by 1ndash3 splitting Int J
Wavelets Multiresolut Inf Process 6 209ndash222 (2008)[531] D Rosca On a norm equivalence on L2(S2) Results Math 53 399ndash405 (2009)[532] D Rosca New uniform grids on the sphere Astron Astrophys 520 (2010) Art A63[533] D Rosca Uniform and refinable grids on elliptic domains and on some surfaces of
revolution Appl Math Comput 217 7812ndash7817 (2011)[534] D Rosca Wavelet analysis on some surfaces of revolution via area preserving projection
Appl Comput Harmon Anal 30 262ndash272 (2011)[535] D Rosca J-P Antoine Locally supported orthogonal wavelet bases on the sphere via
stereographic projection Math Probl Eng 2009 124904 (2009)[536] D Rosca J-P Antoine Constructing wavelet frames and orthogonal wavelet bases on the
sphere in Recent Advances in Signal Processing ed by S Miron (IN-TECH ViennaAustria and Rijeka Croatia 2010) pp 59ndash76
[537] D Rosca G Plonka Uniform spherical grids via area preserving projection from the cubeto the sphere J Comput Appl Math 236 1033ndash1041 (2011)
[538] D Rosca G Plonka An area preserving projection from the regular octahedron to thesphere Results Math 63 429ndash444 (2012)
[539] H Rossi M Vergne Analytic continuation of the holomorphic discrete series for a semi-simple Lie group Acta Math 136 1ndash59 (1976)
[540] DJ Rotenberg Application of Sturmian functions to the Schroedinger three-body prob-lem Elastic e+ndashH scattering Ann Phys (NY) 19 262ndash278 (1962)
[541] C Rovelli Zakopane lectures on loop gravity in Proceedings of 3rd Quantum Gravityand Quantum Geometry School 28 Febndash13 March 2011 (Zakopane Poland 2011)arXiv11023660v5
[542] C Rovelli S Speziale A semiclassical tetrahedron Class Quant Grav 23 5861ndash5870(2006)
[543] DJ Rowe Coherent state theory of the noncompact symplectic group J Math Phys 252662ndash2271 (1984)
[544] DJ Rowe Microscopic theory of the nuclear collective model Rep Prog Phys 48 1419ndash1480 (1985)
[545] DJ Rowe Vector coherent state representations and their inner products J Phys A MathGen 45 244003 (2012) (This paper belongs to the special issue [38])
[546] DJ Rowe J Repka Vector-coherent-state theory as a theory of induced representationsJ Math Phys 32 2614ndash2634 (1991)
[547] DJ Rowe G Rosensteel R Gilmore Vector coherent state representation theory J MathPhys 26 2787ndash2791 (1985)
[548] A Royer Phase states and phase operators for the quantum harmonic oscillator Phys RevA 53 70ndash108 (1996)
[549] J Saletan Contraction of Lie groups J Math Phys 2 1ndash21 (1961)[550] G Saracco A Grossmann P Tchamitchian Use of wavelet transforms in the study of
propagation of transient acoustic signals across a plane interface between two homoge-neous media in Wavelets Time-Frequency Methods and Phase Space (Proc Marseille1987) ed by J-M Combes A Grossmann P Tchamitchian 2nd edn (Springer Berlin1990) pp 139ndash146
[551] P Schroumlder W Sweldens Spherical wavelets Efficiently representing functions on thesphere in Computer Graphics Proceedings (SIGGRAPH95) (ACM Siggraph Los Angeles1995) pp 161ndash175
References 569
[552] E Schroumldinger Der stetige Uumlbergang von der Mikro- zur Makromechanik Naturwiss 14664ndash666 (1926)
[553] S Scodeller Oslash Rudjord FK Hansen D Marinucci D Geller A Mayeli IntroducingMexican needlets for CMB analysis Issues for practical applications and comparison withstandard needlets Astrophys J 733 (2011) Art 121
[554] H Scutaru Coherent states and induced representations Lett Math Phys 2 101ndash107(1977)
[555] B Simon Distributions and their Hermite expansions J Math Phys 12 140ndash148 (1971)[556] B Simon The classical moment problem as a self-adjoint finite difference operator Adv
Math 137 82ndash203 (1998)[557] R Simon ECG Sudarshan N Mukunda Gaussian pure states in quantum mechanics
and the symplectic group Phys Rev A37 3028ndash3038 (1988)[558] S Sivakumar Studies on nonlinear coherent states J Opt B Quant Semiclass Opt 2
R61ndashR75 (2000)[559] E Slezak A Bijaoui G Mars Identification of structures from galaxy counts Use of the
wavelet transform Astron Astroph 227 301ndash316 (1990)[560] A Solomon A characteristic functional for deformed photon phenomenology Phys Lett
A 196 29ndash34 (1994)[561] SB Sontz Paragrassmann algebras as quantum spaces Part I Reproducing kernels in
Geometric Methods in Physics XXXI Workshop 2012 (Trends in Mathematics ed byP Kielanowski et al Birkhaumluser Verlag Basel 2013) pp 47ndash63
[562] SB Sontz Paragrassmann algebras as quantum spaces Part II Toeplitz operators J OperTh (2013 to appear) arXiv12055493
[563] SB Sontz A reproducing kernel and Toeplitz operators in the quantum plane Preprint(2013) arXiv13056986 [math-ph]
[564] SB Sontz Toeplitz quantization of an algebra with conjugation Preprint (2013)arXiv13085454 [math-ph]
[565] M Spera On a generalized Uncertainty Principle coherent states and the moment mapJ Geom Phys 12 165ndash182 (1993)
[566] J-L Starck EJ Candegraves DL Donoho The curvelet transform for image denoising IEEETrans Image Proc 11 670ndash684 (2002)
[567] J-L Starck DL Donoho E J Candegraves Astronomical image representation by the curvelettransform Astron Astroph 398 785ndash800 (2003)
[568] J-L Starck Y Moudden P Abrial M Nguyen Wavelets ridgelets and curvelets on thesphere Astron Astroph 446 1191ndash1204 (2006)
[569] MB Stenzel The Segal-Bargmann transform on a symmetric space of compact type JFunct Analysis 165 44ndash58 (1994)
[570] ECG Sudarshan Equivalence of semiclassical and quantum mechanical descriptions ofstatistical light beams Phys Rev Lett 10 277ndash279 (1963)
[571] A Suvichakorn H Ratiney A Bucur S Cavassila J-P Antoine Toward a quantitativeanalysis of in vivo magnetic resonance proton spectroscopic signals using the continuousMorlet wavelet transform Meas Sci Technol 20 (2009) Art 104029
[572] W Sweldens The lifting scheme A custom-design construction of biorthogonal waveletsApplied Comput Harmon Anal 3 1186ndash1200 (1996)
[573] W Sweldens The lifting scheme A construction of second generation wavelets SIAM JMath Anal 29 511ndash546 (1998)
[574] FH Szafraniec The reproducing kernel Hilbert space and its multiplication operatorsin Complex Analysis and Related Topics ed by E Ramirez de Arellano et al OperatorTheory Advances and Applications vol 114 (Birkhaumluser Basel 2000) pp 254ndash263
[575] FH Szafraniec Multipliers in the reproducing kernel Hilbert space subnormality andnoncommutative complex analysis in Reproducing Kernel Spaces and Applications edby D Alpay Operator Theory Advances and Applications vol 143 (Birkhaumluser Basel2003) pp 313ndash331
570 References
[576] R Takahashi Sur les repreacutesentations unitaires des groupes de Lorentz geacuteneacuteraliseacutes BullSoc Math France 91 289ndash433 (1963)
[577] MC Teich BEA Saleh Squeezed states of light Quantum Opt 1 152ndash191 (1989)[578] R Terrier L Demanet IA Grenier J-P Antoine Wavelet analysis of EGRET data in
Proceedings of the 27th International Cosmic Ray Conference (ICRC 2001) (CopernicusGesellschaft DE 2001) pp 2923ndash2926
[579] T Thiemann Gauge field theory coherent states (GCS) 1 General properties Class QuantGrav 18 2025ndash2064 (2001)
[580] T Thiemann O Winkler Gauge field theory coherent states (GCS) 2 Peakednessproperties Class Quant Grav 18 2561ndash2636 (2001)
[581] T Thiemann O Winkler Gauge field theory coherent states (GCS) 3 Ehrenfest theoremsClass Quant Grav 18 4629ndash4682 (2001)
[582] T Thiemann O Winkler Gauge field theory coherent states (GCS) 4 Infinite tensorproduct and thermodynamical limit Class Quant Grav 18 4997ndash5054 (2001)
[583] K Thirulagasanthar ST Ali Regular subspaces of a quaternionic Hilbert space fromquaternionic Hermite polynomials and associated coherent states J Math Phys 54013506 (2013)
[584] K Thirulogasanthar G Honnouvo A Krzyzak Coherent states and Hermite polynomialson quaternionic Hilbert spaces J Phys A Math Theor 43 385205 (2010)
[585] Tokamak see Wikipedia httpenwikipediaorgwikiTokamak[586] B Torreacutesani Wavelets associated with representations of the affine Weyl-Heisenberg
group J Math Phys 32 1273ndash1279 (1991)[587] B Torreacutesani Time-frequency representation Wavelet packets and optimal decomposition
Ann Inst H Poincareacute 56 215ndash234 (1992)[588] B Torreacutesani Position-frequency analysis for signals defined on spheres Signal Proc 43
341ndash346 (2005)[589] DA Trifonov Generalized intelligent states and squeezing J Math Phys 35 2297ndash2308
(1994)[590] AS Trushechkin IV Volovich Localization properties of squeezed quantum states in
nanoscale space domains preprint (2013) arXiv13046277v1 [quant-ph][591] M Unser N Chenouard A unifying parametric framework for 2D steerable wavelet
transforms SIAM J Imaging Sci 6 102ndash135 (2013)[592] P Vandergheynst J-F Gobbers Directional dyadic wavelet transforms Design and
algorithms IEEE Trans Image Proc 11 363ndash372 (2002)[593] P Vandergheynst J-P Antoine E Van Vyve A Goldberg I Doghri Modelling and
simulation of an impact test using wavelets analytical and finite element models Int JSolids Struct 38 5481ndash5508 (2001)
[594] L Vanhamme RD Fierro S Van Huffel R de Beer Fast removal of residual water inproton spectra J Magn Reson 132 197ndash203 (1998)
[595] J Ville Theacuteorie et applications de la notion de signal analytique Cacircbles et Trans 2 61ndash74(1948)
[596] J Voisin On some unitary representations of the Galilei group I Irreducible representa-tions J Math Phys 6 1519ndash1529 (1965)
[597] A Vourdas Analytic representations in quantum mechanics J Phys A Math Gen 39R65ndashR141 (2006)
[598] DF Walls Squeezed states of light Nature 306 141ndash146 (1983)[599] YK Wang FT Hioe Phase transition in the Dicke maser model Phys Rev A 7 831ndash836
(1973)[600] PSP Wang J Yang A review of wavelet-based edge detection methods Int J Patt
Recogn Artif Intell 26 1255011 (2012)[601] I Weinreich A construction of C1-wavelets on the two-dimensional sphere Appl Comput
Harmon Anal 10 1ndash26 (2001)[602] H Weyl Quantenmechanik und Gruppentheorie Z Phys 46 1ndash46 (1927)
References 571
[603] Y Wiaux L Jacques P Vandergheynst Correspondence principle between spherical andEuclidean wavelets Astrophys J 632 15ndash28 (2005)
[604] Y Wiaux L Jacques P Vielva P Vandergheynst Fast directional correlation on the spherewith steerable filters Astrophys J 652 820ndash832 (2006)
[605] Y Wiaux JD McEwen P Vandergheynst O Blanc Exact reconstruction with directionalwavelets on the sphere Mon Not R Astron Soc 388 770ndash788 (2008)
[606] WM Wieland Complex Ashtekar variables and reality conditions for Holstrsquos action AnnHenri Poincareacute 13 425ndash448 (2012)
[607] EP Wigner On the quantum correction for thermodynamic equilibrium Phys Rev 40749ndash759 (1932)
[608] RM Willette RD Nowak Platelets A multiscale approach for recovering edges andsurfaces in photon-limited medical imaging IEEE Trans Med Imaging 22 332ndash350(2003)
[609] W Wisnoe P Gajan A Strzelecki C Lempereur J-M Matheacute The use of the two-dimensional wavelet transform in flow visualization processing in Progress in WaveletAnalysis and Applications (Proc Toulouse 1992) ed by Y Meyer S Roques (EdFrontiegraveres Gif-sur-Yvette 1993) pp 455ndash458
[610] K Woacutedkiewicz On the quantum mechanics of squeezed states J Modern Optics 34 941ndash948(1987)
[611] JA Yeazell M Mallalieu CR Stroud Jr Observation of the collapse and revival of aRydberg electronic wave packet Phys Rev Lett 64 2007ndash2010 (1990)
[612] JA Yeazell CR Stroud Jr Observation of fractional revivals in the evolution of aRydberg atomic wave packet Phys Rev A 43 5153ndash5156 (1991)
[613] HP Yuen Two-photon coherent states of the radiation field Phys Rev A 13 2226ndash2243(1976)
[614] J Zak Balian-Low theorem for Landau levels Phys Rev Lett 79 533ndash536 (1997)[615] J Zak Orthonormal sets of localized functions for a Landau level J Math Phys 39 4195ndash
4200 (1998) and references quoted there[616] AA Zakharova On the properties of generalized frames Math Notes 83 190ndash200 (2008)[617] W-M Zhang DH Feng R Gilmore Coherent states Theory and some applications Rev
Mod Phys 26 867ndash927 (1990)[618] I Zlatev W-M Zhang DH Feng Possibility that Schroumldingerrsquos conjecture for the
hydrogen atom coherent states is not attainable Phys Rev A 50 R1973ndashR1975 (1994)[619] WH Zurek Decoherence einselection and the quantum origins of the classical Rev Mod
Phys 75 715ndash775 (2003)[620] WH Zurek S Habib JP Paz Coherent states via decoherence Phys Rev Lett 70 1187ndash
1190 (1993)[621] K Zyczkowski Squeezed states in a quantum chaotic system J Phys A Math Theor 22
of SU(11) 81 296 297HilbertClowast-modules 164holomorphic 140nonholomorphic 151nonlinear 146of affine Galilei group 505of affine Poincareacute group 509of affine Weyl-Heisenberg group GaWH
497of compact semisimple Lie groups 174of Euclidean group E(n) 266of Galilei group G (11) 290of isochronous Galilei group 237of non-semisimple Lie groups 179of noncompact semisimple Lie groups 177of Poincareacute group Puarr
+(11) 283massless case 288
of Poincareacute group Puarr+(13) 279
of Schroumldinger group 508quasi-coherent states 186quaternionic 164
ST Ali et al Coherent States Wavelets and Their Generalizations Theoreticaland Mathematical Physics DOI 101007978-1-4614-8535-3copy Springer Science+Business Media New York 2014
573
574 Index
coherent states (CS) (cont)spin or SU(2) 175square integrable covariant 166 180 264vector (VCS) 73 108 112 170weighted 184 523
of affine Weyl-Heisenberg group GaWH497
of Poincareacute group Puarr+(11) 284
cohomology group 393 403coboundaries 403cochains 402cocycle 403
algebraic 387Cauchy 418Cauchy-Paul 354 419 425conical 418difference 417 462directional 416 440kinematical 499local 488metabolite-based 355 374minimal uncertainty 425multiselective 440on a graph 493on the sphere S
2 458on the sphere S
n 479on the torus T2 481steerable 439von Mises 440
wedgelet transform 455Wigner function 322Wigner-Ville transform 349Windowed Fourier or Gabor transform 349
ZZak transform 518
References
A Books and Theses
B Articles
Index
References 561
[357] K Guo G Kutyniok D Labate Sparse multidimensional representations usinganisotropic dilation and shear operators in Wavelets and Spines (Athens GA 2005)(Nashboro Press Nashville TN 2006) pp 189ndash201
[358] K Guo D Labate W-Q Lim G Weiss E Wilson Wavelets with composite dilationsand their MRA properties Appl Comput Harmon Anal 20 202ndash236 (2006)
[359] EA Gutkin Overcomplete subspace systems and operator symbols Funct Anal Appl 9260ndash261 (1975)
[360] G Gyoumlrgyi Integration of the dynamical symmetry groups for the 1r potential Acta PhysAcad Sci Hung 27 435ndash439 (1969)
[361] BC Hall The Segal-Bargmann ldquoCoherent Staterdquo transform for compact Lie groups JFunct Analysis 122 103ndash151 (1994)
[362] B Hall JJ Mitchell Coherent states on spheres J Math Phys 43 1211ndash1236 (2002)[363] DK Hammond P Vandergheynst R Gribonval Wavelets on graphs via spectral theory
Appl Comput Harmon Anal 30 129ndash150 (2011)[364] Y Hassouni EMF Curado MA Rego-Monteiro Construction of coherent states for
physical algebraic system Phys Rev A 71 022104 (2005)[365] J He H Liu Admissible wavelets associated with the affine automorphism group of the
Siegel upper half-plane J Math Anal Appl 208 58ndash70 (1997)[366] J He H Liu Admissible wavelets associated with the classical domain of type one
Approx Appl 14 (1998) 89ndash105[367] J He L Peng Wavelet transform on the symmetric matrix space preprint Beijing (1997)
(unpublished)[368] J He L Peng Admissible wavelets on the unit disk Complex Variables 35 109ndash119
(1998)[369] DM Healy Jr FE Schroeck Jr On informational completeness of covariant localization
observables and Wigner coefficients J Math Phys 36 453ndash507 (1995)[370] C Heil D Walnut Continuous and discrete wavelet transforms SIAM Review 31 628ndash
666 (1989)[371] K Hepp EH Lieb On the superradiant phase transition for molecules in a quantized
radiation field The Dicke maser model Ann Phys (NY) 76 360ndash404 (1973)[372] K Hepp EH Lieb Equilibrium statistical mechanics of matter interacting with the
quantized radiation field Phys Rev A 8 2517ndash2525 (1973)[373] JA Hogan JD Lakey Extensions of the Heisenberg group by dilations and frames Appl
Comput Harmon Anal 2 174ndash199 (1995)[374] AL Hohoueacuteto K Thirulogasanthar ST Ali J-P Antoine Coherent states lattices and
square integrability of representations J Phys A Math Gen36 11817ndash11835 (2003)[375] M Holschneider On the wavelet transformation of fractal objects J Stat Phys 50 963ndash
993 (1988)[376] M Holschneider Wavelet analysis on the circle J Math Phys 31 39ndash44 (1990)[377] M Holschneider Inverse Radon transforms through inverse wavelet transforms Inv Probl
7 853ndash861 (1991)[378] M Holschneider Localization properties of wavelet transforms J Math Phys 34 3227ndash
3244 (1993)[379] M Holschneider General inversion formulas for wavelet transforms J Math Phys 34
4190ndash4198 (1993)[380] M Holschneider Wavelet analysis over abelian groups Applied Comput Harmon Anal
2 52ndash60 (1995)[381] M Holschneider Continuous wavelet transforms on the sphere J Math Phys 37 4156ndash
4165 (1996)[382] M Holschneider I Iglewska-Nowak Poisson wavelets on the sphere J Fourier Anal
Appl 13 405ndash419 (2007)
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[383] M Holschneider R Kronland-Martinet J Morlet P Tchamitchian A real-time algorithmfor signal analysis with the help of wavelet transform in Wavelets Time-FrequencyMethods and Phase Space (Proc Marseille 1987) ed by J-M Combes A Grossmann PTchamitchian 2nd edn (Springer Berlin 1990) pp 286ndash297
[384] M Holschneider P Tchamitchian Pointwise analysis of Riemannrsquos ldquonondifferentiablerdquofunction Invent Math 105 157ndash175 (1991)
[385] GR Honarasa MK Tavassoly M Hatami R Roknizadeh Nonclassical properties ofcoherent states and excited coherent states for continuous spectra J Phys A Math Theor44 085303 (2011)
[386] M Hongoh Coherent states associated with the continuous spectrum of noncompactgroups J Math Phys 18 2081ndash2085 (1977)
[387] A Horzela FH Szafraniec A measure free approach to coherent states J Phys A MathGen 45 244018 (2012)
[388] W-L Hwang S Mallat Characterization of self-similar multifractals with waveletmaxima Appl Comput Harmon Anal 1 316ndash328 (1994)
[389] W-L Hwang C-S Lu P-C Chung Shape from texture Estimation of planar surfaceorientation through the ridge surfaces of continuous wavelet transform IEEE Trans ImageProc 7 773ndash780 (1998)
[390] I Iglewska-Nowak M Holschneider Frames of Poisson wavelets on the sphere ApplComput Harmon Anal 28 227ndash248 (2010)
[391] E Inoumlnuuml EP Wigner On the contraction of groups and their representations Proc NatAcad Sci U S 39 510ndash524 (1953)
[392] S Iqbal F Saif Generalized coherent states and their statistical characteristics in power-law potentials J Math Phys 52 082105 (2011)
[393] CJ Isham JR Klauder Coherent states for n-dimensional Euclidean groups E(n) andtheir application J MathPhys 32 607ndash620 (1991)
[394] L Jacques J-P Antoine Multiselective pyramidal decomposition of images Wavelets withadaptive angular selectivity Int J Wavelets Multires Inform Proc 5 785ndash814 (2007)
[395] L Jacques L Duval C Chaux G Peyreacute A panorama on multiscale geometric rep-resentations intertwining spatial directional and frequency selectivity Signal Proc 912699ndash2730 (2011)
[396] HR Jalali M K Tavassoly On the ladder operators and nonclassicality of generalizedcoherent state associated with a particle in an infinite square well preprint (2013)arXiv13034100v1 [quant-ph]
[397] C Johnston On the pseudo-dilation representations of Flornes Grossmann Holschneiderand Torreacutesani Appl Comput Harmon Anal 3 377ndash385 (1997)
[398] G Kaiser Phase-space approach to relativistic quantum mechanics I Coherent staterepresentation for massive scalar particles J MathPhys 18 952ndash959 (1977)
[399] G Kaiser Phase-space approach to relativistic quantum mechanics II Geometrical aspectsJ MathPhys 19 502ndash507 (1978)
[400] C Kalisa B Torreacutesani N-dimensional affine Weyl-Heisenberg wavelets Ann Inst HPoincareacute 59 201ndash236 (1993)
[401] W Kaminski J Lewandowski T Pawłowski Quantum constraints Dirac observables andevolution group averaging versus the Schroumldinger picture in LQC Class Quant Grav 26245016 (2009)
[402] MR Karim ST Ali A relativistic windowed Fourier transform preprint ConcordiaUniversity Montreacuteal (1997) (unpublished)
[403] M R Karim ST Ali M Bodruzzaman A relativistic windowed Fourier transform inProceedings of IEEE SoutheastCon 2000 Nashville Tennessee pp 253ndash260 (2000)
[404] T Kawazoe Wavelet transforms associated to a principal series representation of semisim-ple Lie groups I II Proc Japan Acad Ser A ndash Math Sci 71 154ndash157 158ndash160 (1995)
[405] T Kawazoe Wavelet transform associated to an induced representation of SL(n+ 2R)Ann Inst H Poincareacute 65 1ndash13 (1996)
References 563
[406] P Kittipoom G Kutyniok W-Q Lim Irregular shearlet frames Geometry and approxi-mation properties J Fourier Anal Appl 17 604ndash639 (2011)
[407] P Kittipoom G Kutyniok W-Q Lim Construction of compactly supported shearletframes Constr Approx 35 21ndash72 (2012)
[408] J Kiukas P Lahti K Ylinenc Phase space quantization and the operator moment problemJ Math Phys 47 072104 (2006)
[409] JR Klauder Continuous-representation theory I Postulates of continuous-representationtheory J Math Phys 4 1055ndash1058 (1963)
[410] JR Klauder Continuous-representation theory II Generalized relation between quantumand classical dynamics J Math Phys 4 1058ndash1073 (1963)
[411] JR Klauder Path integrals for affine variables in Functional Integration Theory andApplications ed by J-P Antoine E Tirapegui (Plenum Press New York and London1980) pp 101ndash119
[412] JR Klauder Are coherent states the natural language of quantum mechanics inFundamental Aspects of Quantum Theory ed by V Gorini A Frigerio NATO ASI Seriesvol B 144 (Plenum Press New York 1986) pp 1ndash12
[413] JR Klauder Quantization without quantization Ann Phys (NY) 237 147ndash160 (1995)[414] JR Klauder Coherent states for the hydrogen atom J Phys A Math Gen 29 L293ndash
L296 (1996)[415] JR Klauder An affinity for affine quantum gravity Proc Steklov Inst Math 272 169ndash176
(2011) and references therein[416] JR Klauder RF Streater A wavelet transform for the Poincareacute group J Math Phys 32
1609ndash1611 (1991)[417] JR Klauder RF Streater Wavelets and the Poincareacute half-plane J Math Phys 35 471ndash
478 (1994)[418] JR Klauder K Penson J-M Sixdeniers Constructing coherent states through solutions
of Stieltjes and Hausdorff moment problems Phys Rev A 64 013817 (2001)[419] A Kleppner RL Lipsman The Plancherel formula for group extensions Ann Ec Norm
Sup 5 459ndash516 (1972)[420] AB Klimov C Muntildeoz Coherent isotropic and squeezed states in a N-qubit system Phys
Scr 87 038110 (2013)[421] A Klyashko Dynamical symmetry approach to entanglement in Physics and Theoretical
Computer Science From Numbers and Languages to (Quantum) Cryptography - NATOSecurity through Science Series D - Information and Communication Security vol 7 edby J-P Gazeau J Nesetril B Rovan (IOS Press Washington DC 2007) pp 25ndash54
[422] S Kobayashi Irreducibility of certain unitary representations J Math Soc Japan 20 638ndash642 (1968)
[423] K Kowalski J Rembielinski LC Papaloucas Coherent states for a quantum particle ona circle J Phys A Math Gen 29 4149ndash4167 (1996)
[424] K Kowalski J Rembielinski Quantum mechanics on a sphere and coherent states J PhysA Math Gen 33 6035ndash6048 (2000)
[425] K Kowalski J Rembielinski The Bargmann representation for the quantum mechanicson a sphere J Math Phys 42 4138ndash4147 (2001)
[426] C Kristjansen J Plefka GW Semenoff M Staudacher A new double-scaling limit ofN = 4 super-Yang-Mills theory and pp-wave strings Nuclear Phys B 643 3ndash30 (2002)
[427] M Kulesh M Holschneider MS Diallo Geophysical wavelet library Applications ofthe continuous wavelet transform to the polarization and dispersion analysis of signalsComput Geosci 34 1732ndash1752 (2008)
[428] R Kunze On the Frobenius reciprocity theorem for square integrable representationsPacific J Math 53 465ndash471 (1974)
[429] Y Kuroda A Wada T Yamazaki K Nagayama Postacquisition data processing methodfor suppression of the solvent signal I J Magn Reson 84 604ndash610 (1989)
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[430] Y Kuroda A Wada T Yamazaki K Nagayama Postacquisition data processing methodfor suppression of the solvent signal II The weighted first derivative J Magn Reson 88141ndash145 (1990)
[431] G Kutyniok D Labate Resolution of the wavefront set using continuous shearlets TransAmer Math Soc 361 2719ndash2754 (2009)
[432] G Kutyniok W-Q Lim Compactly supported shearlets are optimally sparse J ApproxTheory 163 1564ndash1589 (2011)
[433] D Labate W-Q Lim G Kutyniok G Weiss Sparse multidimensional representationusing shearlets in Wavelets XI (San Diego CA 2005) ed by M Papadakis A Laine MUnser SPIE Proceedings vol 5914 (SPIE Bellingham WA 2005) pp 254ndash262
[434] P Lahti J-P Pellonpaumlauml Continuous variable tomographic measurements Phys Lett A373 3435ndash3438 (2009)
[435] Lambertrsquos projection see WikipediahttpenwikipediaorgwikiLambert_azimuthal_equal-area_projection
[436] J-P Leduc F Mujica R Murenzi MJT Smith Missile-tracking algorithm using target-adapted spatio-temporal wavelets in Automatic Object Recognition VII SPIE Proceedingsvol 5914 (SPIE Bellingham WA 1997) pp 400ndash411
[437] J-P Leduc F Mujica R Murenzi MJT Smith Spatio-temporal wavelet transforms formotion tracking in IEEE ICASSP 1997 vol 4 (1997) pp 3013ndash3016
[438] J-P Leduc F Mujica R Murenzi MJT Smith Spatio-temporal continuous waveletsapplied to missile warhead detection and tracking in SPIE VCIP rsquo97 vol 3024 ed byJ Biemond EJ Delp (1997) pp 787ndash798
[439] B Leistedt JD McEwen Exact wavelets on the ball IEEE Trans Signal Proc 60 1564ndash1589 (2012)
[440] PG Lemarieacute Y Meyer Ondelettes et bases hilbertiennes Rev Math Iberoamer 2 1ndash18(1986)
[441] C Lemke A Schuck Jr J-P Antoine D Sima Metabolite-sensitive analysis of magneticresonance spectroscopic signals using the continuous wavelet transform Meas SciTechnol 22 (2011) Art 114013
[442] J-M Leacutevy-Leblond Galilei group and non-relativistic quantum mechanics J Math Phys4 776-788 (1963)
[443] J-M Leacutevy-Leblond Galilei group and Galilean invariance in Group Theory and ItsApplications vol II ed by EM Loebl (Academic New York 1971) pp 221ndash299
[444] J-M Leacutevy-Leblond On the conceptual nature of the physical constants Riv Nuovo Cim7 187ndash214 (1977)
[445] EH Lieb The classical limit of quantum spin systems Commun Math Phys 31 327ndash340(1973)
[446] G Lindblad B Nagel Continuous bases for unitary irreducible representations of SU(11)Ann Inst H Poincareacute 13 27ndash56 (1970)
[447] W Lisiecki Kaumlhler coherent states orbits for representations of semisimple Lie groupsAnn Inst H Poincareacute 53 857ndash890 (1990)
[448] A Lisowska Moment-based fast wedgelet transform J Math Imaging Vis 39 180ndash192(2011)
[449] H Liu L Peng Admissible wavelets associated with the Heisenberg group Pacific JMath 180 101ndash123 (1997)
[450] E Livine S Speziale Physical boundary state for the quantum tetrahedron Class QuantGrav 25 085003 (2008)
[451] F Low Complete sets of wave packets in A Passion for Physics ndash Essay in Honor ofGeoffrey Chew ed by C DeTar (World Scientific Singapore 1985) pp 17ndash22
[452] G Mack All unitary ray representations of the conformal group SU(22) with positiveenergy Commun Math Phys 55 1ndash28 (1977)
[453] GW Mackey Imprimitivity for representations of locally compact groups I Proc NatAcad Sci 35 537ndash545 (1949)
References 565
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[455] M Mallalieu CR Stroud Jr Rydberg wave packets fractional revivals and classicalorbits in Coherent States Past Present and Future (Proc Oak Ridge 1993) ed by DHFeng JR Klauder M Strayer (World Scientific Singapore 1994) pp 301ndash314
[456] SG Mallat Multifrequency channel decompositions of images and wavelet models IEEETrans Acoust Speech Signal Proc 37 2091ndash2110 (1989)
[457] SG Mallat A theory for multiresolution signal decomposition The wavelet representa-tion IEEE Trans Pattern Anal Machine Intell 11 674ndash693 (1989)
[458] S Mallat W-L Hwang Singularity detection and processing with wavelets IEEE TransInform Theory 38 617ndash643 (1992)
[459] S Mallat Z Zhang Matching pursuits with time frequency dictionaries IEEE TransSignal Proc 41 3397ndash3415 (1993)
[460] S Mallat S Zhong Wavelet maxima representation in Wavelets and Applications (ProcMarseille 1989) ed by Y Meyer (Masson and Springer Paris and Berlin 1991) pp 207ndash284
[461] VI Manrsquoko G Marmo ECG Sudarshan F Zaccaria f -oscillators and non-linearcoherent states Phys Scr 55 528ndash541 (1997)
[462] D Marinucci D Pietrobon A Baldi P Baldi P Cabella G Kerkyacharian P Natoli DPicard N Vittorio Spherical needlets for CMB data analysis Mon Not R Astron Soc383 539ndash545 (2008)
[463] D Marion M Ikura A Bax Improved solvent suppression in one- and two-dimensionalNMR spectra by convolution of time-domain data J Magn Reson 84 425ndash430 (1989)
[464] Y Meyer Principe drsquoincertitude bases hilbertiennes et algegravebres drsquoopeacuterateurs SeacuteminaireBourbaki 662 (1985ndash1986)
[465] Y Meyer Principe drsquoincertitude bases hilbertiennes et algegravebres drsquoopeacuterateurs Asteacuterisque145ndash146 209ndash223 (1987)
[466] Y Meyer H Xu Wavelet analysis and chirps Appl Comput Harmon Anal 4 366ndash379(1997)
[467] L Michel Invariance in quantum mechanics and group extensions in Group TheoreticalConcepts and Methods in Elementary Particle Physics ed by F Guumlrsey (Gordon andBreach New York and London 1964) pp 135ndash200
[468] J Mickelsson J Niederle Contractions of representations of the de Sitter groupsCommun Math Phys 27 167ndash180 (1972)
[469] MM Miller Convergence of the Sudarshan expansion for the diagonal coherent-stateweight functional J Math Phys 9 1270ndash1274 (1968)
[470] V F Molchanov Harmonic analysis on homogeneous spaces in Representation Theoryand Noncommutative Harmonic Analysis II ed by AA Kirillov (Springer Berlin 1995)
[471] MI Monastyrsky AM Perelomov Coherent states and symmetric spaces II Ann InstH Poincareacute 23 23ndash48 (1975)
[472] B Moran S Howard D Cochran Positive-operator-valued measures A general settingfor frames in Excursions in Harmonic Analysis vol 1 2 ed by TD Andrews R BalanJJ Benedetto W Czaja KA Okoudjou (Birkhaumluser Boston 2013) pp 49ndash64
[473] H Moscovici Coherent states representations of nilpotent Lie groups Commun MathPhys 54 63ndash68 (1977)
[474] H Moscovici A Verona Coherent states and square integrable representations Ann InstH Poincareacute 29 139ndash156 (1978)
[475] F Mujica R Murenzi MJT Smith J-P Leduc Robust tracking in compressed imagesequences J Electr Imaging 7 746ndash754 (1998)
[476] R Murenzi Wavelet transforms associated to the n-dimensional Euclidean group withdilations Signals in more than one dimension in Wavelets Time-Frequency Methodsand Phase Space (Proc Marseille 1987) ed by J-M Combes A Grossmann PTchamitchian 2nd edn (Springer Berlin 1990) pp 239ndash246
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[478] B Nagel Generalized eigenvectors in group representations in Studies in MathematicalPhysics (Proc Istanbul 1970) ed by AO Barut (Reidel Dordrecht and Boston 1970)pp 135ndash154
[479] MA Naımark Dokl Akad Nauk SSSR 41 359ndash361 (1943) see also B Sz-NagyExtensions of linear transformations in Hilbert space which extend beyond this spaceAppendix to F Riesz B Sz-Nagy Functional Analysis (Frederick Ungar New York 1960)
[480] FJ Narcowich P Petrushev JD Ward Localized tight frames on spheres SIAM J MathAnal 38 574ndash594 (2006)
[481] M Nauenberg Quantum wave packets on Kepler elliptic orbits Phys Rev A 40 1133ndash1136 (1989)
[482] M Nauenberg C Stroud J Yeazell The classical limit of an atom Scient Amer 27024ndash29 (1994)
[483] H Neumann Transformation properties of observables Helv Phys Acta 45 811ndash819(1972)
[484] U Niederer The maximal kinematical invariance group of the free Schroumldinger equationHelv Phys Acta 45 802ndash881 (1972)
[485] MM Nieto LM Simmons Jr Coherent states for general potentials I Formalism IIConfining one-dimensional examples III Nonconfining one-dimensional examples PhysRev D 20 1321ndash1331 1332ndash1341 1342ndash1350 (1979)
[486] MM Nieto LM Simmons Jr Coherent states for general potentials Phys Rev Lett 41207ndash210 (1987)
[487] A Odzijewicz On reproducing kernels and quantization of states Commun Math Phys114 577ndash597 (1988)
[488] A Odzijewicz Coherent states and geometric quantization Commun Math Phys 150385ndash413 (1992)
[489] A Odzijewicz Quantum algebras and q-special functions related to coherent states mapsof the disc Commun Math Phys 192 183ndash215 (1998)
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Wavelets Multiresolut Inf Process 6 209ndash222 (2008)[531] D Rosca On a norm equivalence on L2(S2) Results Math 53 399ndash405 (2009)[532] D Rosca New uniform grids on the sphere Astron Astrophys 520 (2010) Art A63[533] D Rosca Uniform and refinable grids on elliptic domains and on some surfaces of
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Appl Comput Harmon Anal 30 262ndash272 (2011)[535] D Rosca J-P Antoine Locally supported orthogonal wavelet bases on the sphere via
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[537] D Rosca G Plonka Uniform spherical grids via area preserving projection from the cubeto the sphere J Comput Appl Math 236 1033ndash1041 (2011)
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[539] H Rossi M Vergne Analytic continuation of the holomorphic discrete series for a semi-simple Lie group Acta Math 136 1ndash59 (1976)
[540] DJ Rotenberg Application of Sturmian functions to the Schroedinger three-body prob-lem Elastic e+ndashH scattering Ann Phys (NY) 19 262ndash278 (1962)
[541] C Rovelli Zakopane lectures on loop gravity in Proceedings of 3rd Quantum Gravityand Quantum Geometry School 28 Febndash13 March 2011 (Zakopane Poland 2011)arXiv11023660v5
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[546] DJ Rowe J Repka Vector-coherent-state theory as a theory of induced representationsJ Math Phys 32 2614ndash2634 (1991)
[547] DJ Rowe G Rosensteel R Gilmore Vector coherent state representation theory J MathPhys 26 2787ndash2791 (1985)
[548] A Royer Phase states and phase operators for the quantum harmonic oscillator Phys RevA 53 70ndash108 (1996)
[549] J Saletan Contraction of Lie groups J Math Phys 2 1ndash21 (1961)[550] G Saracco A Grossmann P Tchamitchian Use of wavelet transforms in the study of
propagation of transient acoustic signals across a plane interface between two homoge-neous media in Wavelets Time-Frequency Methods and Phase Space (Proc Marseille1987) ed by J-M Combes A Grossmann P Tchamitchian 2nd edn (Springer Berlin1990) pp 139ndash146
[551] P Schroumlder W Sweldens Spherical wavelets Efficiently representing functions on thesphere in Computer Graphics Proceedings (SIGGRAPH95) (ACM Siggraph Los Angeles1995) pp 161ndash175
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[554] H Scutaru Coherent states and induced representations Lett Math Phys 2 101ndash107(1977)
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R61ndashR75 (2000)[559] E Slezak A Bijaoui G Mars Identification of structures from galaxy counts Use of the
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Geometric Methods in Physics XXXI Workshop 2012 (Trends in Mathematics ed byP Kielanowski et al Birkhaumluser Verlag Basel 2013) pp 47ndash63
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[573] W Sweldens The lifting scheme A construction of second generation wavelets SIAM JMath Anal 29 511ndash546 (1998)
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[575] FH Szafraniec Multipliers in the reproducing kernel Hilbert space subnormality andnoncommutative complex analysis in Reproducing Kernel Spaces and Applications edby D Alpay Operator Theory Advances and Applications vol 143 (Birkhaumluser Basel2003) pp 313ndash331
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[579] T Thiemann Gauge field theory coherent states (GCS) 1 General properties Class QuantGrav 18 2025ndash2064 (2001)
[580] T Thiemann O Winkler Gauge field theory coherent states (GCS) 2 Peakednessproperties Class Quant Grav 18 2561ndash2636 (2001)
[581] T Thiemann O Winkler Gauge field theory coherent states (GCS) 3 Ehrenfest theoremsClass Quant Grav 18 4629ndash4682 (2001)
[582] T Thiemann O Winkler Gauge field theory coherent states (GCS) 4 Infinite tensorproduct and thermodynamical limit Class Quant Grav 18 4997ndash5054 (2001)
[583] K Thirulagasanthar ST Ali Regular subspaces of a quaternionic Hilbert space fromquaternionic Hermite polynomials and associated coherent states J Math Phys 54013506 (2013)
[584] K Thirulogasanthar G Honnouvo A Krzyzak Coherent states and Hermite polynomialson quaternionic Hilbert spaces J Phys A Math Theor 43 385205 (2010)
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341ndash346 (2005)[589] DA Trifonov Generalized intelligent states and squeezing J Math Phys 35 2297ndash2308
(1994)[590] AS Trushechkin IV Volovich Localization properties of squeezed quantum states in
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simulation of an impact test using wavelets analytical and finite element models Int JSolids Struct 38 5481ndash5508 (2001)
[594] L Vanhamme RD Fierro S Van Huffel R de Beer Fast removal of residual water inproton spectra J Magn Reson 132 197ndash203 (1998)
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[598] DF Walls Squeezed states of light Nature 306 141ndash146 (1983)[599] YK Wang FT Hioe Phase transition in the Dicke maser model Phys Rev A 7 831ndash836
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Recogn Artif Intell 26 1255011 (2012)[601] I Weinreich A construction of C1-wavelets on the two-dimensional sphere Appl Comput
Harmon Anal 10 1ndash26 (2001)[602] H Weyl Quantenmechanik und Gruppentheorie Z Phys 46 1ndash46 (1927)
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[609] W Wisnoe P Gajan A Strzelecki C Lempereur J-M Matheacute The use of the two-dimensional wavelet transform in flow visualization processing in Progress in WaveletAnalysis and Applications (Proc Toulouse 1992) ed by Y Meyer S Roques (EdFrontiegraveres Gif-sur-Yvette 1993) pp 455ndash458
[610] K Woacutedkiewicz On the quantum mechanics of squeezed states J Modern Optics 34 941ndash948(1987)
[611] JA Yeazell M Mallalieu CR Stroud Jr Observation of the collapse and revival of aRydberg electronic wave packet Phys Rev Lett 64 2007ndash2010 (1990)
[612] JA Yeazell CR Stroud Jr Observation of fractional revivals in the evolution of aRydberg atomic wave packet Phys Rev A 43 5153ndash5156 (1991)
[613] HP Yuen Two-photon coherent states of the radiation field Phys Rev A 13 2226ndash2243(1976)
[614] J Zak Balian-Low theorem for Landau levels Phys Rev Lett 79 533ndash536 (1997)[615] J Zak Orthonormal sets of localized functions for a Landau level J Math Phys 39 4195ndash
4200 (1998) and references quoted there[616] AA Zakharova On the properties of generalized frames Math Notes 83 190ndash200 (2008)[617] W-M Zhang DH Feng R Gilmore Coherent states Theory and some applications Rev
Mod Phys 26 867ndash927 (1990)[618] I Zlatev W-M Zhang DH Feng Possibility that Schroumldingerrsquos conjecture for the
hydrogen atom coherent states is not attainable Phys Rev A 50 R1973ndashR1975 (1994)[619] WH Zurek Decoherence einselection and the quantum origins of the classical Rev Mod
Phys 75 715ndash775 (2003)[620] WH Zurek S Habib JP Paz Coherent states via decoherence Phys Rev Lett 70 1187ndash
1190 (1993)[621] K Zyczkowski Squeezed states in a quantum chaotic system J Phys A Math Theor 22
of SU(11) 81 296 297HilbertClowast-modules 164holomorphic 140nonholomorphic 151nonlinear 146of affine Galilei group 505of affine Poincareacute group 509of affine Weyl-Heisenberg group GaWH
497of compact semisimple Lie groups 174of Euclidean group E(n) 266of Galilei group G (11) 290of isochronous Galilei group 237of non-semisimple Lie groups 179of noncompact semisimple Lie groups 177of Poincareacute group Puarr
+(11) 283massless case 288
of Poincareacute group Puarr+(13) 279
of Schroumldinger group 508quasi-coherent states 186quaternionic 164
ST Ali et al Coherent States Wavelets and Their Generalizations Theoreticaland Mathematical Physics DOI 101007978-1-4614-8535-3copy Springer Science+Business Media New York 2014
573
574 Index
coherent states (CS) (cont)spin or SU(2) 175square integrable covariant 166 180 264vector (VCS) 73 108 112 170weighted 184 523
of affine Weyl-Heisenberg group GaWH497
of Poincareacute group Puarr+(11) 284
cohomology group 393 403coboundaries 403cochains 402cocycle 403
algebraic 387Cauchy 418Cauchy-Paul 354 419 425conical 418difference 417 462directional 416 440kinematical 499local 488metabolite-based 355 374minimal uncertainty 425multiselective 440on a graph 493on the sphere S
2 458on the sphere S
n 479on the torus T2 481steerable 439von Mises 440
wedgelet transform 455Wigner function 322Wigner-Ville transform 349Windowed Fourier or Gabor transform 349
ZZak transform 518
References
A Books and Theses
B Articles
Index
562 References
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[384] M Holschneider P Tchamitchian Pointwise analysis of Riemannrsquos ldquonondifferentiablerdquofunction Invent Math 105 157ndash175 (1991)
[385] GR Honarasa MK Tavassoly M Hatami R Roknizadeh Nonclassical properties ofcoherent states and excited coherent states for continuous spectra J Phys A Math Theor44 085303 (2011)
[386] M Hongoh Coherent states associated with the continuous spectrum of noncompactgroups J Math Phys 18 2081ndash2085 (1977)
[387] A Horzela FH Szafraniec A measure free approach to coherent states J Phys A MathGen 45 244018 (2012)
[388] W-L Hwang S Mallat Characterization of self-similar multifractals with waveletmaxima Appl Comput Harmon Anal 1 316ndash328 (1994)
[389] W-L Hwang C-S Lu P-C Chung Shape from texture Estimation of planar surfaceorientation through the ridge surfaces of continuous wavelet transform IEEE Trans ImageProc 7 773ndash780 (1998)
[390] I Iglewska-Nowak M Holschneider Frames of Poisson wavelets on the sphere ApplComput Harmon Anal 28 227ndash248 (2010)
[391] E Inoumlnuuml EP Wigner On the contraction of groups and their representations Proc NatAcad Sci U S 39 510ndash524 (1953)
[392] S Iqbal F Saif Generalized coherent states and their statistical characteristics in power-law potentials J Math Phys 52 082105 (2011)
[393] CJ Isham JR Klauder Coherent states for n-dimensional Euclidean groups E(n) andtheir application J MathPhys 32 607ndash620 (1991)
[394] L Jacques J-P Antoine Multiselective pyramidal decomposition of images Wavelets withadaptive angular selectivity Int J Wavelets Multires Inform Proc 5 785ndash814 (2007)
[395] L Jacques L Duval C Chaux G Peyreacute A panorama on multiscale geometric rep-resentations intertwining spatial directional and frequency selectivity Signal Proc 912699ndash2730 (2011)
[396] HR Jalali M K Tavassoly On the ladder operators and nonclassicality of generalizedcoherent state associated with a particle in an infinite square well preprint (2013)arXiv13034100v1 [quant-ph]
[397] C Johnston On the pseudo-dilation representations of Flornes Grossmann Holschneiderand Torreacutesani Appl Comput Harmon Anal 3 377ndash385 (1997)
[398] G Kaiser Phase-space approach to relativistic quantum mechanics I Coherent staterepresentation for massive scalar particles J MathPhys 18 952ndash959 (1977)
[399] G Kaiser Phase-space approach to relativistic quantum mechanics II Geometrical aspectsJ MathPhys 19 502ndash507 (1978)
[400] C Kalisa B Torreacutesani N-dimensional affine Weyl-Heisenberg wavelets Ann Inst HPoincareacute 59 201ndash236 (1993)
[401] W Kaminski J Lewandowski T Pawłowski Quantum constraints Dirac observables andevolution group averaging versus the Schroumldinger picture in LQC Class Quant Grav 26245016 (2009)
[402] MR Karim ST Ali A relativistic windowed Fourier transform preprint ConcordiaUniversity Montreacuteal (1997) (unpublished)
[403] M R Karim ST Ali M Bodruzzaman A relativistic windowed Fourier transform inProceedings of IEEE SoutheastCon 2000 Nashville Tennessee pp 253ndash260 (2000)
[404] T Kawazoe Wavelet transforms associated to a principal series representation of semisim-ple Lie groups I II Proc Japan Acad Ser A ndash Math Sci 71 154ndash157 158ndash160 (1995)
[405] T Kawazoe Wavelet transform associated to an induced representation of SL(n+ 2R)Ann Inst H Poincareacute 65 1ndash13 (1996)
References 563
[406] P Kittipoom G Kutyniok W-Q Lim Irregular shearlet frames Geometry and approxi-mation properties J Fourier Anal Appl 17 604ndash639 (2011)
[407] P Kittipoom G Kutyniok W-Q Lim Construction of compactly supported shearletframes Constr Approx 35 21ndash72 (2012)
[408] J Kiukas P Lahti K Ylinenc Phase space quantization and the operator moment problemJ Math Phys 47 072104 (2006)
[409] JR Klauder Continuous-representation theory I Postulates of continuous-representationtheory J Math Phys 4 1055ndash1058 (1963)
[410] JR Klauder Continuous-representation theory II Generalized relation between quantumand classical dynamics J Math Phys 4 1058ndash1073 (1963)
[411] JR Klauder Path integrals for affine variables in Functional Integration Theory andApplications ed by J-P Antoine E Tirapegui (Plenum Press New York and London1980) pp 101ndash119
[412] JR Klauder Are coherent states the natural language of quantum mechanics inFundamental Aspects of Quantum Theory ed by V Gorini A Frigerio NATO ASI Seriesvol B 144 (Plenum Press New York 1986) pp 1ndash12
[413] JR Klauder Quantization without quantization Ann Phys (NY) 237 147ndash160 (1995)[414] JR Klauder Coherent states for the hydrogen atom J Phys A Math Gen 29 L293ndash
L296 (1996)[415] JR Klauder An affinity for affine quantum gravity Proc Steklov Inst Math 272 169ndash176
(2011) and references therein[416] JR Klauder RF Streater A wavelet transform for the Poincareacute group J Math Phys 32
1609ndash1611 (1991)[417] JR Klauder RF Streater Wavelets and the Poincareacute half-plane J Math Phys 35 471ndash
478 (1994)[418] JR Klauder K Penson J-M Sixdeniers Constructing coherent states through solutions
of Stieltjes and Hausdorff moment problems Phys Rev A 64 013817 (2001)[419] A Kleppner RL Lipsman The Plancherel formula for group extensions Ann Ec Norm
Sup 5 459ndash516 (1972)[420] AB Klimov C Muntildeoz Coherent isotropic and squeezed states in a N-qubit system Phys
Scr 87 038110 (2013)[421] A Klyashko Dynamical symmetry approach to entanglement in Physics and Theoretical
Computer Science From Numbers and Languages to (Quantum) Cryptography - NATOSecurity through Science Series D - Information and Communication Security vol 7 edby J-P Gazeau J Nesetril B Rovan (IOS Press Washington DC 2007) pp 25ndash54
[422] S Kobayashi Irreducibility of certain unitary representations J Math Soc Japan 20 638ndash642 (1968)
[423] K Kowalski J Rembielinski LC Papaloucas Coherent states for a quantum particle ona circle J Phys A Math Gen 29 4149ndash4167 (1996)
[424] K Kowalski J Rembielinski Quantum mechanics on a sphere and coherent states J PhysA Math Gen 33 6035ndash6048 (2000)
[425] K Kowalski J Rembielinski The Bargmann representation for the quantum mechanicson a sphere J Math Phys 42 4138ndash4147 (2001)
[426] C Kristjansen J Plefka GW Semenoff M Staudacher A new double-scaling limit ofN = 4 super-Yang-Mills theory and pp-wave strings Nuclear Phys B 643 3ndash30 (2002)
[427] M Kulesh M Holschneider MS Diallo Geophysical wavelet library Applications ofthe continuous wavelet transform to the polarization and dispersion analysis of signalsComput Geosci 34 1732ndash1752 (2008)
[428] R Kunze On the Frobenius reciprocity theorem for square integrable representationsPacific J Math 53 465ndash471 (1974)
[429] Y Kuroda A Wada T Yamazaki K Nagayama Postacquisition data processing methodfor suppression of the solvent signal I J Magn Reson 84 604ndash610 (1989)
564 References
[430] Y Kuroda A Wada T Yamazaki K Nagayama Postacquisition data processing methodfor suppression of the solvent signal II The weighted first derivative J Magn Reson 88141ndash145 (1990)
[431] G Kutyniok D Labate Resolution of the wavefront set using continuous shearlets TransAmer Math Soc 361 2719ndash2754 (2009)
[432] G Kutyniok W-Q Lim Compactly supported shearlets are optimally sparse J ApproxTheory 163 1564ndash1589 (2011)
[433] D Labate W-Q Lim G Kutyniok G Weiss Sparse multidimensional representationusing shearlets in Wavelets XI (San Diego CA 2005) ed by M Papadakis A Laine MUnser SPIE Proceedings vol 5914 (SPIE Bellingham WA 2005) pp 254ndash262
[434] P Lahti J-P Pellonpaumlauml Continuous variable tomographic measurements Phys Lett A373 3435ndash3438 (2009)
[435] Lambertrsquos projection see WikipediahttpenwikipediaorgwikiLambert_azimuthal_equal-area_projection
[436] J-P Leduc F Mujica R Murenzi MJT Smith Missile-tracking algorithm using target-adapted spatio-temporal wavelets in Automatic Object Recognition VII SPIE Proceedingsvol 5914 (SPIE Bellingham WA 1997) pp 400ndash411
[437] J-P Leduc F Mujica R Murenzi MJT Smith Spatio-temporal wavelet transforms formotion tracking in IEEE ICASSP 1997 vol 4 (1997) pp 3013ndash3016
[438] J-P Leduc F Mujica R Murenzi MJT Smith Spatio-temporal continuous waveletsapplied to missile warhead detection and tracking in SPIE VCIP rsquo97 vol 3024 ed byJ Biemond EJ Delp (1997) pp 787ndash798
[439] B Leistedt JD McEwen Exact wavelets on the ball IEEE Trans Signal Proc 60 1564ndash1589 (2012)
[440] PG Lemarieacute Y Meyer Ondelettes et bases hilbertiennes Rev Math Iberoamer 2 1ndash18(1986)
[441] C Lemke A Schuck Jr J-P Antoine D Sima Metabolite-sensitive analysis of magneticresonance spectroscopic signals using the continuous wavelet transform Meas SciTechnol 22 (2011) Art 114013
[442] J-M Leacutevy-Leblond Galilei group and non-relativistic quantum mechanics J Math Phys4 776-788 (1963)
[443] J-M Leacutevy-Leblond Galilei group and Galilean invariance in Group Theory and ItsApplications vol II ed by EM Loebl (Academic New York 1971) pp 221ndash299
[444] J-M Leacutevy-Leblond On the conceptual nature of the physical constants Riv Nuovo Cim7 187ndash214 (1977)
[445] EH Lieb The classical limit of quantum spin systems Commun Math Phys 31 327ndash340(1973)
[446] G Lindblad B Nagel Continuous bases for unitary irreducible representations of SU(11)Ann Inst H Poincareacute 13 27ndash56 (1970)
[447] W Lisiecki Kaumlhler coherent states orbits for representations of semisimple Lie groupsAnn Inst H Poincareacute 53 857ndash890 (1990)
[448] A Lisowska Moment-based fast wedgelet transform J Math Imaging Vis 39 180ndash192(2011)
[449] H Liu L Peng Admissible wavelets associated with the Heisenberg group Pacific JMath 180 101ndash123 (1997)
[450] E Livine S Speziale Physical boundary state for the quantum tetrahedron Class QuantGrav 25 085003 (2008)
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[452] G Mack All unitary ray representations of the conformal group SU(22) with positiveenergy Commun Math Phys 55 1ndash28 (1977)
[453] GW Mackey Imprimitivity for representations of locally compact groups I Proc NatAcad Sci 35 537ndash545 (1949)
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[455] M Mallalieu CR Stroud Jr Rydberg wave packets fractional revivals and classicalorbits in Coherent States Past Present and Future (Proc Oak Ridge 1993) ed by DHFeng JR Klauder M Strayer (World Scientific Singapore 1994) pp 301ndash314
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[457] SG Mallat A theory for multiresolution signal decomposition The wavelet representa-tion IEEE Trans Pattern Anal Machine Intell 11 674ndash693 (1989)
[458] S Mallat W-L Hwang Singularity detection and processing with wavelets IEEE TransInform Theory 38 617ndash643 (1992)
[459] S Mallat Z Zhang Matching pursuits with time frequency dictionaries IEEE TransSignal Proc 41 3397ndash3415 (1993)
[460] S Mallat S Zhong Wavelet maxima representation in Wavelets and Applications (ProcMarseille 1989) ed by Y Meyer (Masson and Springer Paris and Berlin 1991) pp 207ndash284
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[466] Y Meyer H Xu Wavelet analysis and chirps Appl Comput Harmon Anal 4 366ndash379(1997)
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Wavelets Multiresolut Inf Process 6 209ndash222 (2008)[531] D Rosca On a norm equivalence on L2(S2) Results Math 53 399ndash405 (2009)[532] D Rosca New uniform grids on the sphere Astron Astrophys 520 (2010) Art A63[533] D Rosca Uniform and refinable grids on elliptic domains and on some surfaces of
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[541] C Rovelli Zakopane lectures on loop gravity in Proceedings of 3rd Quantum Gravityand Quantum Geometry School 28 Febndash13 March 2011 (Zakopane Poland 2011)arXiv11023660v5
[542] C Rovelli S Speziale A semiclassical tetrahedron Class Quant Grav 23 5861ndash5870(2006)
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[547] DJ Rowe G Rosensteel R Gilmore Vector coherent state representation theory J MathPhys 26 2787ndash2791 (1985)
[548] A Royer Phase states and phase operators for the quantum harmonic oscillator Phys RevA 53 70ndash108 (1996)
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propagation of transient acoustic signals across a plane interface between two homoge-neous media in Wavelets Time-Frequency Methods and Phase Space (Proc Marseille1987) ed by J-M Combes A Grossmann P Tchamitchian 2nd edn (Springer Berlin1990) pp 139ndash146
[551] P Schroumlder W Sweldens Spherical wavelets Efficiently representing functions on thesphere in Computer Graphics Proceedings (SIGGRAPH95) (ACM Siggraph Los Angeles1995) pp 161ndash175
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[554] H Scutaru Coherent states and induced representations Lett Math Phys 2 101ndash107(1977)
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R61ndashR75 (2000)[559] E Slezak A Bijaoui G Mars Identification of structures from galaxy counts Use of the
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Geometric Methods in Physics XXXI Workshop 2012 (Trends in Mathematics ed byP Kielanowski et al Birkhaumluser Verlag Basel 2013) pp 47ndash63
[562] SB Sontz Paragrassmann algebras as quantum spaces Part II Toeplitz operators J OperTh (2013 to appear) arXiv12055493
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[575] FH Szafraniec Multipliers in the reproducing kernel Hilbert space subnormality andnoncommutative complex analysis in Reproducing Kernel Spaces and Applications edby D Alpay Operator Theory Advances and Applications vol 143 (Birkhaumluser Basel2003) pp 313ndash331
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Proceedings of the 27th International Cosmic Ray Conference (ICRC 2001) (CopernicusGesellschaft DE 2001) pp 2923ndash2926
[579] T Thiemann Gauge field theory coherent states (GCS) 1 General properties Class QuantGrav 18 2025ndash2064 (2001)
[580] T Thiemann O Winkler Gauge field theory coherent states (GCS) 2 Peakednessproperties Class Quant Grav 18 2561ndash2636 (2001)
[581] T Thiemann O Winkler Gauge field theory coherent states (GCS) 3 Ehrenfest theoremsClass Quant Grav 18 4629ndash4682 (2001)
[582] T Thiemann O Winkler Gauge field theory coherent states (GCS) 4 Infinite tensorproduct and thermodynamical limit Class Quant Grav 18 4997ndash5054 (2001)
[583] K Thirulagasanthar ST Ali Regular subspaces of a quaternionic Hilbert space fromquaternionic Hermite polynomials and associated coherent states J Math Phys 54013506 (2013)
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Ann Inst H Poincareacute 56 215ndash234 (1992)[588] B Torreacutesani Position-frequency analysis for signals defined on spheres Signal Proc 43
341ndash346 (2005)[589] DA Trifonov Generalized intelligent states and squeezing J Math Phys 35 2297ndash2308
(1994)[590] AS Trushechkin IV Volovich Localization properties of squeezed quantum states in
nanoscale space domains preprint (2013) arXiv13046277v1 [quant-ph][591] M Unser N Chenouard A unifying parametric framework for 2D steerable wavelet
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algorithms IEEE Trans Image Proc 11 363ndash372 (2002)[593] P Vandergheynst J-P Antoine E Van Vyve A Goldberg I Doghri Modelling and
simulation of an impact test using wavelets analytical and finite element models Int JSolids Struct 38 5481ndash5508 (2001)
[594] L Vanhamme RD Fierro S Van Huffel R de Beer Fast removal of residual water inproton spectra J Magn Reson 132 197ndash203 (1998)
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[596] J Voisin On some unitary representations of the Galilei group I Irreducible representa-tions J Math Phys 6 1519ndash1529 (1965)
[597] A Vourdas Analytic representations in quantum mechanics J Phys A Math Gen 39R65ndashR141 (2006)
[598] DF Walls Squeezed states of light Nature 306 141ndash146 (1983)[599] YK Wang FT Hioe Phase transition in the Dicke maser model Phys Rev A 7 831ndash836
(1973)[600] PSP Wang J Yang A review of wavelet-based edge detection methods Int J Patt
Recogn Artif Intell 26 1255011 (2012)[601] I Weinreich A construction of C1-wavelets on the two-dimensional sphere Appl Comput
Harmon Anal 10 1ndash26 (2001)[602] H Weyl Quantenmechanik und Gruppentheorie Z Phys 46 1ndash46 (1927)
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[609] W Wisnoe P Gajan A Strzelecki C Lempereur J-M Matheacute The use of the two-dimensional wavelet transform in flow visualization processing in Progress in WaveletAnalysis and Applications (Proc Toulouse 1992) ed by Y Meyer S Roques (EdFrontiegraveres Gif-sur-Yvette 1993) pp 455ndash458
[610] K Woacutedkiewicz On the quantum mechanics of squeezed states J Modern Optics 34 941ndash948(1987)
[611] JA Yeazell M Mallalieu CR Stroud Jr Observation of the collapse and revival of aRydberg electronic wave packet Phys Rev Lett 64 2007ndash2010 (1990)
[612] JA Yeazell CR Stroud Jr Observation of fractional revivals in the evolution of aRydberg atomic wave packet Phys Rev A 43 5153ndash5156 (1991)
[613] HP Yuen Two-photon coherent states of the radiation field Phys Rev A 13 2226ndash2243(1976)
[614] J Zak Balian-Low theorem for Landau levels Phys Rev Lett 79 533ndash536 (1997)[615] J Zak Orthonormal sets of localized functions for a Landau level J Math Phys 39 4195ndash
4200 (1998) and references quoted there[616] AA Zakharova On the properties of generalized frames Math Notes 83 190ndash200 (2008)[617] W-M Zhang DH Feng R Gilmore Coherent states Theory and some applications Rev
Mod Phys 26 867ndash927 (1990)[618] I Zlatev W-M Zhang DH Feng Possibility that Schroumldingerrsquos conjecture for the
hydrogen atom coherent states is not attainable Phys Rev A 50 R1973ndashR1975 (1994)[619] WH Zurek Decoherence einselection and the quantum origins of the classical Rev Mod
Phys 75 715ndash775 (2003)[620] WH Zurek S Habib JP Paz Coherent states via decoherence Phys Rev Lett 70 1187ndash
1190 (1993)[621] K Zyczkowski Squeezed states in a quantum chaotic system J Phys A Math Theor 22
of SU(11) 81 296 297HilbertClowast-modules 164holomorphic 140nonholomorphic 151nonlinear 146of affine Galilei group 505of affine Poincareacute group 509of affine Weyl-Heisenberg group GaWH
497of compact semisimple Lie groups 174of Euclidean group E(n) 266of Galilei group G (11) 290of isochronous Galilei group 237of non-semisimple Lie groups 179of noncompact semisimple Lie groups 177of Poincareacute group Puarr
+(11) 283massless case 288
of Poincareacute group Puarr+(13) 279
of Schroumldinger group 508quasi-coherent states 186quaternionic 164
ST Ali et al Coherent States Wavelets and Their Generalizations Theoreticaland Mathematical Physics DOI 101007978-1-4614-8535-3copy Springer Science+Business Media New York 2014
573
574 Index
coherent states (CS) (cont)spin or SU(2) 175square integrable covariant 166 180 264vector (VCS) 73 108 112 170weighted 184 523
of affine Weyl-Heisenberg group GaWH497
of Poincareacute group Puarr+(11) 284
cohomology group 393 403coboundaries 403cochains 402cocycle 403
algebraic 387Cauchy 418Cauchy-Paul 354 419 425conical 418difference 417 462directional 416 440kinematical 499local 488metabolite-based 355 374minimal uncertainty 425multiselective 440on a graph 493on the sphere S
2 458on the sphere S
n 479on the torus T2 481steerable 439von Mises 440
wedgelet transform 455Wigner function 322Wigner-Ville transform 349Windowed Fourier or Gabor transform 349
ZZak transform 518
References
A Books and Theses
B Articles
Index
References 563
[406] P Kittipoom G Kutyniok W-Q Lim Irregular shearlet frames Geometry and approxi-mation properties J Fourier Anal Appl 17 604ndash639 (2011)
[407] P Kittipoom G Kutyniok W-Q Lim Construction of compactly supported shearletframes Constr Approx 35 21ndash72 (2012)
[408] J Kiukas P Lahti K Ylinenc Phase space quantization and the operator moment problemJ Math Phys 47 072104 (2006)
[409] JR Klauder Continuous-representation theory I Postulates of continuous-representationtheory J Math Phys 4 1055ndash1058 (1963)
[410] JR Klauder Continuous-representation theory II Generalized relation between quantumand classical dynamics J Math Phys 4 1058ndash1073 (1963)
[411] JR Klauder Path integrals for affine variables in Functional Integration Theory andApplications ed by J-P Antoine E Tirapegui (Plenum Press New York and London1980) pp 101ndash119
[412] JR Klauder Are coherent states the natural language of quantum mechanics inFundamental Aspects of Quantum Theory ed by V Gorini A Frigerio NATO ASI Seriesvol B 144 (Plenum Press New York 1986) pp 1ndash12
[413] JR Klauder Quantization without quantization Ann Phys (NY) 237 147ndash160 (1995)[414] JR Klauder Coherent states for the hydrogen atom J Phys A Math Gen 29 L293ndash
L296 (1996)[415] JR Klauder An affinity for affine quantum gravity Proc Steklov Inst Math 272 169ndash176
(2011) and references therein[416] JR Klauder RF Streater A wavelet transform for the Poincareacute group J Math Phys 32
1609ndash1611 (1991)[417] JR Klauder RF Streater Wavelets and the Poincareacute half-plane J Math Phys 35 471ndash
478 (1994)[418] JR Klauder K Penson J-M Sixdeniers Constructing coherent states through solutions
of Stieltjes and Hausdorff moment problems Phys Rev A 64 013817 (2001)[419] A Kleppner RL Lipsman The Plancherel formula for group extensions Ann Ec Norm
Sup 5 459ndash516 (1972)[420] AB Klimov C Muntildeoz Coherent isotropic and squeezed states in a N-qubit system Phys
Scr 87 038110 (2013)[421] A Klyashko Dynamical symmetry approach to entanglement in Physics and Theoretical
Computer Science From Numbers and Languages to (Quantum) Cryptography - NATOSecurity through Science Series D - Information and Communication Security vol 7 edby J-P Gazeau J Nesetril B Rovan (IOS Press Washington DC 2007) pp 25ndash54
[422] S Kobayashi Irreducibility of certain unitary representations J Math Soc Japan 20 638ndash642 (1968)
[423] K Kowalski J Rembielinski LC Papaloucas Coherent states for a quantum particle ona circle J Phys A Math Gen 29 4149ndash4167 (1996)
[424] K Kowalski J Rembielinski Quantum mechanics on a sphere and coherent states J PhysA Math Gen 33 6035ndash6048 (2000)
[425] K Kowalski J Rembielinski The Bargmann representation for the quantum mechanicson a sphere J Math Phys 42 4138ndash4147 (2001)
[426] C Kristjansen J Plefka GW Semenoff M Staudacher A new double-scaling limit ofN = 4 super-Yang-Mills theory and pp-wave strings Nuclear Phys B 643 3ndash30 (2002)
[427] M Kulesh M Holschneider MS Diallo Geophysical wavelet library Applications ofthe continuous wavelet transform to the polarization and dispersion analysis of signalsComput Geosci 34 1732ndash1752 (2008)
[428] R Kunze On the Frobenius reciprocity theorem for square integrable representationsPacific J Math 53 465ndash471 (1974)
[429] Y Kuroda A Wada T Yamazaki K Nagayama Postacquisition data processing methodfor suppression of the solvent signal I J Magn Reson 84 604ndash610 (1989)
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[431] G Kutyniok D Labate Resolution of the wavefront set using continuous shearlets TransAmer Math Soc 361 2719ndash2754 (2009)
[432] G Kutyniok W-Q Lim Compactly supported shearlets are optimally sparse J ApproxTheory 163 1564ndash1589 (2011)
[433] D Labate W-Q Lim G Kutyniok G Weiss Sparse multidimensional representationusing shearlets in Wavelets XI (San Diego CA 2005) ed by M Papadakis A Laine MUnser SPIE Proceedings vol 5914 (SPIE Bellingham WA 2005) pp 254ndash262
[434] P Lahti J-P Pellonpaumlauml Continuous variable tomographic measurements Phys Lett A373 3435ndash3438 (2009)
[435] Lambertrsquos projection see WikipediahttpenwikipediaorgwikiLambert_azimuthal_equal-area_projection
[436] J-P Leduc F Mujica R Murenzi MJT Smith Missile-tracking algorithm using target-adapted spatio-temporal wavelets in Automatic Object Recognition VII SPIE Proceedingsvol 5914 (SPIE Bellingham WA 1997) pp 400ndash411
[437] J-P Leduc F Mujica R Murenzi MJT Smith Spatio-temporal wavelet transforms formotion tracking in IEEE ICASSP 1997 vol 4 (1997) pp 3013ndash3016
[438] J-P Leduc F Mujica R Murenzi MJT Smith Spatio-temporal continuous waveletsapplied to missile warhead detection and tracking in SPIE VCIP rsquo97 vol 3024 ed byJ Biemond EJ Delp (1997) pp 787ndash798
[439] B Leistedt JD McEwen Exact wavelets on the ball IEEE Trans Signal Proc 60 1564ndash1589 (2012)
[440] PG Lemarieacute Y Meyer Ondelettes et bases hilbertiennes Rev Math Iberoamer 2 1ndash18(1986)
[441] C Lemke A Schuck Jr J-P Antoine D Sima Metabolite-sensitive analysis of magneticresonance spectroscopic signals using the continuous wavelet transform Meas SciTechnol 22 (2011) Art 114013
[442] J-M Leacutevy-Leblond Galilei group and non-relativistic quantum mechanics J Math Phys4 776-788 (1963)
[443] J-M Leacutevy-Leblond Galilei group and Galilean invariance in Group Theory and ItsApplications vol II ed by EM Loebl (Academic New York 1971) pp 221ndash299
[444] J-M Leacutevy-Leblond On the conceptual nature of the physical constants Riv Nuovo Cim7 187ndash214 (1977)
[445] EH Lieb The classical limit of quantum spin systems Commun Math Phys 31 327ndash340(1973)
[446] G Lindblad B Nagel Continuous bases for unitary irreducible representations of SU(11)Ann Inst H Poincareacute 13 27ndash56 (1970)
[447] W Lisiecki Kaumlhler coherent states orbits for representations of semisimple Lie groupsAnn Inst H Poincareacute 53 857ndash890 (1990)
[448] A Lisowska Moment-based fast wedgelet transform J Math Imaging Vis 39 180ndash192(2011)
[449] H Liu L Peng Admissible wavelets associated with the Heisenberg group Pacific JMath 180 101ndash123 (1997)
[450] E Livine S Speziale Physical boundary state for the quantum tetrahedron Class QuantGrav 25 085003 (2008)
[451] F Low Complete sets of wave packets in A Passion for Physics ndash Essay in Honor ofGeoffrey Chew ed by C DeTar (World Scientific Singapore 1985) pp 17ndash22
[452] G Mack All unitary ray representations of the conformal group SU(22) with positiveenergy Commun Math Phys 55 1ndash28 (1977)
[453] GW Mackey Imprimitivity for representations of locally compact groups I Proc NatAcad Sci 35 537ndash545 (1949)
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[457] SG Mallat A theory for multiresolution signal decomposition The wavelet representa-tion IEEE Trans Pattern Anal Machine Intell 11 674ndash693 (1989)
[458] S Mallat W-L Hwang Singularity detection and processing with wavelets IEEE TransInform Theory 38 617ndash643 (1992)
[459] S Mallat Z Zhang Matching pursuits with time frequency dictionaries IEEE TransSignal Proc 41 3397ndash3415 (1993)
[460] S Mallat S Zhong Wavelet maxima representation in Wavelets and Applications (ProcMarseille 1989) ed by Y Meyer (Masson and Springer Paris and Berlin 1991) pp 207ndash284
[461] VI Manrsquoko G Marmo ECG Sudarshan F Zaccaria f -oscillators and non-linearcoherent states Phys Scr 55 528ndash541 (1997)
[462] D Marinucci D Pietrobon A Baldi P Baldi P Cabella G Kerkyacharian P Natoli DPicard N Vittorio Spherical needlets for CMB data analysis Mon Not R Astron Soc383 539ndash545 (2008)
[463] D Marion M Ikura A Bax Improved solvent suppression in one- and two-dimensionalNMR spectra by convolution of time-domain data J Magn Reson 84 425ndash430 (1989)
[464] Y Meyer Principe drsquoincertitude bases hilbertiennes et algegravebres drsquoopeacuterateurs SeacuteminaireBourbaki 662 (1985ndash1986)
[465] Y Meyer Principe drsquoincertitude bases hilbertiennes et algegravebres drsquoopeacuterateurs Asteacuterisque145ndash146 209ndash223 (1987)
[466] Y Meyer H Xu Wavelet analysis and chirps Appl Comput Harmon Anal 4 366ndash379(1997)
[467] L Michel Invariance in quantum mechanics and group extensions in Group TheoreticalConcepts and Methods in Elementary Particle Physics ed by F Guumlrsey (Gordon andBreach New York and London 1964) pp 135ndash200
[468] J Mickelsson J Niederle Contractions of representations of the de Sitter groupsCommun Math Phys 27 167ndash180 (1972)
[469] MM Miller Convergence of the Sudarshan expansion for the diagonal coherent-stateweight functional J Math Phys 9 1270ndash1274 (1968)
[470] V F Molchanov Harmonic analysis on homogeneous spaces in Representation Theoryand Noncommutative Harmonic Analysis II ed by AA Kirillov (Springer Berlin 1995)
[471] MI Monastyrsky AM Perelomov Coherent states and symmetric spaces II Ann InstH Poincareacute 23 23ndash48 (1975)
[472] B Moran S Howard D Cochran Positive-operator-valued measures A general settingfor frames in Excursions in Harmonic Analysis vol 1 2 ed by TD Andrews R BalanJJ Benedetto W Czaja KA Okoudjou (Birkhaumluser Boston 2013) pp 49ndash64
[473] H Moscovici Coherent states representations of nilpotent Lie groups Commun MathPhys 54 63ndash68 (1977)
[474] H Moscovici A Verona Coherent states and square integrable representations Ann InstH Poincareacute 29 139ndash156 (1978)
[475] F Mujica R Murenzi MJT Smith J-P Leduc Robust tracking in compressed imagesequences J Electr Imaging 7 746ndash754 (1998)
[476] R Murenzi Wavelet transforms associated to the n-dimensional Euclidean group withdilations Signals in more than one dimension in Wavelets Time-Frequency Methodsand Phase Space (Proc Marseille 1987) ed by J-M Combes A Grossmann PTchamitchian 2nd edn (Springer Berlin 1990) pp 239ndash246
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[479] MA Naımark Dokl Akad Nauk SSSR 41 359ndash361 (1943) see also B Sz-NagyExtensions of linear transformations in Hilbert space which extend beyond this spaceAppendix to F Riesz B Sz-Nagy Functional Analysis (Frederick Ungar New York 1960)
[480] FJ Narcowich P Petrushev JD Ward Localized tight frames on spheres SIAM J MathAnal 38 574ndash594 (2006)
[481] M Nauenberg Quantum wave packets on Kepler elliptic orbits Phys Rev A 40 1133ndash1136 (1989)
[482] M Nauenberg C Stroud J Yeazell The classical limit of an atom Scient Amer 27024ndash29 (1994)
[483] H Neumann Transformation properties of observables Helv Phys Acta 45 811ndash819(1972)
[484] U Niederer The maximal kinematical invariance group of the free Schroumldinger equationHelv Phys Acta 45 802ndash881 (1972)
[485] MM Nieto LM Simmons Jr Coherent states for general potentials I Formalism IIConfining one-dimensional examples III Nonconfining one-dimensional examples PhysRev D 20 1321ndash1331 1332ndash1341 1342ndash1350 (1979)
[486] MM Nieto LM Simmons Jr Coherent states for general potentials Phys Rev Lett 41207ndash210 (1987)
[487] A Odzijewicz On reproducing kernels and quantization of states Commun Math Phys114 577ndash597 (1988)
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[489] A Odzijewicz Quantum algebras and q-special functions related to coherent states mapsof the disc Commun Math Phys 192 183ndash215 (1998)
[490] A Odzijewicz M Horowski A Tereszkiewicz Integrable multi-boson systems andorthogonal polynomials J Phys A Math Gen 34 4353ndash4376 (2001)
[491] G Oacutelafsson B Oslashrsted The holomorphic discrete series for affine symmetric spaces JFunct Anal 81 126ndash159 (1988)
[492] G Oacutelafsson H Schlichtkrull Representation theory Radon transform and the heatequation on a Riemannian symmetric space Contemp Math 449 315ndash344 (2008)
[493] E Onofri A note on coherent state representations of Lie groups J Math Phys 16 1087ndash1089 (1975)
[494] E Onofri Dynamical quantization of the Kepler manifold J Math Phys 17 401ndash408(1976)
[495] D Oriti R Pereira L Sindoni Coherent states in quantum gravity A construction basedon the flux representation of loop quantum gravity J Phys A Math Theor 45 244004(2012)
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[498] Z Pasternak-Winiarski On reproducing kernels for holomorphic vector bundles inQuantization and Infinite Dimensional Systems (Proc Białowieza Poland 1993) ed by J-P Antoine ST Ali W Lisiecki IM Mladenov A Odzijewicz (Plenum Press New Yorkand London 1994) pp 109ndash112
[499] T Paul Affine coherent states and the radial Schroumldinger equation I preprint CPT-84P1710 (1984) (unpublished)
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[501] AM Perelomov On the completeness of a system of coherent states Theor Math Phys6 156ndash164 (1971)
[502] AM Perelomov Coherent states for arbitrary Lie group Commun Math Phys 26 222ndash236 (1972)
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[504] M Perroud Projective representations of the Schroumldinger group Helv Phys Acta 50 233ndash252 (1977)
[505] J Phillips A note on square-integrable representations J Funct Anal 20 83ndash92 (1975)[506] D Pietrobon P Baldi D Marinucci Integrated Sachs-Wolfe effect from the cross
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[508] V Pop D Rosca Generalized piecewise constant orthogonal wavelet bases on 2D-domains Appl Anal 90 715ndash723 (2011)
[509] G Poumlschl E Teller Bemerkungen zur Quantenmechanik des anharmonischen OszillatorsZ Physik 83 143ndash151 (1933)
[510] D Potts G Steidl M Tasche Kernels of spherical harmonics and spherical frames inAdvanced Topics in Multivariate Approximation ed by F Fontanella K Jetter PJ Laurent(World Scientific Singapore 1996) pp 287ndash301
[511] E Prugovecki Consistent formulation of relativistic dynamics for massive spin-zeroparticles in external fields Phys Rev D 18 3655ndash3673 (1978) (Appendix C)
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[514] C Quesne Generalized vector coherent states of sp(2NR) vector operators and ofsp(2NR) sup u(N) reduced Wigner coefficients J Phys A Math Gen 24 2697ndash2714(1991)
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[516] A Rahimi A Najati YN Dehghan Continuous frames in Hilbert spaces Methods FunctAnal Topol 12 170ndash182 (2006)
[517] H Rauhut M Roumlsler Radial multiresolution in dimension three Constr Approx 22 193ndash218 (2005)
[518] JH Rawnsley Coherent states and Kaumlhler manifolds Quart J Math Oxford 28(2) 403ndash415 (1977)
[519] J Renaud The contraction of the SU(11) discrete series of representations by means ofcoherent states J Math Phys 37 3168ndash3179 (1996)
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[521] D Robert La coheacuterence dans tous ses eacutetats SMF Gazette 132 (2012)[522] JE Roberts The Dirac bra and ket formalism J Math Phys 7 1097ndash1104 (1966)[523] JE Roberts Rigged Hilbert spaces in quantum mechanics Commun Math Phys 3 98ndash
119 (1966)[524] S Roques F Bourzeix K Bouyoucef Soft-thresholding technique and restoration of
3C273 jet Astrophys Space Sci Nr 239 297ndash304 (1996)[525] D Rosca Haar wavelets on spherical triangulations in Advances in Multiresolution for
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501ndash511 (2007)[529] D Rosca Wavelet bases on the sphere obtained by radial projection J Fourier Anal Appl
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Wavelets Multiresolut Inf Process 6 209ndash222 (2008)[531] D Rosca On a norm equivalence on L2(S2) Results Math 53 399ndash405 (2009)[532] D Rosca New uniform grids on the sphere Astron Astrophys 520 (2010) Art A63[533] D Rosca Uniform and refinable grids on elliptic domains and on some surfaces of
revolution Appl Math Comput 217 7812ndash7817 (2011)[534] D Rosca Wavelet analysis on some surfaces of revolution via area preserving projection
Appl Comput Harmon Anal 30 262ndash272 (2011)[535] D Rosca J-P Antoine Locally supported orthogonal wavelet bases on the sphere via
stereographic projection Math Probl Eng 2009 124904 (2009)[536] D Rosca J-P Antoine Constructing wavelet frames and orthogonal wavelet bases on the
sphere in Recent Advances in Signal Processing ed by S Miron (IN-TECH ViennaAustria and Rijeka Croatia 2010) pp 59ndash76
[537] D Rosca G Plonka Uniform spherical grids via area preserving projection from the cubeto the sphere J Comput Appl Math 236 1033ndash1041 (2011)
[538] D Rosca G Plonka An area preserving projection from the regular octahedron to thesphere Results Math 63 429ndash444 (2012)
[539] H Rossi M Vergne Analytic continuation of the holomorphic discrete series for a semi-simple Lie group Acta Math 136 1ndash59 (1976)
[540] DJ Rotenberg Application of Sturmian functions to the Schroedinger three-body prob-lem Elastic e+ndashH scattering Ann Phys (NY) 19 262ndash278 (1962)
[541] C Rovelli Zakopane lectures on loop gravity in Proceedings of 3rd Quantum Gravityand Quantum Geometry School 28 Febndash13 March 2011 (Zakopane Poland 2011)arXiv11023660v5
[542] C Rovelli S Speziale A semiclassical tetrahedron Class Quant Grav 23 5861ndash5870(2006)
[543] DJ Rowe Coherent state theory of the noncompact symplectic group J Math Phys 252662ndash2271 (1984)
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[545] DJ Rowe Vector coherent state representations and their inner products J Phys A MathGen 45 244003 (2012) (This paper belongs to the special issue [38])
[546] DJ Rowe J Repka Vector-coherent-state theory as a theory of induced representationsJ Math Phys 32 2614ndash2634 (1991)
[547] DJ Rowe G Rosensteel R Gilmore Vector coherent state representation theory J MathPhys 26 2787ndash2791 (1985)
[548] A Royer Phase states and phase operators for the quantum harmonic oscillator Phys RevA 53 70ndash108 (1996)
[549] J Saletan Contraction of Lie groups J Math Phys 2 1ndash21 (1961)[550] G Saracco A Grossmann P Tchamitchian Use of wavelet transforms in the study of
propagation of transient acoustic signals across a plane interface between two homoge-neous media in Wavelets Time-Frequency Methods and Phase Space (Proc Marseille1987) ed by J-M Combes A Grossmann P Tchamitchian 2nd edn (Springer Berlin1990) pp 139ndash146
[551] P Schroumlder W Sweldens Spherical wavelets Efficiently representing functions on thesphere in Computer Graphics Proceedings (SIGGRAPH95) (ACM Siggraph Los Angeles1995) pp 161ndash175
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[554] H Scutaru Coherent states and induced representations Lett Math Phys 2 101ndash107(1977)
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Math 137 82ndash203 (1998)[557] R Simon ECG Sudarshan N Mukunda Gaussian pure states in quantum mechanics
and the symplectic group Phys Rev A37 3028ndash3038 (1988)[558] S Sivakumar Studies on nonlinear coherent states J Opt B Quant Semiclass Opt 2
R61ndashR75 (2000)[559] E Slezak A Bijaoui G Mars Identification of structures from galaxy counts Use of the
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A 196 29ndash34 (1994)[561] SB Sontz Paragrassmann algebras as quantum spaces Part I Reproducing kernels in
Geometric Methods in Physics XXXI Workshop 2012 (Trends in Mathematics ed byP Kielanowski et al Birkhaumluser Verlag Basel 2013) pp 47ndash63
[562] SB Sontz Paragrassmann algebras as quantum spaces Part II Toeplitz operators J OperTh (2013 to appear) arXiv12055493
[563] SB Sontz A reproducing kernel and Toeplitz operators in the quantum plane Preprint(2013) arXiv13056986 [math-ph]
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[572] W Sweldens The lifting scheme A custom-design construction of biorthogonal waveletsApplied Comput Harmon Anal 3 1186ndash1200 (1996)
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[575] FH Szafraniec Multipliers in the reproducing kernel Hilbert space subnormality andnoncommutative complex analysis in Reproducing Kernel Spaces and Applications edby D Alpay Operator Theory Advances and Applications vol 143 (Birkhaumluser Basel2003) pp 313ndash331
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Proceedings of the 27th International Cosmic Ray Conference (ICRC 2001) (CopernicusGesellschaft DE 2001) pp 2923ndash2926
[579] T Thiemann Gauge field theory coherent states (GCS) 1 General properties Class QuantGrav 18 2025ndash2064 (2001)
[580] T Thiemann O Winkler Gauge field theory coherent states (GCS) 2 Peakednessproperties Class Quant Grav 18 2561ndash2636 (2001)
[581] T Thiemann O Winkler Gauge field theory coherent states (GCS) 3 Ehrenfest theoremsClass Quant Grav 18 4629ndash4682 (2001)
[582] T Thiemann O Winkler Gauge field theory coherent states (GCS) 4 Infinite tensorproduct and thermodynamical limit Class Quant Grav 18 4997ndash5054 (2001)
[583] K Thirulagasanthar ST Ali Regular subspaces of a quaternionic Hilbert space fromquaternionic Hermite polynomials and associated coherent states J Math Phys 54013506 (2013)
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Ann Inst H Poincareacute 56 215ndash234 (1992)[588] B Torreacutesani Position-frequency analysis for signals defined on spheres Signal Proc 43
341ndash346 (2005)[589] DA Trifonov Generalized intelligent states and squeezing J Math Phys 35 2297ndash2308
(1994)[590] AS Trushechkin IV Volovich Localization properties of squeezed quantum states in
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simulation of an impact test using wavelets analytical and finite element models Int JSolids Struct 38 5481ndash5508 (2001)
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[595] J Ville Theacuteorie et applications de la notion de signal analytique Cacircbles et Trans 2 61ndash74(1948)
[596] J Voisin On some unitary representations of the Galilei group I Irreducible representa-tions J Math Phys 6 1519ndash1529 (1965)
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[598] DF Walls Squeezed states of light Nature 306 141ndash146 (1983)[599] YK Wang FT Hioe Phase transition in the Dicke maser model Phys Rev A 7 831ndash836
(1973)[600] PSP Wang J Yang A review of wavelet-based edge detection methods Int J Patt
Recogn Artif Intell 26 1255011 (2012)[601] I Weinreich A construction of C1-wavelets on the two-dimensional sphere Appl Comput
Harmon Anal 10 1ndash26 (2001)[602] H Weyl Quantenmechanik und Gruppentheorie Z Phys 46 1ndash46 (1927)
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[605] Y Wiaux JD McEwen P Vandergheynst O Blanc Exact reconstruction with directionalwavelets on the sphere Mon Not R Astron Soc 388 770ndash788 (2008)
[606] WM Wieland Complex Ashtekar variables and reality conditions for Holstrsquos action AnnHenri Poincareacute 13 425ndash448 (2012)
[607] EP Wigner On the quantum correction for thermodynamic equilibrium Phys Rev 40749ndash759 (1932)
[608] RM Willette RD Nowak Platelets A multiscale approach for recovering edges andsurfaces in photon-limited medical imaging IEEE Trans Med Imaging 22 332ndash350(2003)
[609] W Wisnoe P Gajan A Strzelecki C Lempereur J-M Matheacute The use of the two-dimensional wavelet transform in flow visualization processing in Progress in WaveletAnalysis and Applications (Proc Toulouse 1992) ed by Y Meyer S Roques (EdFrontiegraveres Gif-sur-Yvette 1993) pp 455ndash458
[610] K Woacutedkiewicz On the quantum mechanics of squeezed states J Modern Optics 34 941ndash948(1987)
[611] JA Yeazell M Mallalieu CR Stroud Jr Observation of the collapse and revival of aRydberg electronic wave packet Phys Rev Lett 64 2007ndash2010 (1990)
[612] JA Yeazell CR Stroud Jr Observation of fractional revivals in the evolution of aRydberg atomic wave packet Phys Rev A 43 5153ndash5156 (1991)
[613] HP Yuen Two-photon coherent states of the radiation field Phys Rev A 13 2226ndash2243(1976)
[614] J Zak Balian-Low theorem for Landau levels Phys Rev Lett 79 533ndash536 (1997)[615] J Zak Orthonormal sets of localized functions for a Landau level J Math Phys 39 4195ndash
4200 (1998) and references quoted there[616] AA Zakharova On the properties of generalized frames Math Notes 83 190ndash200 (2008)[617] W-M Zhang DH Feng R Gilmore Coherent states Theory and some applications Rev
Mod Phys 26 867ndash927 (1990)[618] I Zlatev W-M Zhang DH Feng Possibility that Schroumldingerrsquos conjecture for the
hydrogen atom coherent states is not attainable Phys Rev A 50 R1973ndashR1975 (1994)[619] WH Zurek Decoherence einselection and the quantum origins of the classical Rev Mod
Phys 75 715ndash775 (2003)[620] WH Zurek S Habib JP Paz Coherent states via decoherence Phys Rev Lett 70 1187ndash
1190 (1993)[621] K Zyczkowski Squeezed states in a quantum chaotic system J Phys A Math Theor 22
of SU(11) 81 296 297HilbertClowast-modules 164holomorphic 140nonholomorphic 151nonlinear 146of affine Galilei group 505of affine Poincareacute group 509of affine Weyl-Heisenberg group GaWH
497of compact semisimple Lie groups 174of Euclidean group E(n) 266of Galilei group G (11) 290of isochronous Galilei group 237of non-semisimple Lie groups 179of noncompact semisimple Lie groups 177of Poincareacute group Puarr
+(11) 283massless case 288
of Poincareacute group Puarr+(13) 279
of Schroumldinger group 508quasi-coherent states 186quaternionic 164
ST Ali et al Coherent States Wavelets and Their Generalizations Theoreticaland Mathematical Physics DOI 101007978-1-4614-8535-3copy Springer Science+Business Media New York 2014
573
574 Index
coherent states (CS) (cont)spin or SU(2) 175square integrable covariant 166 180 264vector (VCS) 73 108 112 170weighted 184 523
of affine Weyl-Heisenberg group GaWH497
of Poincareacute group Puarr+(11) 284
cohomology group 393 403coboundaries 403cochains 402cocycle 403
algebraic 387Cauchy 418Cauchy-Paul 354 419 425conical 418difference 417 462directional 416 440kinematical 499local 488metabolite-based 355 374minimal uncertainty 425multiselective 440on a graph 493on the sphere S
2 458on the sphere S
n 479on the torus T2 481steerable 439von Mises 440
wedgelet transform 455Wigner function 322Wigner-Ville transform 349Windowed Fourier or Gabor transform 349
ZZak transform 518
References
A Books and Theses
B Articles
Index
564 References
[430] Y Kuroda A Wada T Yamazaki K Nagayama Postacquisition data processing methodfor suppression of the solvent signal II The weighted first derivative J Magn Reson 88141ndash145 (1990)
[431] G Kutyniok D Labate Resolution of the wavefront set using continuous shearlets TransAmer Math Soc 361 2719ndash2754 (2009)
[432] G Kutyniok W-Q Lim Compactly supported shearlets are optimally sparse J ApproxTheory 163 1564ndash1589 (2011)
[433] D Labate W-Q Lim G Kutyniok G Weiss Sparse multidimensional representationusing shearlets in Wavelets XI (San Diego CA 2005) ed by M Papadakis A Laine MUnser SPIE Proceedings vol 5914 (SPIE Bellingham WA 2005) pp 254ndash262
[434] P Lahti J-P Pellonpaumlauml Continuous variable tomographic measurements Phys Lett A373 3435ndash3438 (2009)
[435] Lambertrsquos projection see WikipediahttpenwikipediaorgwikiLambert_azimuthal_equal-area_projection
[436] J-P Leduc F Mujica R Murenzi MJT Smith Missile-tracking algorithm using target-adapted spatio-temporal wavelets in Automatic Object Recognition VII SPIE Proceedingsvol 5914 (SPIE Bellingham WA 1997) pp 400ndash411
[437] J-P Leduc F Mujica R Murenzi MJT Smith Spatio-temporal wavelet transforms formotion tracking in IEEE ICASSP 1997 vol 4 (1997) pp 3013ndash3016
[438] J-P Leduc F Mujica R Murenzi MJT Smith Spatio-temporal continuous waveletsapplied to missile warhead detection and tracking in SPIE VCIP rsquo97 vol 3024 ed byJ Biemond EJ Delp (1997) pp 787ndash798
[439] B Leistedt JD McEwen Exact wavelets on the ball IEEE Trans Signal Proc 60 1564ndash1589 (2012)
[440] PG Lemarieacute Y Meyer Ondelettes et bases hilbertiennes Rev Math Iberoamer 2 1ndash18(1986)
[441] C Lemke A Schuck Jr J-P Antoine D Sima Metabolite-sensitive analysis of magneticresonance spectroscopic signals using the continuous wavelet transform Meas SciTechnol 22 (2011) Art 114013
[442] J-M Leacutevy-Leblond Galilei group and non-relativistic quantum mechanics J Math Phys4 776-788 (1963)
[443] J-M Leacutevy-Leblond Galilei group and Galilean invariance in Group Theory and ItsApplications vol II ed by EM Loebl (Academic New York 1971) pp 221ndash299
[444] J-M Leacutevy-Leblond On the conceptual nature of the physical constants Riv Nuovo Cim7 187ndash214 (1977)
[445] EH Lieb The classical limit of quantum spin systems Commun Math Phys 31 327ndash340(1973)
[446] G Lindblad B Nagel Continuous bases for unitary irreducible representations of SU(11)Ann Inst H Poincareacute 13 27ndash56 (1970)
[447] W Lisiecki Kaumlhler coherent states orbits for representations of semisimple Lie groupsAnn Inst H Poincareacute 53 857ndash890 (1990)
[448] A Lisowska Moment-based fast wedgelet transform J Math Imaging Vis 39 180ndash192(2011)
[449] H Liu L Peng Admissible wavelets associated with the Heisenberg group Pacific JMath 180 101ndash123 (1997)
[450] E Livine S Speziale Physical boundary state for the quantum tetrahedron Class QuantGrav 25 085003 (2008)
[451] F Low Complete sets of wave packets in A Passion for Physics ndash Essay in Honor ofGeoffrey Chew ed by C DeTar (World Scientific Singapore 1985) pp 17ndash22
[452] G Mack All unitary ray representations of the conformal group SU(22) with positiveenergy Commun Math Phys 55 1ndash28 (1977)
[453] GW Mackey Imprimitivity for representations of locally compact groups I Proc NatAcad Sci 35 537ndash545 (1949)
References 565
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[455] M Mallalieu CR Stroud Jr Rydberg wave packets fractional revivals and classicalorbits in Coherent States Past Present and Future (Proc Oak Ridge 1993) ed by DHFeng JR Klauder M Strayer (World Scientific Singapore 1994) pp 301ndash314
[456] SG Mallat Multifrequency channel decompositions of images and wavelet models IEEETrans Acoust Speech Signal Proc 37 2091ndash2110 (1989)
[457] SG Mallat A theory for multiresolution signal decomposition The wavelet representa-tion IEEE Trans Pattern Anal Machine Intell 11 674ndash693 (1989)
[458] S Mallat W-L Hwang Singularity detection and processing with wavelets IEEE TransInform Theory 38 617ndash643 (1992)
[459] S Mallat Z Zhang Matching pursuits with time frequency dictionaries IEEE TransSignal Proc 41 3397ndash3415 (1993)
[460] S Mallat S Zhong Wavelet maxima representation in Wavelets and Applications (ProcMarseille 1989) ed by Y Meyer (Masson and Springer Paris and Berlin 1991) pp 207ndash284
[461] VI Manrsquoko G Marmo ECG Sudarshan F Zaccaria f -oscillators and non-linearcoherent states Phys Scr 55 528ndash541 (1997)
[462] D Marinucci D Pietrobon A Baldi P Baldi P Cabella G Kerkyacharian P Natoli DPicard N Vittorio Spherical needlets for CMB data analysis Mon Not R Astron Soc383 539ndash545 (2008)
[463] D Marion M Ikura A Bax Improved solvent suppression in one- and two-dimensionalNMR spectra by convolution of time-domain data J Magn Reson 84 425ndash430 (1989)
[464] Y Meyer Principe drsquoincertitude bases hilbertiennes et algegravebres drsquoopeacuterateurs SeacuteminaireBourbaki 662 (1985ndash1986)
[465] Y Meyer Principe drsquoincertitude bases hilbertiennes et algegravebres drsquoopeacuterateurs Asteacuterisque145ndash146 209ndash223 (1987)
[466] Y Meyer H Xu Wavelet analysis and chirps Appl Comput Harmon Anal 4 366ndash379(1997)
[467] L Michel Invariance in quantum mechanics and group extensions in Group TheoreticalConcepts and Methods in Elementary Particle Physics ed by F Guumlrsey (Gordon andBreach New York and London 1964) pp 135ndash200
[468] J Mickelsson J Niederle Contractions of representations of the de Sitter groupsCommun Math Phys 27 167ndash180 (1972)
[469] MM Miller Convergence of the Sudarshan expansion for the diagonal coherent-stateweight functional J Math Phys 9 1270ndash1274 (1968)
[470] V F Molchanov Harmonic analysis on homogeneous spaces in Representation Theoryand Noncommutative Harmonic Analysis II ed by AA Kirillov (Springer Berlin 1995)
[471] MI Monastyrsky AM Perelomov Coherent states and symmetric spaces II Ann InstH Poincareacute 23 23ndash48 (1975)
[472] B Moran S Howard D Cochran Positive-operator-valued measures A general settingfor frames in Excursions in Harmonic Analysis vol 1 2 ed by TD Andrews R BalanJJ Benedetto W Czaja KA Okoudjou (Birkhaumluser Boston 2013) pp 49ndash64
[473] H Moscovici Coherent states representations of nilpotent Lie groups Commun MathPhys 54 63ndash68 (1977)
[474] H Moscovici A Verona Coherent states and square integrable representations Ann InstH Poincareacute 29 139ndash156 (1978)
[475] F Mujica R Murenzi MJT Smith J-P Leduc Robust tracking in compressed imagesequences J Electr Imaging 7 746ndash754 (1998)
[476] R Murenzi Wavelet transforms associated to the n-dimensional Euclidean group withdilations Signals in more than one dimension in Wavelets Time-Frequency Methodsand Phase Space (Proc Marseille 1987) ed by J-M Combes A Grossmann PTchamitchian 2nd edn (Springer Berlin 1990) pp 239ndash246
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[478] B Nagel Generalized eigenvectors in group representations in Studies in MathematicalPhysics (Proc Istanbul 1970) ed by AO Barut (Reidel Dordrecht and Boston 1970)pp 135ndash154
[479] MA Naımark Dokl Akad Nauk SSSR 41 359ndash361 (1943) see also B Sz-NagyExtensions of linear transformations in Hilbert space which extend beyond this spaceAppendix to F Riesz B Sz-Nagy Functional Analysis (Frederick Ungar New York 1960)
[480] FJ Narcowich P Petrushev JD Ward Localized tight frames on spheres SIAM J MathAnal 38 574ndash594 (2006)
[481] M Nauenberg Quantum wave packets on Kepler elliptic orbits Phys Rev A 40 1133ndash1136 (1989)
[482] M Nauenberg C Stroud J Yeazell The classical limit of an atom Scient Amer 27024ndash29 (1994)
[483] H Neumann Transformation properties of observables Helv Phys Acta 45 811ndash819(1972)
[484] U Niederer The maximal kinematical invariance group of the free Schroumldinger equationHelv Phys Acta 45 802ndash881 (1972)
[485] MM Nieto LM Simmons Jr Coherent states for general potentials I Formalism IIConfining one-dimensional examples III Nonconfining one-dimensional examples PhysRev D 20 1321ndash1331 1332ndash1341 1342ndash1350 (1979)
[486] MM Nieto LM Simmons Jr Coherent states for general potentials Phys Rev Lett 41207ndash210 (1987)
[487] A Odzijewicz On reproducing kernels and quantization of states Commun Math Phys114 577ndash597 (1988)
[488] A Odzijewicz Coherent states and geometric quantization Commun Math Phys 150385ndash413 (1992)
[489] A Odzijewicz Quantum algebras and q-special functions related to coherent states mapsof the disc Commun Math Phys 192 183ndash215 (1998)
[490] A Odzijewicz M Horowski A Tereszkiewicz Integrable multi-boson systems andorthogonal polynomials J Phys A Math Gen 34 4353ndash4376 (2001)
[491] G Oacutelafsson B Oslashrsted The holomorphic discrete series for affine symmetric spaces JFunct Anal 81 126ndash159 (1988)
[492] G Oacutelafsson H Schlichtkrull Representation theory Radon transform and the heatequation on a Riemannian symmetric space Contemp Math 449 315ndash344 (2008)
[493] E Onofri A note on coherent state representations of Lie groups J Math Phys 16 1087ndash1089 (1975)
[494] E Onofri Dynamical quantization of the Kepler manifold J Math Phys 17 401ndash408(1976)
[495] D Oriti R Pereira L Sindoni Coherent states in quantum gravity A construction basedon the flux representation of loop quantum gravity J Phys A Math Theor 45 244004(2012)
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[497] Z Pasternak-Winiarski On the dependence of the reproducing kernel on the weight ofintegration J Funct Anal 94 110ndash134 (1990)
[498] Z Pasternak-Winiarski On reproducing kernels for holomorphic vector bundles inQuantization and Infinite Dimensional Systems (Proc Białowieza Poland 1993) ed by J-P Antoine ST Ali W Lisiecki IM Mladenov A Odzijewicz (Plenum Press New Yorkand London 1994) pp 109ndash112
[499] T Paul Affine coherent states and the radial Schroumldinger equation I preprint CPT-84P1710 (1984) (unpublished)
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[501] AM Perelomov On the completeness of a system of coherent states Theor Math Phys6 156ndash164 (1971)
[502] AM Perelomov Coherent states for arbitrary Lie group Commun Math Phys 26 222ndash236 (1972)
[503] AM Perelomov Coherent states and symmetric spaces Commun Math Phys 44 197ndash210 (1975)
[504] M Perroud Projective representations of the Schroumldinger group Helv Phys Acta 50 233ndash252 (1977)
[505] J Phillips A note on square-integrable representations J Funct Anal 20 83ndash92 (1975)[506] D Pietrobon P Baldi D Marinucci Integrated Sachs-Wolfe effect from the cross
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[508] V Pop D Rosca Generalized piecewise constant orthogonal wavelet bases on 2D-domains Appl Anal 90 715ndash723 (2011)
[509] G Poumlschl E Teller Bemerkungen zur Quantenmechanik des anharmonischen OszillatorsZ Physik 83 143ndash151 (1933)
[510] D Potts G Steidl M Tasche Kernels of spherical harmonics and spherical frames inAdvanced Topics in Multivariate Approximation ed by F Fontanella K Jetter PJ Laurent(World Scientific Singapore 1996) pp 287ndash301
[511] E Prugovecki Consistent formulation of relativistic dynamics for massive spin-zeroparticles in external fields Phys Rev D 18 3655ndash3673 (1978) (Appendix C)
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[516] A Rahimi A Najati YN Dehghan Continuous frames in Hilbert spaces Methods FunctAnal Topol 12 170ndash182 (2006)
[517] H Rauhut M Roumlsler Radial multiresolution in dimension three Constr Approx 22 193ndash218 (2005)
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[521] D Robert La coheacuterence dans tous ses eacutetats SMF Gazette 132 (2012)[522] JE Roberts The Dirac bra and ket formalism J Math Phys 7 1097ndash1104 (1966)[523] JE Roberts Rigged Hilbert spaces in quantum mechanics Commun Math Phys 3 98ndash
119 (1966)[524] S Roques F Bourzeix K Bouyoucef Soft-thresholding technique and restoration of
3C273 jet Astrophys Space Sci Nr 239 297ndash304 (1996)[525] D Rosca Haar wavelets on spherical triangulations in Advances in Multiresolution for
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Wavelets Multiresolut Inf Process 6 209ndash222 (2008)[531] D Rosca On a norm equivalence on L2(S2) Results Math 53 399ndash405 (2009)[532] D Rosca New uniform grids on the sphere Astron Astrophys 520 (2010) Art A63[533] D Rosca Uniform and refinable grids on elliptic domains and on some surfaces of
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Appl Comput Harmon Anal 30 262ndash272 (2011)[535] D Rosca J-P Antoine Locally supported orthogonal wavelet bases on the sphere via
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[537] D Rosca G Plonka Uniform spherical grids via area preserving projection from the cubeto the sphere J Comput Appl Math 236 1033ndash1041 (2011)
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[539] H Rossi M Vergne Analytic continuation of the holomorphic discrete series for a semi-simple Lie group Acta Math 136 1ndash59 (1976)
[540] DJ Rotenberg Application of Sturmian functions to the Schroedinger three-body prob-lem Elastic e+ndashH scattering Ann Phys (NY) 19 262ndash278 (1962)
[541] C Rovelli Zakopane lectures on loop gravity in Proceedings of 3rd Quantum Gravityand Quantum Geometry School 28 Febndash13 March 2011 (Zakopane Poland 2011)arXiv11023660v5
[542] C Rovelli S Speziale A semiclassical tetrahedron Class Quant Grav 23 5861ndash5870(2006)
[543] DJ Rowe Coherent state theory of the noncompact symplectic group J Math Phys 252662ndash2271 (1984)
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[546] DJ Rowe J Repka Vector-coherent-state theory as a theory of induced representationsJ Math Phys 32 2614ndash2634 (1991)
[547] DJ Rowe G Rosensteel R Gilmore Vector coherent state representation theory J MathPhys 26 2787ndash2791 (1985)
[548] A Royer Phase states and phase operators for the quantum harmonic oscillator Phys RevA 53 70ndash108 (1996)
[549] J Saletan Contraction of Lie groups J Math Phys 2 1ndash21 (1961)[550] G Saracco A Grossmann P Tchamitchian Use of wavelet transforms in the study of
propagation of transient acoustic signals across a plane interface between two homoge-neous media in Wavelets Time-Frequency Methods and Phase Space (Proc Marseille1987) ed by J-M Combes A Grossmann P Tchamitchian 2nd edn (Springer Berlin1990) pp 139ndash146
[551] P Schroumlder W Sweldens Spherical wavelets Efficiently representing functions on thesphere in Computer Graphics Proceedings (SIGGRAPH95) (ACM Siggraph Los Angeles1995) pp 161ndash175
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[554] H Scutaru Coherent states and induced representations Lett Math Phys 2 101ndash107(1977)
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and the symplectic group Phys Rev A37 3028ndash3038 (1988)[558] S Sivakumar Studies on nonlinear coherent states J Opt B Quant Semiclass Opt 2
R61ndashR75 (2000)[559] E Slezak A Bijaoui G Mars Identification of structures from galaxy counts Use of the
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Geometric Methods in Physics XXXI Workshop 2012 (Trends in Mathematics ed byP Kielanowski et al Birkhaumluser Verlag Basel 2013) pp 47ndash63
[562] SB Sontz Paragrassmann algebras as quantum spaces Part II Toeplitz operators J OperTh (2013 to appear) arXiv12055493
[563] SB Sontz A reproducing kernel and Toeplitz operators in the quantum plane Preprint(2013) arXiv13056986 [math-ph]
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[572] W Sweldens The lifting scheme A custom-design construction of biorthogonal waveletsApplied Comput Harmon Anal 3 1186ndash1200 (1996)
[573] W Sweldens The lifting scheme A construction of second generation wavelets SIAM JMath Anal 29 511ndash546 (1998)
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[579] T Thiemann Gauge field theory coherent states (GCS) 1 General properties Class QuantGrav 18 2025ndash2064 (2001)
[580] T Thiemann O Winkler Gauge field theory coherent states (GCS) 2 Peakednessproperties Class Quant Grav 18 2561ndash2636 (2001)
[581] T Thiemann O Winkler Gauge field theory coherent states (GCS) 3 Ehrenfest theoremsClass Quant Grav 18 4629ndash4682 (2001)
[582] T Thiemann O Winkler Gauge field theory coherent states (GCS) 4 Infinite tensorproduct and thermodynamical limit Class Quant Grav 18 4997ndash5054 (2001)
[583] K Thirulagasanthar ST Ali Regular subspaces of a quaternionic Hilbert space fromquaternionic Hermite polynomials and associated coherent states J Math Phys 54013506 (2013)
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Ann Inst H Poincareacute 56 215ndash234 (1992)[588] B Torreacutesani Position-frequency analysis for signals defined on spheres Signal Proc 43
341ndash346 (2005)[589] DA Trifonov Generalized intelligent states and squeezing J Math Phys 35 2297ndash2308
(1994)[590] AS Trushechkin IV Volovich Localization properties of squeezed quantum states in
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simulation of an impact test using wavelets analytical and finite element models Int JSolids Struct 38 5481ndash5508 (2001)
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[596] J Voisin On some unitary representations of the Galilei group I Irreducible representa-tions J Math Phys 6 1519ndash1529 (1965)
[597] A Vourdas Analytic representations in quantum mechanics J Phys A Math Gen 39R65ndashR141 (2006)
[598] DF Walls Squeezed states of light Nature 306 141ndash146 (1983)[599] YK Wang FT Hioe Phase transition in the Dicke maser model Phys Rev A 7 831ndash836
(1973)[600] PSP Wang J Yang A review of wavelet-based edge detection methods Int J Patt
Recogn Artif Intell 26 1255011 (2012)[601] I Weinreich A construction of C1-wavelets on the two-dimensional sphere Appl Comput
Harmon Anal 10 1ndash26 (2001)[602] H Weyl Quantenmechanik und Gruppentheorie Z Phys 46 1ndash46 (1927)
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[603] Y Wiaux L Jacques P Vandergheynst Correspondence principle between spherical andEuclidean wavelets Astrophys J 632 15ndash28 (2005)
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[605] Y Wiaux JD McEwen P Vandergheynst O Blanc Exact reconstruction with directionalwavelets on the sphere Mon Not R Astron Soc 388 770ndash788 (2008)
[606] WM Wieland Complex Ashtekar variables and reality conditions for Holstrsquos action AnnHenri Poincareacute 13 425ndash448 (2012)
[607] EP Wigner On the quantum correction for thermodynamic equilibrium Phys Rev 40749ndash759 (1932)
[608] RM Willette RD Nowak Platelets A multiscale approach for recovering edges andsurfaces in photon-limited medical imaging IEEE Trans Med Imaging 22 332ndash350(2003)
[609] W Wisnoe P Gajan A Strzelecki C Lempereur J-M Matheacute The use of the two-dimensional wavelet transform in flow visualization processing in Progress in WaveletAnalysis and Applications (Proc Toulouse 1992) ed by Y Meyer S Roques (EdFrontiegraveres Gif-sur-Yvette 1993) pp 455ndash458
[610] K Woacutedkiewicz On the quantum mechanics of squeezed states J Modern Optics 34 941ndash948(1987)
[611] JA Yeazell M Mallalieu CR Stroud Jr Observation of the collapse and revival of aRydberg electronic wave packet Phys Rev Lett 64 2007ndash2010 (1990)
[612] JA Yeazell CR Stroud Jr Observation of fractional revivals in the evolution of aRydberg atomic wave packet Phys Rev A 43 5153ndash5156 (1991)
[613] HP Yuen Two-photon coherent states of the radiation field Phys Rev A 13 2226ndash2243(1976)
[614] J Zak Balian-Low theorem for Landau levels Phys Rev Lett 79 533ndash536 (1997)[615] J Zak Orthonormal sets of localized functions for a Landau level J Math Phys 39 4195ndash
4200 (1998) and references quoted there[616] AA Zakharova On the properties of generalized frames Math Notes 83 190ndash200 (2008)[617] W-M Zhang DH Feng R Gilmore Coherent states Theory and some applications Rev
Mod Phys 26 867ndash927 (1990)[618] I Zlatev W-M Zhang DH Feng Possibility that Schroumldingerrsquos conjecture for the
hydrogen atom coherent states is not attainable Phys Rev A 50 R1973ndashR1975 (1994)[619] WH Zurek Decoherence einselection and the quantum origins of the classical Rev Mod
Phys 75 715ndash775 (2003)[620] WH Zurek S Habib JP Paz Coherent states via decoherence Phys Rev Lett 70 1187ndash
1190 (1993)[621] K Zyczkowski Squeezed states in a quantum chaotic system J Phys A Math Theor 22
of SU(11) 81 296 297HilbertClowast-modules 164holomorphic 140nonholomorphic 151nonlinear 146of affine Galilei group 505of affine Poincareacute group 509of affine Weyl-Heisenberg group GaWH
497of compact semisimple Lie groups 174of Euclidean group E(n) 266of Galilei group G (11) 290of isochronous Galilei group 237of non-semisimple Lie groups 179of noncompact semisimple Lie groups 177of Poincareacute group Puarr
+(11) 283massless case 288
of Poincareacute group Puarr+(13) 279
of Schroumldinger group 508quasi-coherent states 186quaternionic 164
ST Ali et al Coherent States Wavelets and Their Generalizations Theoreticaland Mathematical Physics DOI 101007978-1-4614-8535-3copy Springer Science+Business Media New York 2014
573
574 Index
coherent states (CS) (cont)spin or SU(2) 175square integrable covariant 166 180 264vector (VCS) 73 108 112 170weighted 184 523
of affine Weyl-Heisenberg group GaWH497
of Poincareacute group Puarr+(11) 284
cohomology group 393 403coboundaries 403cochains 402cocycle 403
algebraic 387Cauchy 418Cauchy-Paul 354 419 425conical 418difference 417 462directional 416 440kinematical 499local 488metabolite-based 355 374minimal uncertainty 425multiselective 440on a graph 493on the sphere S
2 458on the sphere S
n 479on the torus T2 481steerable 439von Mises 440
wedgelet transform 455Wigner function 322Wigner-Ville transform 349Windowed Fourier or Gabor transform 349
ZZak transform 518
References
A Books and Theses
B Articles
Index
References 565
[454] S Majid M Rodriguez-Plaza Random walk and the heat equation on superspace andanyspace J Math Phys 35 3753ndash3760 (1994)
[455] M Mallalieu CR Stroud Jr Rydberg wave packets fractional revivals and classicalorbits in Coherent States Past Present and Future (Proc Oak Ridge 1993) ed by DHFeng JR Klauder M Strayer (World Scientific Singapore 1994) pp 301ndash314
[456] SG Mallat Multifrequency channel decompositions of images and wavelet models IEEETrans Acoust Speech Signal Proc 37 2091ndash2110 (1989)
[457] SG Mallat A theory for multiresolution signal decomposition The wavelet representa-tion IEEE Trans Pattern Anal Machine Intell 11 674ndash693 (1989)
[458] S Mallat W-L Hwang Singularity detection and processing with wavelets IEEE TransInform Theory 38 617ndash643 (1992)
[459] S Mallat Z Zhang Matching pursuits with time frequency dictionaries IEEE TransSignal Proc 41 3397ndash3415 (1993)
[460] S Mallat S Zhong Wavelet maxima representation in Wavelets and Applications (ProcMarseille 1989) ed by Y Meyer (Masson and Springer Paris and Berlin 1991) pp 207ndash284
[461] VI Manrsquoko G Marmo ECG Sudarshan F Zaccaria f -oscillators and non-linearcoherent states Phys Scr 55 528ndash541 (1997)
[462] D Marinucci D Pietrobon A Baldi P Baldi P Cabella G Kerkyacharian P Natoli DPicard N Vittorio Spherical needlets for CMB data analysis Mon Not R Astron Soc383 539ndash545 (2008)
[463] D Marion M Ikura A Bax Improved solvent suppression in one- and two-dimensionalNMR spectra by convolution of time-domain data J Magn Reson 84 425ndash430 (1989)
[464] Y Meyer Principe drsquoincertitude bases hilbertiennes et algegravebres drsquoopeacuterateurs SeacuteminaireBourbaki 662 (1985ndash1986)
[465] Y Meyer Principe drsquoincertitude bases hilbertiennes et algegravebres drsquoopeacuterateurs Asteacuterisque145ndash146 209ndash223 (1987)
[466] Y Meyer H Xu Wavelet analysis and chirps Appl Comput Harmon Anal 4 366ndash379(1997)
[467] L Michel Invariance in quantum mechanics and group extensions in Group TheoreticalConcepts and Methods in Elementary Particle Physics ed by F Guumlrsey (Gordon andBreach New York and London 1964) pp 135ndash200
[468] J Mickelsson J Niederle Contractions of representations of the de Sitter groupsCommun Math Phys 27 167ndash180 (1972)
[469] MM Miller Convergence of the Sudarshan expansion for the diagonal coherent-stateweight functional J Math Phys 9 1270ndash1274 (1968)
[470] V F Molchanov Harmonic analysis on homogeneous spaces in Representation Theoryand Noncommutative Harmonic Analysis II ed by AA Kirillov (Springer Berlin 1995)
[471] MI Monastyrsky AM Perelomov Coherent states and symmetric spaces II Ann InstH Poincareacute 23 23ndash48 (1975)
[472] B Moran S Howard D Cochran Positive-operator-valued measures A general settingfor frames in Excursions in Harmonic Analysis vol 1 2 ed by TD Andrews R BalanJJ Benedetto W Czaja KA Okoudjou (Birkhaumluser Boston 2013) pp 49ndash64
[473] H Moscovici Coherent states representations of nilpotent Lie groups Commun MathPhys 54 63ndash68 (1977)
[474] H Moscovici A Verona Coherent states and square integrable representations Ann InstH Poincareacute 29 139ndash156 (1978)
[475] F Mujica R Murenzi MJT Smith J-P Leduc Robust tracking in compressed imagesequences J Electr Imaging 7 746ndash754 (1998)
[476] R Murenzi Wavelet transforms associated to the n-dimensional Euclidean group withdilations Signals in more than one dimension in Wavelets Time-Frequency Methodsand Phase Space (Proc Marseille 1987) ed by J-M Combes A Grossmann PTchamitchian 2nd edn (Springer Berlin 1990) pp 239ndash246
566 References
[477] MA Muschietti B Torreacutesani Pyramidal algorithms for LittlewoodndashPaley decomposi-tions SIAM J Math Anal 26 925ndash943 (1995)
[478] B Nagel Generalized eigenvectors in group representations in Studies in MathematicalPhysics (Proc Istanbul 1970) ed by AO Barut (Reidel Dordrecht and Boston 1970)pp 135ndash154
[479] MA Naımark Dokl Akad Nauk SSSR 41 359ndash361 (1943) see also B Sz-NagyExtensions of linear transformations in Hilbert space which extend beyond this spaceAppendix to F Riesz B Sz-Nagy Functional Analysis (Frederick Ungar New York 1960)
[480] FJ Narcowich P Petrushev JD Ward Localized tight frames on spheres SIAM J MathAnal 38 574ndash594 (2006)
[481] M Nauenberg Quantum wave packets on Kepler elliptic orbits Phys Rev A 40 1133ndash1136 (1989)
[482] M Nauenberg C Stroud J Yeazell The classical limit of an atom Scient Amer 27024ndash29 (1994)
[483] H Neumann Transformation properties of observables Helv Phys Acta 45 811ndash819(1972)
[484] U Niederer The maximal kinematical invariance group of the free Schroumldinger equationHelv Phys Acta 45 802ndash881 (1972)
[485] MM Nieto LM Simmons Jr Coherent states for general potentials I Formalism IIConfining one-dimensional examples III Nonconfining one-dimensional examples PhysRev D 20 1321ndash1331 1332ndash1341 1342ndash1350 (1979)
[486] MM Nieto LM Simmons Jr Coherent states for general potentials Phys Rev Lett 41207ndash210 (1987)
[487] A Odzijewicz On reproducing kernels and quantization of states Commun Math Phys114 577ndash597 (1988)
[488] A Odzijewicz Coherent states and geometric quantization Commun Math Phys 150385ndash413 (1992)
[489] A Odzijewicz Quantum algebras and q-special functions related to coherent states mapsof the disc Commun Math Phys 192 183ndash215 (1998)
[490] A Odzijewicz M Horowski A Tereszkiewicz Integrable multi-boson systems andorthogonal polynomials J Phys A Math Gen 34 4353ndash4376 (2001)
[491] G Oacutelafsson B Oslashrsted The holomorphic discrete series for affine symmetric spaces JFunct Anal 81 126ndash159 (1988)
[492] G Oacutelafsson H Schlichtkrull Representation theory Radon transform and the heatequation on a Riemannian symmetric space Contemp Math 449 315ndash344 (2008)
[493] E Onofri A note on coherent state representations of Lie groups J Math Phys 16 1087ndash1089 (1975)
[494] E Onofri Dynamical quantization of the Kepler manifold J Math Phys 17 401ndash408(1976)
[495] D Oriti R Pereira L Sindoni Coherent states in quantum gravity A construction basedon the flux representation of loop quantum gravity J Phys A Math Theor 45 244004(2012)
[496] LC Papaloucas J Rembielinski W Tybor Vectorlike coherent states with noncompactstability group J Math Phys 30 2406ndash2410 (1989)
[497] Z Pasternak-Winiarski On the dependence of the reproducing kernel on the weight ofintegration J Funct Anal 94 110ndash134 (1990)
[498] Z Pasternak-Winiarski On reproducing kernels for holomorphic vector bundles inQuantization and Infinite Dimensional Systems (Proc Białowieza Poland 1993) ed by J-P Antoine ST Ali W Lisiecki IM Mladenov A Odzijewicz (Plenum Press New Yorkand London 1994) pp 109ndash112
[499] T Paul Affine coherent states and the radial Schroumldinger equation I preprint CPT-84P1710 (1984) (unpublished)
References 567
[500] T Paul K Seip Wavelets in quantum mechanics in Wavelets and Their Applications edby MB Ruskai G Beylkin R Coifman I Daubechies S Mallat Y Meyer L Raphael(Jones and Bartlett Boston 1992) pp 303ndash322
[501] AM Perelomov On the completeness of a system of coherent states Theor Math Phys6 156ndash164 (1971)
[502] AM Perelomov Coherent states for arbitrary Lie group Commun Math Phys 26 222ndash236 (1972)
[503] AM Perelomov Coherent states and symmetric spaces Commun Math Phys 44 197ndash210 (1975)
[504] M Perroud Projective representations of the Schroumldinger group Helv Phys Acta 50 233ndash252 (1977)
[505] J Phillips A note on square-integrable representations J Funct Anal 20 83ndash92 (1975)[506] D Pietrobon P Baldi D Marinucci Integrated Sachs-Wolfe effect from the cross
correlation of WMAP3 year and the NRAO VLA sky survey data New results andconstraints on dark energy Phys Rev D 74 043524 (2006)
[507] WWF Pijnappel A van den Boogaart R de Beer D van Ormondt SVD-basedquantification of magnetic resonance signals J Magn Reson 97 122ndash134 (1992)
[508] V Pop D Rosca Generalized piecewise constant orthogonal wavelet bases on 2D-domains Appl Anal 90 715ndash723 (2011)
[509] G Poumlschl E Teller Bemerkungen zur Quantenmechanik des anharmonischen OszillatorsZ Physik 83 143ndash151 (1933)
[510] D Potts G Steidl M Tasche Kernels of spherical harmonics and spherical frames inAdvanced Topics in Multivariate Approximation ed by F Fontanella K Jetter PJ Laurent(World Scientific Singapore 1996) pp 287ndash301
[511] E Prugovecki Consistent formulation of relativistic dynamics for massive spin-zeroparticles in external fields Phys Rev D 18 3655ndash3673 (1978) (Appendix C)
[512] E Prugovecki Relativistic quantum kinematics on stochastic phase space for massiveparticles J MathPhys 19 2261ndash2270 (1978)
[513] C Quesne Coherent states of the real symplectic group in a complex analytic parametriza-tion I II J Math Phys 27 428ndash441 869ndash878 (1986)
[514] C Quesne Generalized vector coherent states of sp(2NR) vector operators and ofsp(2NR) sup u(N) reduced Wigner coefficients J Phys A Math Gen 24 2697ndash2714(1991)
[515] JM Radcliffe Some properties of spin coherent states J Phys A Math Gen 4 313ndash323(1971)
[516] A Rahimi A Najati YN Dehghan Continuous frames in Hilbert spaces Methods FunctAnal Topol 12 170ndash182 (2006)
[517] H Rauhut M Roumlsler Radial multiresolution in dimension three Constr Approx 22 193ndash218 (2005)
[518] JH Rawnsley Coherent states and Kaumlhler manifolds Quart J Math Oxford 28(2) 403ndash415 (1977)
[519] J Renaud The contraction of the SU(11) discrete series of representations by means ofcoherent states J Math Phys 37 3168ndash3179 (1996)
[520] A Reacutenyi Representations for real numbers and their ergodic properties Acta Math AcadSci Hungary 8(3ndash4) 477ndash493 (1957)
[521] D Robert La coheacuterence dans tous ses eacutetats SMF Gazette 132 (2012)[522] JE Roberts The Dirac bra and ket formalism J Math Phys 7 1097ndash1104 (1966)[523] JE Roberts Rigged Hilbert spaces in quantum mechanics Commun Math Phys 3 98ndash
119 (1966)[524] S Roques F Bourzeix K Bouyoucef Soft-thresholding technique and restoration of
3C273 jet Astrophys Space Sci Nr 239 297ndash304 (1996)[525] D Rosca Haar wavelets on spherical triangulations in Advances in Multiresolution for
Geometric Modelling ed by NA Dogson MS Floater MA Sabin (Springer Berlin2005) pp 407ndash419
568 References
[526] D Rosca Locally supported rational spline wavelets on the sphere Math Comput 741803ndash1829 (2005)
[527] D Rosca Wavelets defined on closed surfaces J Comput Anal Appl 8 121ndash132 (2006)[528] D Rosca Weighted Haar wavelets on the sphere Int J Wavelets Multiresol Inf Proc 5
501ndash511 (2007)[529] D Rosca Wavelet bases on the sphere obtained by radial projection J Fourier Anal Appl
13 421ndash434 (2007)[530] D Rosca Piecewise constant wavelets on triangulations obtained by 1ndash3 splitting Int J
Wavelets Multiresolut Inf Process 6 209ndash222 (2008)[531] D Rosca On a norm equivalence on L2(S2) Results Math 53 399ndash405 (2009)[532] D Rosca New uniform grids on the sphere Astron Astrophys 520 (2010) Art A63[533] D Rosca Uniform and refinable grids on elliptic domains and on some surfaces of
revolution Appl Math Comput 217 7812ndash7817 (2011)[534] D Rosca Wavelet analysis on some surfaces of revolution via area preserving projection
Appl Comput Harmon Anal 30 262ndash272 (2011)[535] D Rosca J-P Antoine Locally supported orthogonal wavelet bases on the sphere via
stereographic projection Math Probl Eng 2009 124904 (2009)[536] D Rosca J-P Antoine Constructing wavelet frames and orthogonal wavelet bases on the
sphere in Recent Advances in Signal Processing ed by S Miron (IN-TECH ViennaAustria and Rijeka Croatia 2010) pp 59ndash76
[537] D Rosca G Plonka Uniform spherical grids via area preserving projection from the cubeto the sphere J Comput Appl Math 236 1033ndash1041 (2011)
[538] D Rosca G Plonka An area preserving projection from the regular octahedron to thesphere Results Math 63 429ndash444 (2012)
[539] H Rossi M Vergne Analytic continuation of the holomorphic discrete series for a semi-simple Lie group Acta Math 136 1ndash59 (1976)
[540] DJ Rotenberg Application of Sturmian functions to the Schroedinger three-body prob-lem Elastic e+ndashH scattering Ann Phys (NY) 19 262ndash278 (1962)
[541] C Rovelli Zakopane lectures on loop gravity in Proceedings of 3rd Quantum Gravityand Quantum Geometry School 28 Febndash13 March 2011 (Zakopane Poland 2011)arXiv11023660v5
[542] C Rovelli S Speziale A semiclassical tetrahedron Class Quant Grav 23 5861ndash5870(2006)
[543] DJ Rowe Coherent state theory of the noncompact symplectic group J Math Phys 252662ndash2271 (1984)
[544] DJ Rowe Microscopic theory of the nuclear collective model Rep Prog Phys 48 1419ndash1480 (1985)
[545] DJ Rowe Vector coherent state representations and their inner products J Phys A MathGen 45 244003 (2012) (This paper belongs to the special issue [38])
[546] DJ Rowe J Repka Vector-coherent-state theory as a theory of induced representationsJ Math Phys 32 2614ndash2634 (1991)
[547] DJ Rowe G Rosensteel R Gilmore Vector coherent state representation theory J MathPhys 26 2787ndash2791 (1985)
[548] A Royer Phase states and phase operators for the quantum harmonic oscillator Phys RevA 53 70ndash108 (1996)
[549] J Saletan Contraction of Lie groups J Math Phys 2 1ndash21 (1961)[550] G Saracco A Grossmann P Tchamitchian Use of wavelet transforms in the study of
propagation of transient acoustic signals across a plane interface between two homoge-neous media in Wavelets Time-Frequency Methods and Phase Space (Proc Marseille1987) ed by J-M Combes A Grossmann P Tchamitchian 2nd edn (Springer Berlin1990) pp 139ndash146
[551] P Schroumlder W Sweldens Spherical wavelets Efficiently representing functions on thesphere in Computer Graphics Proceedings (SIGGRAPH95) (ACM Siggraph Los Angeles1995) pp 161ndash175
References 569
[552] E Schroumldinger Der stetige Uumlbergang von der Mikro- zur Makromechanik Naturwiss 14664ndash666 (1926)
[553] S Scodeller Oslash Rudjord FK Hansen D Marinucci D Geller A Mayeli IntroducingMexican needlets for CMB analysis Issues for practical applications and comparison withstandard needlets Astrophys J 733 (2011) Art 121
[554] H Scutaru Coherent states and induced representations Lett Math Phys 2 101ndash107(1977)
[555] B Simon Distributions and their Hermite expansions J Math Phys 12 140ndash148 (1971)[556] B Simon The classical moment problem as a self-adjoint finite difference operator Adv
Math 137 82ndash203 (1998)[557] R Simon ECG Sudarshan N Mukunda Gaussian pure states in quantum mechanics
and the symplectic group Phys Rev A37 3028ndash3038 (1988)[558] S Sivakumar Studies on nonlinear coherent states J Opt B Quant Semiclass Opt 2
R61ndashR75 (2000)[559] E Slezak A Bijaoui G Mars Identification of structures from galaxy counts Use of the
wavelet transform Astron Astroph 227 301ndash316 (1990)[560] A Solomon A characteristic functional for deformed photon phenomenology Phys Lett
A 196 29ndash34 (1994)[561] SB Sontz Paragrassmann algebras as quantum spaces Part I Reproducing kernels in
Geometric Methods in Physics XXXI Workshop 2012 (Trends in Mathematics ed byP Kielanowski et al Birkhaumluser Verlag Basel 2013) pp 47ndash63
[562] SB Sontz Paragrassmann algebras as quantum spaces Part II Toeplitz operators J OperTh (2013 to appear) arXiv12055493
[563] SB Sontz A reproducing kernel and Toeplitz operators in the quantum plane Preprint(2013) arXiv13056986 [math-ph]
[564] SB Sontz Toeplitz quantization of an algebra with conjugation Preprint (2013)arXiv13085454 [math-ph]
[565] M Spera On a generalized Uncertainty Principle coherent states and the moment mapJ Geom Phys 12 165ndash182 (1993)
[566] J-L Starck EJ Candegraves DL Donoho The curvelet transform for image denoising IEEETrans Image Proc 11 670ndash684 (2002)
[567] J-L Starck DL Donoho E J Candegraves Astronomical image representation by the curvelettransform Astron Astroph 398 785ndash800 (2003)
[568] J-L Starck Y Moudden P Abrial M Nguyen Wavelets ridgelets and curvelets on thesphere Astron Astroph 446 1191ndash1204 (2006)
[569] MB Stenzel The Segal-Bargmann transform on a symmetric space of compact type JFunct Analysis 165 44ndash58 (1994)
[570] ECG Sudarshan Equivalence of semiclassical and quantum mechanical descriptions ofstatistical light beams Phys Rev Lett 10 277ndash279 (1963)
[571] A Suvichakorn H Ratiney A Bucur S Cavassila J-P Antoine Toward a quantitativeanalysis of in vivo magnetic resonance proton spectroscopic signals using the continuousMorlet wavelet transform Meas Sci Technol 20 (2009) Art 104029
[572] W Sweldens The lifting scheme A custom-design construction of biorthogonal waveletsApplied Comput Harmon Anal 3 1186ndash1200 (1996)
[573] W Sweldens The lifting scheme A construction of second generation wavelets SIAM JMath Anal 29 511ndash546 (1998)
[574] FH Szafraniec The reproducing kernel Hilbert space and its multiplication operatorsin Complex Analysis and Related Topics ed by E Ramirez de Arellano et al OperatorTheory Advances and Applications vol 114 (Birkhaumluser Basel 2000) pp 254ndash263
[575] FH Szafraniec Multipliers in the reproducing kernel Hilbert space subnormality andnoncommutative complex analysis in Reproducing Kernel Spaces and Applications edby D Alpay Operator Theory Advances and Applications vol 143 (Birkhaumluser Basel2003) pp 313ndash331
570 References
[576] R Takahashi Sur les repreacutesentations unitaires des groupes de Lorentz geacuteneacuteraliseacutes BullSoc Math France 91 289ndash433 (1963)
[577] MC Teich BEA Saleh Squeezed states of light Quantum Opt 1 152ndash191 (1989)[578] R Terrier L Demanet IA Grenier J-P Antoine Wavelet analysis of EGRET data in
Proceedings of the 27th International Cosmic Ray Conference (ICRC 2001) (CopernicusGesellschaft DE 2001) pp 2923ndash2926
[579] T Thiemann Gauge field theory coherent states (GCS) 1 General properties Class QuantGrav 18 2025ndash2064 (2001)
[580] T Thiemann O Winkler Gauge field theory coherent states (GCS) 2 Peakednessproperties Class Quant Grav 18 2561ndash2636 (2001)
[581] T Thiemann O Winkler Gauge field theory coherent states (GCS) 3 Ehrenfest theoremsClass Quant Grav 18 4629ndash4682 (2001)
[582] T Thiemann O Winkler Gauge field theory coherent states (GCS) 4 Infinite tensorproduct and thermodynamical limit Class Quant Grav 18 4997ndash5054 (2001)
[583] K Thirulagasanthar ST Ali Regular subspaces of a quaternionic Hilbert space fromquaternionic Hermite polynomials and associated coherent states J Math Phys 54013506 (2013)
[584] K Thirulogasanthar G Honnouvo A Krzyzak Coherent states and Hermite polynomialson quaternionic Hilbert spaces J Phys A Math Theor 43 385205 (2010)
[585] Tokamak see Wikipedia httpenwikipediaorgwikiTokamak[586] B Torreacutesani Wavelets associated with representations of the affine Weyl-Heisenberg
group J Math Phys 32 1273ndash1279 (1991)[587] B Torreacutesani Time-frequency representation Wavelet packets and optimal decomposition
Ann Inst H Poincareacute 56 215ndash234 (1992)[588] B Torreacutesani Position-frequency analysis for signals defined on spheres Signal Proc 43
341ndash346 (2005)[589] DA Trifonov Generalized intelligent states and squeezing J Math Phys 35 2297ndash2308
(1994)[590] AS Trushechkin IV Volovich Localization properties of squeezed quantum states in
nanoscale space domains preprint (2013) arXiv13046277v1 [quant-ph][591] M Unser N Chenouard A unifying parametric framework for 2D steerable wavelet
transforms SIAM J Imaging Sci 6 102ndash135 (2013)[592] P Vandergheynst J-F Gobbers Directional dyadic wavelet transforms Design and
algorithms IEEE Trans Image Proc 11 363ndash372 (2002)[593] P Vandergheynst J-P Antoine E Van Vyve A Goldberg I Doghri Modelling and
simulation of an impact test using wavelets analytical and finite element models Int JSolids Struct 38 5481ndash5508 (2001)
[594] L Vanhamme RD Fierro S Van Huffel R de Beer Fast removal of residual water inproton spectra J Magn Reson 132 197ndash203 (1998)
[595] J Ville Theacuteorie et applications de la notion de signal analytique Cacircbles et Trans 2 61ndash74(1948)
[596] J Voisin On some unitary representations of the Galilei group I Irreducible representa-tions J Math Phys 6 1519ndash1529 (1965)
[597] A Vourdas Analytic representations in quantum mechanics J Phys A Math Gen 39R65ndashR141 (2006)
[598] DF Walls Squeezed states of light Nature 306 141ndash146 (1983)[599] YK Wang FT Hioe Phase transition in the Dicke maser model Phys Rev A 7 831ndash836
(1973)[600] PSP Wang J Yang A review of wavelet-based edge detection methods Int J Patt
Recogn Artif Intell 26 1255011 (2012)[601] I Weinreich A construction of C1-wavelets on the two-dimensional sphere Appl Comput
Harmon Anal 10 1ndash26 (2001)[602] H Weyl Quantenmechanik und Gruppentheorie Z Phys 46 1ndash46 (1927)
References 571
[603] Y Wiaux L Jacques P Vandergheynst Correspondence principle between spherical andEuclidean wavelets Astrophys J 632 15ndash28 (2005)
[604] Y Wiaux L Jacques P Vielva P Vandergheynst Fast directional correlation on the spherewith steerable filters Astrophys J 652 820ndash832 (2006)
[605] Y Wiaux JD McEwen P Vandergheynst O Blanc Exact reconstruction with directionalwavelets on the sphere Mon Not R Astron Soc 388 770ndash788 (2008)
[606] WM Wieland Complex Ashtekar variables and reality conditions for Holstrsquos action AnnHenri Poincareacute 13 425ndash448 (2012)
[607] EP Wigner On the quantum correction for thermodynamic equilibrium Phys Rev 40749ndash759 (1932)
[608] RM Willette RD Nowak Platelets A multiscale approach for recovering edges andsurfaces in photon-limited medical imaging IEEE Trans Med Imaging 22 332ndash350(2003)
[609] W Wisnoe P Gajan A Strzelecki C Lempereur J-M Matheacute The use of the two-dimensional wavelet transform in flow visualization processing in Progress in WaveletAnalysis and Applications (Proc Toulouse 1992) ed by Y Meyer S Roques (EdFrontiegraveres Gif-sur-Yvette 1993) pp 455ndash458
[610] K Woacutedkiewicz On the quantum mechanics of squeezed states J Modern Optics 34 941ndash948(1987)
[611] JA Yeazell M Mallalieu CR Stroud Jr Observation of the collapse and revival of aRydberg electronic wave packet Phys Rev Lett 64 2007ndash2010 (1990)
[612] JA Yeazell CR Stroud Jr Observation of fractional revivals in the evolution of aRydberg atomic wave packet Phys Rev A 43 5153ndash5156 (1991)
[613] HP Yuen Two-photon coherent states of the radiation field Phys Rev A 13 2226ndash2243(1976)
[614] J Zak Balian-Low theorem for Landau levels Phys Rev Lett 79 533ndash536 (1997)[615] J Zak Orthonormal sets of localized functions for a Landau level J Math Phys 39 4195ndash
4200 (1998) and references quoted there[616] AA Zakharova On the properties of generalized frames Math Notes 83 190ndash200 (2008)[617] W-M Zhang DH Feng R Gilmore Coherent states Theory and some applications Rev
Mod Phys 26 867ndash927 (1990)[618] I Zlatev W-M Zhang DH Feng Possibility that Schroumldingerrsquos conjecture for the
hydrogen atom coherent states is not attainable Phys Rev A 50 R1973ndashR1975 (1994)[619] WH Zurek Decoherence einselection and the quantum origins of the classical Rev Mod
Phys 75 715ndash775 (2003)[620] WH Zurek S Habib JP Paz Coherent states via decoherence Phys Rev Lett 70 1187ndash
1190 (1993)[621] K Zyczkowski Squeezed states in a quantum chaotic system J Phys A Math Theor 22
of SU(11) 81 296 297HilbertClowast-modules 164holomorphic 140nonholomorphic 151nonlinear 146of affine Galilei group 505of affine Poincareacute group 509of affine Weyl-Heisenberg group GaWH
497of compact semisimple Lie groups 174of Euclidean group E(n) 266of Galilei group G (11) 290of isochronous Galilei group 237of non-semisimple Lie groups 179of noncompact semisimple Lie groups 177of Poincareacute group Puarr
+(11) 283massless case 288
of Poincareacute group Puarr+(13) 279
of Schroumldinger group 508quasi-coherent states 186quaternionic 164
ST Ali et al Coherent States Wavelets and Their Generalizations Theoreticaland Mathematical Physics DOI 101007978-1-4614-8535-3copy Springer Science+Business Media New York 2014
573
574 Index
coherent states (CS) (cont)spin or SU(2) 175square integrable covariant 166 180 264vector (VCS) 73 108 112 170weighted 184 523
of affine Weyl-Heisenberg group GaWH497
of Poincareacute group Puarr+(11) 284
cohomology group 393 403coboundaries 403cochains 402cocycle 403
algebraic 387Cauchy 418Cauchy-Paul 354 419 425conical 418difference 417 462directional 416 440kinematical 499local 488metabolite-based 355 374minimal uncertainty 425multiselective 440on a graph 493on the sphere S
2 458on the sphere S
n 479on the torus T2 481steerable 439von Mises 440
wedgelet transform 455Wigner function 322Wigner-Ville transform 349Windowed Fourier or Gabor transform 349
ZZak transform 518
References
A Books and Theses
B Articles
Index
566 References
[477] MA Muschietti B Torreacutesani Pyramidal algorithms for LittlewoodndashPaley decomposi-tions SIAM J Math Anal 26 925ndash943 (1995)
[478] B Nagel Generalized eigenvectors in group representations in Studies in MathematicalPhysics (Proc Istanbul 1970) ed by AO Barut (Reidel Dordrecht and Boston 1970)pp 135ndash154
[479] MA Naımark Dokl Akad Nauk SSSR 41 359ndash361 (1943) see also B Sz-NagyExtensions of linear transformations in Hilbert space which extend beyond this spaceAppendix to F Riesz B Sz-Nagy Functional Analysis (Frederick Ungar New York 1960)
[480] FJ Narcowich P Petrushev JD Ward Localized tight frames on spheres SIAM J MathAnal 38 574ndash594 (2006)
[481] M Nauenberg Quantum wave packets on Kepler elliptic orbits Phys Rev A 40 1133ndash1136 (1989)
[482] M Nauenberg C Stroud J Yeazell The classical limit of an atom Scient Amer 27024ndash29 (1994)
[483] H Neumann Transformation properties of observables Helv Phys Acta 45 811ndash819(1972)
[484] U Niederer The maximal kinematical invariance group of the free Schroumldinger equationHelv Phys Acta 45 802ndash881 (1972)
[485] MM Nieto LM Simmons Jr Coherent states for general potentials I Formalism IIConfining one-dimensional examples III Nonconfining one-dimensional examples PhysRev D 20 1321ndash1331 1332ndash1341 1342ndash1350 (1979)
[486] MM Nieto LM Simmons Jr Coherent states for general potentials Phys Rev Lett 41207ndash210 (1987)
[487] A Odzijewicz On reproducing kernels and quantization of states Commun Math Phys114 577ndash597 (1988)
[488] A Odzijewicz Coherent states and geometric quantization Commun Math Phys 150385ndash413 (1992)
[489] A Odzijewicz Quantum algebras and q-special functions related to coherent states mapsof the disc Commun Math Phys 192 183ndash215 (1998)
[490] A Odzijewicz M Horowski A Tereszkiewicz Integrable multi-boson systems andorthogonal polynomials J Phys A Math Gen 34 4353ndash4376 (2001)
[491] G Oacutelafsson B Oslashrsted The holomorphic discrete series for affine symmetric spaces JFunct Anal 81 126ndash159 (1988)
[492] G Oacutelafsson H Schlichtkrull Representation theory Radon transform and the heatequation on a Riemannian symmetric space Contemp Math 449 315ndash344 (2008)
[493] E Onofri A note on coherent state representations of Lie groups J Math Phys 16 1087ndash1089 (1975)
[494] E Onofri Dynamical quantization of the Kepler manifold J Math Phys 17 401ndash408(1976)
[495] D Oriti R Pereira L Sindoni Coherent states in quantum gravity A construction basedon the flux representation of loop quantum gravity J Phys A Math Theor 45 244004(2012)
[496] LC Papaloucas J Rembielinski W Tybor Vectorlike coherent states with noncompactstability group J Math Phys 30 2406ndash2410 (1989)
[497] Z Pasternak-Winiarski On the dependence of the reproducing kernel on the weight ofintegration J Funct Anal 94 110ndash134 (1990)
[498] Z Pasternak-Winiarski On reproducing kernels for holomorphic vector bundles inQuantization and Infinite Dimensional Systems (Proc Białowieza Poland 1993) ed by J-P Antoine ST Ali W Lisiecki IM Mladenov A Odzijewicz (Plenum Press New Yorkand London 1994) pp 109ndash112
[499] T Paul Affine coherent states and the radial Schroumldinger equation I preprint CPT-84P1710 (1984) (unpublished)
References 567
[500] T Paul K Seip Wavelets in quantum mechanics in Wavelets and Their Applications edby MB Ruskai G Beylkin R Coifman I Daubechies S Mallat Y Meyer L Raphael(Jones and Bartlett Boston 1992) pp 303ndash322
[501] AM Perelomov On the completeness of a system of coherent states Theor Math Phys6 156ndash164 (1971)
[502] AM Perelomov Coherent states for arbitrary Lie group Commun Math Phys 26 222ndash236 (1972)
[503] AM Perelomov Coherent states and symmetric spaces Commun Math Phys 44 197ndash210 (1975)
[504] M Perroud Projective representations of the Schroumldinger group Helv Phys Acta 50 233ndash252 (1977)
[505] J Phillips A note on square-integrable representations J Funct Anal 20 83ndash92 (1975)[506] D Pietrobon P Baldi D Marinucci Integrated Sachs-Wolfe effect from the cross
correlation of WMAP3 year and the NRAO VLA sky survey data New results andconstraints on dark energy Phys Rev D 74 043524 (2006)
[507] WWF Pijnappel A van den Boogaart R de Beer D van Ormondt SVD-basedquantification of magnetic resonance signals J Magn Reson 97 122ndash134 (1992)
[508] V Pop D Rosca Generalized piecewise constant orthogonal wavelet bases on 2D-domains Appl Anal 90 715ndash723 (2011)
[509] G Poumlschl E Teller Bemerkungen zur Quantenmechanik des anharmonischen OszillatorsZ Physik 83 143ndash151 (1933)
[510] D Potts G Steidl M Tasche Kernels of spherical harmonics and spherical frames inAdvanced Topics in Multivariate Approximation ed by F Fontanella K Jetter PJ Laurent(World Scientific Singapore 1996) pp 287ndash301
[511] E Prugovecki Consistent formulation of relativistic dynamics for massive spin-zeroparticles in external fields Phys Rev D 18 3655ndash3673 (1978) (Appendix C)
[512] E Prugovecki Relativistic quantum kinematics on stochastic phase space for massiveparticles J MathPhys 19 2261ndash2270 (1978)
[513] C Quesne Coherent states of the real symplectic group in a complex analytic parametriza-tion I II J Math Phys 27 428ndash441 869ndash878 (1986)
[514] C Quesne Generalized vector coherent states of sp(2NR) vector operators and ofsp(2NR) sup u(N) reduced Wigner coefficients J Phys A Math Gen 24 2697ndash2714(1991)
[515] JM Radcliffe Some properties of spin coherent states J Phys A Math Gen 4 313ndash323(1971)
[516] A Rahimi A Najati YN Dehghan Continuous frames in Hilbert spaces Methods FunctAnal Topol 12 170ndash182 (2006)
[517] H Rauhut M Roumlsler Radial multiresolution in dimension three Constr Approx 22 193ndash218 (2005)
[518] JH Rawnsley Coherent states and Kaumlhler manifolds Quart J Math Oxford 28(2) 403ndash415 (1977)
[519] J Renaud The contraction of the SU(11) discrete series of representations by means ofcoherent states J Math Phys 37 3168ndash3179 (1996)
[520] A Reacutenyi Representations for real numbers and their ergodic properties Acta Math AcadSci Hungary 8(3ndash4) 477ndash493 (1957)
[521] D Robert La coheacuterence dans tous ses eacutetats SMF Gazette 132 (2012)[522] JE Roberts The Dirac bra and ket formalism J Math Phys 7 1097ndash1104 (1966)[523] JE Roberts Rigged Hilbert spaces in quantum mechanics Commun Math Phys 3 98ndash
119 (1966)[524] S Roques F Bourzeix K Bouyoucef Soft-thresholding technique and restoration of
3C273 jet Astrophys Space Sci Nr 239 297ndash304 (1996)[525] D Rosca Haar wavelets on spherical triangulations in Advances in Multiresolution for
Geometric Modelling ed by NA Dogson MS Floater MA Sabin (Springer Berlin2005) pp 407ndash419
568 References
[526] D Rosca Locally supported rational spline wavelets on the sphere Math Comput 741803ndash1829 (2005)
[527] D Rosca Wavelets defined on closed surfaces J Comput Anal Appl 8 121ndash132 (2006)[528] D Rosca Weighted Haar wavelets on the sphere Int J Wavelets Multiresol Inf Proc 5
501ndash511 (2007)[529] D Rosca Wavelet bases on the sphere obtained by radial projection J Fourier Anal Appl
13 421ndash434 (2007)[530] D Rosca Piecewise constant wavelets on triangulations obtained by 1ndash3 splitting Int J
Wavelets Multiresolut Inf Process 6 209ndash222 (2008)[531] D Rosca On a norm equivalence on L2(S2) Results Math 53 399ndash405 (2009)[532] D Rosca New uniform grids on the sphere Astron Astrophys 520 (2010) Art A63[533] D Rosca Uniform and refinable grids on elliptic domains and on some surfaces of
revolution Appl Math Comput 217 7812ndash7817 (2011)[534] D Rosca Wavelet analysis on some surfaces of revolution via area preserving projection
Appl Comput Harmon Anal 30 262ndash272 (2011)[535] D Rosca J-P Antoine Locally supported orthogonal wavelet bases on the sphere via
stereographic projection Math Probl Eng 2009 124904 (2009)[536] D Rosca J-P Antoine Constructing wavelet frames and orthogonal wavelet bases on the
sphere in Recent Advances in Signal Processing ed by S Miron (IN-TECH ViennaAustria and Rijeka Croatia 2010) pp 59ndash76
[537] D Rosca G Plonka Uniform spherical grids via area preserving projection from the cubeto the sphere J Comput Appl Math 236 1033ndash1041 (2011)
[538] D Rosca G Plonka An area preserving projection from the regular octahedron to thesphere Results Math 63 429ndash444 (2012)
[539] H Rossi M Vergne Analytic continuation of the holomorphic discrete series for a semi-simple Lie group Acta Math 136 1ndash59 (1976)
[540] DJ Rotenberg Application of Sturmian functions to the Schroedinger three-body prob-lem Elastic e+ndashH scattering Ann Phys (NY) 19 262ndash278 (1962)
[541] C Rovelli Zakopane lectures on loop gravity in Proceedings of 3rd Quantum Gravityand Quantum Geometry School 28 Febndash13 March 2011 (Zakopane Poland 2011)arXiv11023660v5
[542] C Rovelli S Speziale A semiclassical tetrahedron Class Quant Grav 23 5861ndash5870(2006)
[543] DJ Rowe Coherent state theory of the noncompact symplectic group J Math Phys 252662ndash2271 (1984)
[544] DJ Rowe Microscopic theory of the nuclear collective model Rep Prog Phys 48 1419ndash1480 (1985)
[545] DJ Rowe Vector coherent state representations and their inner products J Phys A MathGen 45 244003 (2012) (This paper belongs to the special issue [38])
[546] DJ Rowe J Repka Vector-coherent-state theory as a theory of induced representationsJ Math Phys 32 2614ndash2634 (1991)
[547] DJ Rowe G Rosensteel R Gilmore Vector coherent state representation theory J MathPhys 26 2787ndash2791 (1985)
[548] A Royer Phase states and phase operators for the quantum harmonic oscillator Phys RevA 53 70ndash108 (1996)
[549] J Saletan Contraction of Lie groups J Math Phys 2 1ndash21 (1961)[550] G Saracco A Grossmann P Tchamitchian Use of wavelet transforms in the study of
propagation of transient acoustic signals across a plane interface between two homoge-neous media in Wavelets Time-Frequency Methods and Phase Space (Proc Marseille1987) ed by J-M Combes A Grossmann P Tchamitchian 2nd edn (Springer Berlin1990) pp 139ndash146
[551] P Schroumlder W Sweldens Spherical wavelets Efficiently representing functions on thesphere in Computer Graphics Proceedings (SIGGRAPH95) (ACM Siggraph Los Angeles1995) pp 161ndash175
References 569
[552] E Schroumldinger Der stetige Uumlbergang von der Mikro- zur Makromechanik Naturwiss 14664ndash666 (1926)
[553] S Scodeller Oslash Rudjord FK Hansen D Marinucci D Geller A Mayeli IntroducingMexican needlets for CMB analysis Issues for practical applications and comparison withstandard needlets Astrophys J 733 (2011) Art 121
[554] H Scutaru Coherent states and induced representations Lett Math Phys 2 101ndash107(1977)
[555] B Simon Distributions and their Hermite expansions J Math Phys 12 140ndash148 (1971)[556] B Simon The classical moment problem as a self-adjoint finite difference operator Adv
Math 137 82ndash203 (1998)[557] R Simon ECG Sudarshan N Mukunda Gaussian pure states in quantum mechanics
and the symplectic group Phys Rev A37 3028ndash3038 (1988)[558] S Sivakumar Studies on nonlinear coherent states J Opt B Quant Semiclass Opt 2
R61ndashR75 (2000)[559] E Slezak A Bijaoui G Mars Identification of structures from galaxy counts Use of the
wavelet transform Astron Astroph 227 301ndash316 (1990)[560] A Solomon A characteristic functional for deformed photon phenomenology Phys Lett
A 196 29ndash34 (1994)[561] SB Sontz Paragrassmann algebras as quantum spaces Part I Reproducing kernels in
Geometric Methods in Physics XXXI Workshop 2012 (Trends in Mathematics ed byP Kielanowski et al Birkhaumluser Verlag Basel 2013) pp 47ndash63
[562] SB Sontz Paragrassmann algebras as quantum spaces Part II Toeplitz operators J OperTh (2013 to appear) arXiv12055493
[563] SB Sontz A reproducing kernel and Toeplitz operators in the quantum plane Preprint(2013) arXiv13056986 [math-ph]
[564] SB Sontz Toeplitz quantization of an algebra with conjugation Preprint (2013)arXiv13085454 [math-ph]
[565] M Spera On a generalized Uncertainty Principle coherent states and the moment mapJ Geom Phys 12 165ndash182 (1993)
[566] J-L Starck EJ Candegraves DL Donoho The curvelet transform for image denoising IEEETrans Image Proc 11 670ndash684 (2002)
[567] J-L Starck DL Donoho E J Candegraves Astronomical image representation by the curvelettransform Astron Astroph 398 785ndash800 (2003)
[568] J-L Starck Y Moudden P Abrial M Nguyen Wavelets ridgelets and curvelets on thesphere Astron Astroph 446 1191ndash1204 (2006)
[569] MB Stenzel The Segal-Bargmann transform on a symmetric space of compact type JFunct Analysis 165 44ndash58 (1994)
[570] ECG Sudarshan Equivalence of semiclassical and quantum mechanical descriptions ofstatistical light beams Phys Rev Lett 10 277ndash279 (1963)
[571] A Suvichakorn H Ratiney A Bucur S Cavassila J-P Antoine Toward a quantitativeanalysis of in vivo magnetic resonance proton spectroscopic signals using the continuousMorlet wavelet transform Meas Sci Technol 20 (2009) Art 104029
[572] W Sweldens The lifting scheme A custom-design construction of biorthogonal waveletsApplied Comput Harmon Anal 3 1186ndash1200 (1996)
[573] W Sweldens The lifting scheme A construction of second generation wavelets SIAM JMath Anal 29 511ndash546 (1998)
[574] FH Szafraniec The reproducing kernel Hilbert space and its multiplication operatorsin Complex Analysis and Related Topics ed by E Ramirez de Arellano et al OperatorTheory Advances and Applications vol 114 (Birkhaumluser Basel 2000) pp 254ndash263
[575] FH Szafraniec Multipliers in the reproducing kernel Hilbert space subnormality andnoncommutative complex analysis in Reproducing Kernel Spaces and Applications edby D Alpay Operator Theory Advances and Applications vol 143 (Birkhaumluser Basel2003) pp 313ndash331
570 References
[576] R Takahashi Sur les repreacutesentations unitaires des groupes de Lorentz geacuteneacuteraliseacutes BullSoc Math France 91 289ndash433 (1963)
[577] MC Teich BEA Saleh Squeezed states of light Quantum Opt 1 152ndash191 (1989)[578] R Terrier L Demanet IA Grenier J-P Antoine Wavelet analysis of EGRET data in
Proceedings of the 27th International Cosmic Ray Conference (ICRC 2001) (CopernicusGesellschaft DE 2001) pp 2923ndash2926
[579] T Thiemann Gauge field theory coherent states (GCS) 1 General properties Class QuantGrav 18 2025ndash2064 (2001)
[580] T Thiemann O Winkler Gauge field theory coherent states (GCS) 2 Peakednessproperties Class Quant Grav 18 2561ndash2636 (2001)
[581] T Thiemann O Winkler Gauge field theory coherent states (GCS) 3 Ehrenfest theoremsClass Quant Grav 18 4629ndash4682 (2001)
[582] T Thiemann O Winkler Gauge field theory coherent states (GCS) 4 Infinite tensorproduct and thermodynamical limit Class Quant Grav 18 4997ndash5054 (2001)
[583] K Thirulagasanthar ST Ali Regular subspaces of a quaternionic Hilbert space fromquaternionic Hermite polynomials and associated coherent states J Math Phys 54013506 (2013)
[584] K Thirulogasanthar G Honnouvo A Krzyzak Coherent states and Hermite polynomialson quaternionic Hilbert spaces J Phys A Math Theor 43 385205 (2010)
[585] Tokamak see Wikipedia httpenwikipediaorgwikiTokamak[586] B Torreacutesani Wavelets associated with representations of the affine Weyl-Heisenberg
group J Math Phys 32 1273ndash1279 (1991)[587] B Torreacutesani Time-frequency representation Wavelet packets and optimal decomposition
Ann Inst H Poincareacute 56 215ndash234 (1992)[588] B Torreacutesani Position-frequency analysis for signals defined on spheres Signal Proc 43
341ndash346 (2005)[589] DA Trifonov Generalized intelligent states and squeezing J Math Phys 35 2297ndash2308
(1994)[590] AS Trushechkin IV Volovich Localization properties of squeezed quantum states in
nanoscale space domains preprint (2013) arXiv13046277v1 [quant-ph][591] M Unser N Chenouard A unifying parametric framework for 2D steerable wavelet
transforms SIAM J Imaging Sci 6 102ndash135 (2013)[592] P Vandergheynst J-F Gobbers Directional dyadic wavelet transforms Design and
algorithms IEEE Trans Image Proc 11 363ndash372 (2002)[593] P Vandergheynst J-P Antoine E Van Vyve A Goldberg I Doghri Modelling and
simulation of an impact test using wavelets analytical and finite element models Int JSolids Struct 38 5481ndash5508 (2001)
[594] L Vanhamme RD Fierro S Van Huffel R de Beer Fast removal of residual water inproton spectra J Magn Reson 132 197ndash203 (1998)
[595] J Ville Theacuteorie et applications de la notion de signal analytique Cacircbles et Trans 2 61ndash74(1948)
[596] J Voisin On some unitary representations of the Galilei group I Irreducible representa-tions J Math Phys 6 1519ndash1529 (1965)
[597] A Vourdas Analytic representations in quantum mechanics J Phys A Math Gen 39R65ndashR141 (2006)
[598] DF Walls Squeezed states of light Nature 306 141ndash146 (1983)[599] YK Wang FT Hioe Phase transition in the Dicke maser model Phys Rev A 7 831ndash836
(1973)[600] PSP Wang J Yang A review of wavelet-based edge detection methods Int J Patt
Recogn Artif Intell 26 1255011 (2012)[601] I Weinreich A construction of C1-wavelets on the two-dimensional sphere Appl Comput
Harmon Anal 10 1ndash26 (2001)[602] H Weyl Quantenmechanik und Gruppentheorie Z Phys 46 1ndash46 (1927)
References 571
[603] Y Wiaux L Jacques P Vandergheynst Correspondence principle between spherical andEuclidean wavelets Astrophys J 632 15ndash28 (2005)
[604] Y Wiaux L Jacques P Vielva P Vandergheynst Fast directional correlation on the spherewith steerable filters Astrophys J 652 820ndash832 (2006)
[605] Y Wiaux JD McEwen P Vandergheynst O Blanc Exact reconstruction with directionalwavelets on the sphere Mon Not R Astron Soc 388 770ndash788 (2008)
[606] WM Wieland Complex Ashtekar variables and reality conditions for Holstrsquos action AnnHenri Poincareacute 13 425ndash448 (2012)
[607] EP Wigner On the quantum correction for thermodynamic equilibrium Phys Rev 40749ndash759 (1932)
[608] RM Willette RD Nowak Platelets A multiscale approach for recovering edges andsurfaces in photon-limited medical imaging IEEE Trans Med Imaging 22 332ndash350(2003)
[609] W Wisnoe P Gajan A Strzelecki C Lempereur J-M Matheacute The use of the two-dimensional wavelet transform in flow visualization processing in Progress in WaveletAnalysis and Applications (Proc Toulouse 1992) ed by Y Meyer S Roques (EdFrontiegraveres Gif-sur-Yvette 1993) pp 455ndash458
[610] K Woacutedkiewicz On the quantum mechanics of squeezed states J Modern Optics 34 941ndash948(1987)
[611] JA Yeazell M Mallalieu CR Stroud Jr Observation of the collapse and revival of aRydberg electronic wave packet Phys Rev Lett 64 2007ndash2010 (1990)
[612] JA Yeazell CR Stroud Jr Observation of fractional revivals in the evolution of aRydberg atomic wave packet Phys Rev A 43 5153ndash5156 (1991)
[613] HP Yuen Two-photon coherent states of the radiation field Phys Rev A 13 2226ndash2243(1976)
[614] J Zak Balian-Low theorem for Landau levels Phys Rev Lett 79 533ndash536 (1997)[615] J Zak Orthonormal sets of localized functions for a Landau level J Math Phys 39 4195ndash
4200 (1998) and references quoted there[616] AA Zakharova On the properties of generalized frames Math Notes 83 190ndash200 (2008)[617] W-M Zhang DH Feng R Gilmore Coherent states Theory and some applications Rev
Mod Phys 26 867ndash927 (1990)[618] I Zlatev W-M Zhang DH Feng Possibility that Schroumldingerrsquos conjecture for the
hydrogen atom coherent states is not attainable Phys Rev A 50 R1973ndashR1975 (1994)[619] WH Zurek Decoherence einselection and the quantum origins of the classical Rev Mod
Phys 75 715ndash775 (2003)[620] WH Zurek S Habib JP Paz Coherent states via decoherence Phys Rev Lett 70 1187ndash
1190 (1993)[621] K Zyczkowski Squeezed states in a quantum chaotic system J Phys A Math Theor 22
of SU(11) 81 296 297HilbertClowast-modules 164holomorphic 140nonholomorphic 151nonlinear 146of affine Galilei group 505of affine Poincareacute group 509of affine Weyl-Heisenberg group GaWH
497of compact semisimple Lie groups 174of Euclidean group E(n) 266of Galilei group G (11) 290of isochronous Galilei group 237of non-semisimple Lie groups 179of noncompact semisimple Lie groups 177of Poincareacute group Puarr
+(11) 283massless case 288
of Poincareacute group Puarr+(13) 279
of Schroumldinger group 508quasi-coherent states 186quaternionic 164
ST Ali et al Coherent States Wavelets and Their Generalizations Theoreticaland Mathematical Physics DOI 101007978-1-4614-8535-3copy Springer Science+Business Media New York 2014
573
574 Index
coherent states (CS) (cont)spin or SU(2) 175square integrable covariant 166 180 264vector (VCS) 73 108 112 170weighted 184 523
of affine Weyl-Heisenberg group GaWH497
of Poincareacute group Puarr+(11) 284
cohomology group 393 403coboundaries 403cochains 402cocycle 403
algebraic 387Cauchy 418Cauchy-Paul 354 419 425conical 418difference 417 462directional 416 440kinematical 499local 488metabolite-based 355 374minimal uncertainty 425multiselective 440on a graph 493on the sphere S
2 458on the sphere S
n 479on the torus T2 481steerable 439von Mises 440
wedgelet transform 455Wigner function 322Wigner-Ville transform 349Windowed Fourier or Gabor transform 349
ZZak transform 518
References
A Books and Theses
B Articles
Index
References 567
[500] T Paul K Seip Wavelets in quantum mechanics in Wavelets and Their Applications edby MB Ruskai G Beylkin R Coifman I Daubechies S Mallat Y Meyer L Raphael(Jones and Bartlett Boston 1992) pp 303ndash322
[501] AM Perelomov On the completeness of a system of coherent states Theor Math Phys6 156ndash164 (1971)
[502] AM Perelomov Coherent states for arbitrary Lie group Commun Math Phys 26 222ndash236 (1972)
[503] AM Perelomov Coherent states and symmetric spaces Commun Math Phys 44 197ndash210 (1975)
[504] M Perroud Projective representations of the Schroumldinger group Helv Phys Acta 50 233ndash252 (1977)
[505] J Phillips A note on square-integrable representations J Funct Anal 20 83ndash92 (1975)[506] D Pietrobon P Baldi D Marinucci Integrated Sachs-Wolfe effect from the cross
correlation of WMAP3 year and the NRAO VLA sky survey data New results andconstraints on dark energy Phys Rev D 74 043524 (2006)
[507] WWF Pijnappel A van den Boogaart R de Beer D van Ormondt SVD-basedquantification of magnetic resonance signals J Magn Reson 97 122ndash134 (1992)
[508] V Pop D Rosca Generalized piecewise constant orthogonal wavelet bases on 2D-domains Appl Anal 90 715ndash723 (2011)
[509] G Poumlschl E Teller Bemerkungen zur Quantenmechanik des anharmonischen OszillatorsZ Physik 83 143ndash151 (1933)
[510] D Potts G Steidl M Tasche Kernels of spherical harmonics and spherical frames inAdvanced Topics in Multivariate Approximation ed by F Fontanella K Jetter PJ Laurent(World Scientific Singapore 1996) pp 287ndash301
[511] E Prugovecki Consistent formulation of relativistic dynamics for massive spin-zeroparticles in external fields Phys Rev D 18 3655ndash3673 (1978) (Appendix C)
[512] E Prugovecki Relativistic quantum kinematics on stochastic phase space for massiveparticles J MathPhys 19 2261ndash2270 (1978)
[513] C Quesne Coherent states of the real symplectic group in a complex analytic parametriza-tion I II J Math Phys 27 428ndash441 869ndash878 (1986)
[514] C Quesne Generalized vector coherent states of sp(2NR) vector operators and ofsp(2NR) sup u(N) reduced Wigner coefficients J Phys A Math Gen 24 2697ndash2714(1991)
[515] JM Radcliffe Some properties of spin coherent states J Phys A Math Gen 4 313ndash323(1971)
[516] A Rahimi A Najati YN Dehghan Continuous frames in Hilbert spaces Methods FunctAnal Topol 12 170ndash182 (2006)
[517] H Rauhut M Roumlsler Radial multiresolution in dimension three Constr Approx 22 193ndash218 (2005)
[518] JH Rawnsley Coherent states and Kaumlhler manifolds Quart J Math Oxford 28(2) 403ndash415 (1977)
[519] J Renaud The contraction of the SU(11) discrete series of representations by means ofcoherent states J Math Phys 37 3168ndash3179 (1996)
[520] A Reacutenyi Representations for real numbers and their ergodic properties Acta Math AcadSci Hungary 8(3ndash4) 477ndash493 (1957)
[521] D Robert La coheacuterence dans tous ses eacutetats SMF Gazette 132 (2012)[522] JE Roberts The Dirac bra and ket formalism J Math Phys 7 1097ndash1104 (1966)[523] JE Roberts Rigged Hilbert spaces in quantum mechanics Commun Math Phys 3 98ndash
119 (1966)[524] S Roques F Bourzeix K Bouyoucef Soft-thresholding technique and restoration of
3C273 jet Astrophys Space Sci Nr 239 297ndash304 (1996)[525] D Rosca Haar wavelets on spherical triangulations in Advances in Multiresolution for
Geometric Modelling ed by NA Dogson MS Floater MA Sabin (Springer Berlin2005) pp 407ndash419
568 References
[526] D Rosca Locally supported rational spline wavelets on the sphere Math Comput 741803ndash1829 (2005)
[527] D Rosca Wavelets defined on closed surfaces J Comput Anal Appl 8 121ndash132 (2006)[528] D Rosca Weighted Haar wavelets on the sphere Int J Wavelets Multiresol Inf Proc 5
501ndash511 (2007)[529] D Rosca Wavelet bases on the sphere obtained by radial projection J Fourier Anal Appl
13 421ndash434 (2007)[530] D Rosca Piecewise constant wavelets on triangulations obtained by 1ndash3 splitting Int J
Wavelets Multiresolut Inf Process 6 209ndash222 (2008)[531] D Rosca On a norm equivalence on L2(S2) Results Math 53 399ndash405 (2009)[532] D Rosca New uniform grids on the sphere Astron Astrophys 520 (2010) Art A63[533] D Rosca Uniform and refinable grids on elliptic domains and on some surfaces of
revolution Appl Math Comput 217 7812ndash7817 (2011)[534] D Rosca Wavelet analysis on some surfaces of revolution via area preserving projection
Appl Comput Harmon Anal 30 262ndash272 (2011)[535] D Rosca J-P Antoine Locally supported orthogonal wavelet bases on the sphere via
stereographic projection Math Probl Eng 2009 124904 (2009)[536] D Rosca J-P Antoine Constructing wavelet frames and orthogonal wavelet bases on the
sphere in Recent Advances in Signal Processing ed by S Miron (IN-TECH ViennaAustria and Rijeka Croatia 2010) pp 59ndash76
[537] D Rosca G Plonka Uniform spherical grids via area preserving projection from the cubeto the sphere J Comput Appl Math 236 1033ndash1041 (2011)
[538] D Rosca G Plonka An area preserving projection from the regular octahedron to thesphere Results Math 63 429ndash444 (2012)
[539] H Rossi M Vergne Analytic continuation of the holomorphic discrete series for a semi-simple Lie group Acta Math 136 1ndash59 (1976)
[540] DJ Rotenberg Application of Sturmian functions to the Schroedinger three-body prob-lem Elastic e+ndashH scattering Ann Phys (NY) 19 262ndash278 (1962)
[541] C Rovelli Zakopane lectures on loop gravity in Proceedings of 3rd Quantum Gravityand Quantum Geometry School 28 Febndash13 March 2011 (Zakopane Poland 2011)arXiv11023660v5
[542] C Rovelli S Speziale A semiclassical tetrahedron Class Quant Grav 23 5861ndash5870(2006)
[543] DJ Rowe Coherent state theory of the noncompact symplectic group J Math Phys 252662ndash2271 (1984)
[544] DJ Rowe Microscopic theory of the nuclear collective model Rep Prog Phys 48 1419ndash1480 (1985)
[545] DJ Rowe Vector coherent state representations and their inner products J Phys A MathGen 45 244003 (2012) (This paper belongs to the special issue [38])
[546] DJ Rowe J Repka Vector-coherent-state theory as a theory of induced representationsJ Math Phys 32 2614ndash2634 (1991)
[547] DJ Rowe G Rosensteel R Gilmore Vector coherent state representation theory J MathPhys 26 2787ndash2791 (1985)
[548] A Royer Phase states and phase operators for the quantum harmonic oscillator Phys RevA 53 70ndash108 (1996)
[549] J Saletan Contraction of Lie groups J Math Phys 2 1ndash21 (1961)[550] G Saracco A Grossmann P Tchamitchian Use of wavelet transforms in the study of
propagation of transient acoustic signals across a plane interface between two homoge-neous media in Wavelets Time-Frequency Methods and Phase Space (Proc Marseille1987) ed by J-M Combes A Grossmann P Tchamitchian 2nd edn (Springer Berlin1990) pp 139ndash146
[551] P Schroumlder W Sweldens Spherical wavelets Efficiently representing functions on thesphere in Computer Graphics Proceedings (SIGGRAPH95) (ACM Siggraph Los Angeles1995) pp 161ndash175
References 569
[552] E Schroumldinger Der stetige Uumlbergang von der Mikro- zur Makromechanik Naturwiss 14664ndash666 (1926)
[553] S Scodeller Oslash Rudjord FK Hansen D Marinucci D Geller A Mayeli IntroducingMexican needlets for CMB analysis Issues for practical applications and comparison withstandard needlets Astrophys J 733 (2011) Art 121
[554] H Scutaru Coherent states and induced representations Lett Math Phys 2 101ndash107(1977)
[555] B Simon Distributions and their Hermite expansions J Math Phys 12 140ndash148 (1971)[556] B Simon The classical moment problem as a self-adjoint finite difference operator Adv
Math 137 82ndash203 (1998)[557] R Simon ECG Sudarshan N Mukunda Gaussian pure states in quantum mechanics
and the symplectic group Phys Rev A37 3028ndash3038 (1988)[558] S Sivakumar Studies on nonlinear coherent states J Opt B Quant Semiclass Opt 2
R61ndashR75 (2000)[559] E Slezak A Bijaoui G Mars Identification of structures from galaxy counts Use of the
wavelet transform Astron Astroph 227 301ndash316 (1990)[560] A Solomon A characteristic functional for deformed photon phenomenology Phys Lett
A 196 29ndash34 (1994)[561] SB Sontz Paragrassmann algebras as quantum spaces Part I Reproducing kernels in
Geometric Methods in Physics XXXI Workshop 2012 (Trends in Mathematics ed byP Kielanowski et al Birkhaumluser Verlag Basel 2013) pp 47ndash63
[562] SB Sontz Paragrassmann algebras as quantum spaces Part II Toeplitz operators J OperTh (2013 to appear) arXiv12055493
[563] SB Sontz A reproducing kernel and Toeplitz operators in the quantum plane Preprint(2013) arXiv13056986 [math-ph]
[564] SB Sontz Toeplitz quantization of an algebra with conjugation Preprint (2013)arXiv13085454 [math-ph]
[565] M Spera On a generalized Uncertainty Principle coherent states and the moment mapJ Geom Phys 12 165ndash182 (1993)
[566] J-L Starck EJ Candegraves DL Donoho The curvelet transform for image denoising IEEETrans Image Proc 11 670ndash684 (2002)
[567] J-L Starck DL Donoho E J Candegraves Astronomical image representation by the curvelettransform Astron Astroph 398 785ndash800 (2003)
[568] J-L Starck Y Moudden P Abrial M Nguyen Wavelets ridgelets and curvelets on thesphere Astron Astroph 446 1191ndash1204 (2006)
[569] MB Stenzel The Segal-Bargmann transform on a symmetric space of compact type JFunct Analysis 165 44ndash58 (1994)
[570] ECG Sudarshan Equivalence of semiclassical and quantum mechanical descriptions ofstatistical light beams Phys Rev Lett 10 277ndash279 (1963)
[571] A Suvichakorn H Ratiney A Bucur S Cavassila J-P Antoine Toward a quantitativeanalysis of in vivo magnetic resonance proton spectroscopic signals using the continuousMorlet wavelet transform Meas Sci Technol 20 (2009) Art 104029
[572] W Sweldens The lifting scheme A custom-design construction of biorthogonal waveletsApplied Comput Harmon Anal 3 1186ndash1200 (1996)
[573] W Sweldens The lifting scheme A construction of second generation wavelets SIAM JMath Anal 29 511ndash546 (1998)
[574] FH Szafraniec The reproducing kernel Hilbert space and its multiplication operatorsin Complex Analysis and Related Topics ed by E Ramirez de Arellano et al OperatorTheory Advances and Applications vol 114 (Birkhaumluser Basel 2000) pp 254ndash263
[575] FH Szafraniec Multipliers in the reproducing kernel Hilbert space subnormality andnoncommutative complex analysis in Reproducing Kernel Spaces and Applications edby D Alpay Operator Theory Advances and Applications vol 143 (Birkhaumluser Basel2003) pp 313ndash331
570 References
[576] R Takahashi Sur les repreacutesentations unitaires des groupes de Lorentz geacuteneacuteraliseacutes BullSoc Math France 91 289ndash433 (1963)
[577] MC Teich BEA Saleh Squeezed states of light Quantum Opt 1 152ndash191 (1989)[578] R Terrier L Demanet IA Grenier J-P Antoine Wavelet analysis of EGRET data in
Proceedings of the 27th International Cosmic Ray Conference (ICRC 2001) (CopernicusGesellschaft DE 2001) pp 2923ndash2926
[579] T Thiemann Gauge field theory coherent states (GCS) 1 General properties Class QuantGrav 18 2025ndash2064 (2001)
[580] T Thiemann O Winkler Gauge field theory coherent states (GCS) 2 Peakednessproperties Class Quant Grav 18 2561ndash2636 (2001)
[581] T Thiemann O Winkler Gauge field theory coherent states (GCS) 3 Ehrenfest theoremsClass Quant Grav 18 4629ndash4682 (2001)
[582] T Thiemann O Winkler Gauge field theory coherent states (GCS) 4 Infinite tensorproduct and thermodynamical limit Class Quant Grav 18 4997ndash5054 (2001)
[583] K Thirulagasanthar ST Ali Regular subspaces of a quaternionic Hilbert space fromquaternionic Hermite polynomials and associated coherent states J Math Phys 54013506 (2013)
[584] K Thirulogasanthar G Honnouvo A Krzyzak Coherent states and Hermite polynomialson quaternionic Hilbert spaces J Phys A Math Theor 43 385205 (2010)
[585] Tokamak see Wikipedia httpenwikipediaorgwikiTokamak[586] B Torreacutesani Wavelets associated with representations of the affine Weyl-Heisenberg
group J Math Phys 32 1273ndash1279 (1991)[587] B Torreacutesani Time-frequency representation Wavelet packets and optimal decomposition
Ann Inst H Poincareacute 56 215ndash234 (1992)[588] B Torreacutesani Position-frequency analysis for signals defined on spheres Signal Proc 43
341ndash346 (2005)[589] DA Trifonov Generalized intelligent states and squeezing J Math Phys 35 2297ndash2308
(1994)[590] AS Trushechkin IV Volovich Localization properties of squeezed quantum states in
nanoscale space domains preprint (2013) arXiv13046277v1 [quant-ph][591] M Unser N Chenouard A unifying parametric framework for 2D steerable wavelet
transforms SIAM J Imaging Sci 6 102ndash135 (2013)[592] P Vandergheynst J-F Gobbers Directional dyadic wavelet transforms Design and
algorithms IEEE Trans Image Proc 11 363ndash372 (2002)[593] P Vandergheynst J-P Antoine E Van Vyve A Goldberg I Doghri Modelling and
simulation of an impact test using wavelets analytical and finite element models Int JSolids Struct 38 5481ndash5508 (2001)
[594] L Vanhamme RD Fierro S Van Huffel R de Beer Fast removal of residual water inproton spectra J Magn Reson 132 197ndash203 (1998)
[595] J Ville Theacuteorie et applications de la notion de signal analytique Cacircbles et Trans 2 61ndash74(1948)
[596] J Voisin On some unitary representations of the Galilei group I Irreducible representa-tions J Math Phys 6 1519ndash1529 (1965)
[597] A Vourdas Analytic representations in quantum mechanics J Phys A Math Gen 39R65ndashR141 (2006)
[598] DF Walls Squeezed states of light Nature 306 141ndash146 (1983)[599] YK Wang FT Hioe Phase transition in the Dicke maser model Phys Rev A 7 831ndash836
(1973)[600] PSP Wang J Yang A review of wavelet-based edge detection methods Int J Patt
Recogn Artif Intell 26 1255011 (2012)[601] I Weinreich A construction of C1-wavelets on the two-dimensional sphere Appl Comput
Harmon Anal 10 1ndash26 (2001)[602] H Weyl Quantenmechanik und Gruppentheorie Z Phys 46 1ndash46 (1927)
References 571
[603] Y Wiaux L Jacques P Vandergheynst Correspondence principle between spherical andEuclidean wavelets Astrophys J 632 15ndash28 (2005)
[604] Y Wiaux L Jacques P Vielva P Vandergheynst Fast directional correlation on the spherewith steerable filters Astrophys J 652 820ndash832 (2006)
[605] Y Wiaux JD McEwen P Vandergheynst O Blanc Exact reconstruction with directionalwavelets on the sphere Mon Not R Astron Soc 388 770ndash788 (2008)
[606] WM Wieland Complex Ashtekar variables and reality conditions for Holstrsquos action AnnHenri Poincareacute 13 425ndash448 (2012)
[607] EP Wigner On the quantum correction for thermodynamic equilibrium Phys Rev 40749ndash759 (1932)
[608] RM Willette RD Nowak Platelets A multiscale approach for recovering edges andsurfaces in photon-limited medical imaging IEEE Trans Med Imaging 22 332ndash350(2003)
[609] W Wisnoe P Gajan A Strzelecki C Lempereur J-M Matheacute The use of the two-dimensional wavelet transform in flow visualization processing in Progress in WaveletAnalysis and Applications (Proc Toulouse 1992) ed by Y Meyer S Roques (EdFrontiegraveres Gif-sur-Yvette 1993) pp 455ndash458
[610] K Woacutedkiewicz On the quantum mechanics of squeezed states J Modern Optics 34 941ndash948(1987)
[611] JA Yeazell M Mallalieu CR Stroud Jr Observation of the collapse and revival of aRydberg electronic wave packet Phys Rev Lett 64 2007ndash2010 (1990)
[612] JA Yeazell CR Stroud Jr Observation of fractional revivals in the evolution of aRydberg atomic wave packet Phys Rev A 43 5153ndash5156 (1991)
[613] HP Yuen Two-photon coherent states of the radiation field Phys Rev A 13 2226ndash2243(1976)
[614] J Zak Balian-Low theorem for Landau levels Phys Rev Lett 79 533ndash536 (1997)[615] J Zak Orthonormal sets of localized functions for a Landau level J Math Phys 39 4195ndash
4200 (1998) and references quoted there[616] AA Zakharova On the properties of generalized frames Math Notes 83 190ndash200 (2008)[617] W-M Zhang DH Feng R Gilmore Coherent states Theory and some applications Rev
Mod Phys 26 867ndash927 (1990)[618] I Zlatev W-M Zhang DH Feng Possibility that Schroumldingerrsquos conjecture for the
hydrogen atom coherent states is not attainable Phys Rev A 50 R1973ndashR1975 (1994)[619] WH Zurek Decoherence einselection and the quantum origins of the classical Rev Mod
Phys 75 715ndash775 (2003)[620] WH Zurek S Habib JP Paz Coherent states via decoherence Phys Rev Lett 70 1187ndash
1190 (1993)[621] K Zyczkowski Squeezed states in a quantum chaotic system J Phys A Math Theor 22
of SU(11) 81 296 297HilbertClowast-modules 164holomorphic 140nonholomorphic 151nonlinear 146of affine Galilei group 505of affine Poincareacute group 509of affine Weyl-Heisenberg group GaWH
497of compact semisimple Lie groups 174of Euclidean group E(n) 266of Galilei group G (11) 290of isochronous Galilei group 237of non-semisimple Lie groups 179of noncompact semisimple Lie groups 177of Poincareacute group Puarr
+(11) 283massless case 288
of Poincareacute group Puarr+(13) 279
of Schroumldinger group 508quasi-coherent states 186quaternionic 164
ST Ali et al Coherent States Wavelets and Their Generalizations Theoreticaland Mathematical Physics DOI 101007978-1-4614-8535-3copy Springer Science+Business Media New York 2014
573
574 Index
coherent states (CS) (cont)spin or SU(2) 175square integrable covariant 166 180 264vector (VCS) 73 108 112 170weighted 184 523
of affine Weyl-Heisenberg group GaWH497
of Poincareacute group Puarr+(11) 284
cohomology group 393 403coboundaries 403cochains 402cocycle 403
algebraic 387Cauchy 418Cauchy-Paul 354 419 425conical 418difference 417 462directional 416 440kinematical 499local 488metabolite-based 355 374minimal uncertainty 425multiselective 440on a graph 493on the sphere S
2 458on the sphere S
n 479on the torus T2 481steerable 439von Mises 440
wedgelet transform 455Wigner function 322Wigner-Ville transform 349Windowed Fourier or Gabor transform 349
ZZak transform 518
References
A Books and Theses
B Articles
Index
568 References
[526] D Rosca Locally supported rational spline wavelets on the sphere Math Comput 741803ndash1829 (2005)
[527] D Rosca Wavelets defined on closed surfaces J Comput Anal Appl 8 121ndash132 (2006)[528] D Rosca Weighted Haar wavelets on the sphere Int J Wavelets Multiresol Inf Proc 5
501ndash511 (2007)[529] D Rosca Wavelet bases on the sphere obtained by radial projection J Fourier Anal Appl
13 421ndash434 (2007)[530] D Rosca Piecewise constant wavelets on triangulations obtained by 1ndash3 splitting Int J
Wavelets Multiresolut Inf Process 6 209ndash222 (2008)[531] D Rosca On a norm equivalence on L2(S2) Results Math 53 399ndash405 (2009)[532] D Rosca New uniform grids on the sphere Astron Astrophys 520 (2010) Art A63[533] D Rosca Uniform and refinable grids on elliptic domains and on some surfaces of
revolution Appl Math Comput 217 7812ndash7817 (2011)[534] D Rosca Wavelet analysis on some surfaces of revolution via area preserving projection
Appl Comput Harmon Anal 30 262ndash272 (2011)[535] D Rosca J-P Antoine Locally supported orthogonal wavelet bases on the sphere via
stereographic projection Math Probl Eng 2009 124904 (2009)[536] D Rosca J-P Antoine Constructing wavelet frames and orthogonal wavelet bases on the
sphere in Recent Advances in Signal Processing ed by S Miron (IN-TECH ViennaAustria and Rijeka Croatia 2010) pp 59ndash76
[537] D Rosca G Plonka Uniform spherical grids via area preserving projection from the cubeto the sphere J Comput Appl Math 236 1033ndash1041 (2011)
[538] D Rosca G Plonka An area preserving projection from the regular octahedron to thesphere Results Math 63 429ndash444 (2012)
[539] H Rossi M Vergne Analytic continuation of the holomorphic discrete series for a semi-simple Lie group Acta Math 136 1ndash59 (1976)
[540] DJ Rotenberg Application of Sturmian functions to the Schroedinger three-body prob-lem Elastic e+ndashH scattering Ann Phys (NY) 19 262ndash278 (1962)
[541] C Rovelli Zakopane lectures on loop gravity in Proceedings of 3rd Quantum Gravityand Quantum Geometry School 28 Febndash13 March 2011 (Zakopane Poland 2011)arXiv11023660v5
[542] C Rovelli S Speziale A semiclassical tetrahedron Class Quant Grav 23 5861ndash5870(2006)
[543] DJ Rowe Coherent state theory of the noncompact symplectic group J Math Phys 252662ndash2271 (1984)
[544] DJ Rowe Microscopic theory of the nuclear collective model Rep Prog Phys 48 1419ndash1480 (1985)
[545] DJ Rowe Vector coherent state representations and their inner products J Phys A MathGen 45 244003 (2012) (This paper belongs to the special issue [38])
[546] DJ Rowe J Repka Vector-coherent-state theory as a theory of induced representationsJ Math Phys 32 2614ndash2634 (1991)
[547] DJ Rowe G Rosensteel R Gilmore Vector coherent state representation theory J MathPhys 26 2787ndash2791 (1985)
[548] A Royer Phase states and phase operators for the quantum harmonic oscillator Phys RevA 53 70ndash108 (1996)
[549] J Saletan Contraction of Lie groups J Math Phys 2 1ndash21 (1961)[550] G Saracco A Grossmann P Tchamitchian Use of wavelet transforms in the study of
propagation of transient acoustic signals across a plane interface between two homoge-neous media in Wavelets Time-Frequency Methods and Phase Space (Proc Marseille1987) ed by J-M Combes A Grossmann P Tchamitchian 2nd edn (Springer Berlin1990) pp 139ndash146
[551] P Schroumlder W Sweldens Spherical wavelets Efficiently representing functions on thesphere in Computer Graphics Proceedings (SIGGRAPH95) (ACM Siggraph Los Angeles1995) pp 161ndash175
References 569
[552] E Schroumldinger Der stetige Uumlbergang von der Mikro- zur Makromechanik Naturwiss 14664ndash666 (1926)
[553] S Scodeller Oslash Rudjord FK Hansen D Marinucci D Geller A Mayeli IntroducingMexican needlets for CMB analysis Issues for practical applications and comparison withstandard needlets Astrophys J 733 (2011) Art 121
[554] H Scutaru Coherent states and induced representations Lett Math Phys 2 101ndash107(1977)
[555] B Simon Distributions and their Hermite expansions J Math Phys 12 140ndash148 (1971)[556] B Simon The classical moment problem as a self-adjoint finite difference operator Adv
Math 137 82ndash203 (1998)[557] R Simon ECG Sudarshan N Mukunda Gaussian pure states in quantum mechanics
and the symplectic group Phys Rev A37 3028ndash3038 (1988)[558] S Sivakumar Studies on nonlinear coherent states J Opt B Quant Semiclass Opt 2
R61ndashR75 (2000)[559] E Slezak A Bijaoui G Mars Identification of structures from galaxy counts Use of the
wavelet transform Astron Astroph 227 301ndash316 (1990)[560] A Solomon A characteristic functional for deformed photon phenomenology Phys Lett
A 196 29ndash34 (1994)[561] SB Sontz Paragrassmann algebras as quantum spaces Part I Reproducing kernels in
Geometric Methods in Physics XXXI Workshop 2012 (Trends in Mathematics ed byP Kielanowski et al Birkhaumluser Verlag Basel 2013) pp 47ndash63
[562] SB Sontz Paragrassmann algebras as quantum spaces Part II Toeplitz operators J OperTh (2013 to appear) arXiv12055493
[563] SB Sontz A reproducing kernel and Toeplitz operators in the quantum plane Preprint(2013) arXiv13056986 [math-ph]
[564] SB Sontz Toeplitz quantization of an algebra with conjugation Preprint (2013)arXiv13085454 [math-ph]
[565] M Spera On a generalized Uncertainty Principle coherent states and the moment mapJ Geom Phys 12 165ndash182 (1993)
[566] J-L Starck EJ Candegraves DL Donoho The curvelet transform for image denoising IEEETrans Image Proc 11 670ndash684 (2002)
[567] J-L Starck DL Donoho E J Candegraves Astronomical image representation by the curvelettransform Astron Astroph 398 785ndash800 (2003)
[568] J-L Starck Y Moudden P Abrial M Nguyen Wavelets ridgelets and curvelets on thesphere Astron Astroph 446 1191ndash1204 (2006)
[569] MB Stenzel The Segal-Bargmann transform on a symmetric space of compact type JFunct Analysis 165 44ndash58 (1994)
[570] ECG Sudarshan Equivalence of semiclassical and quantum mechanical descriptions ofstatistical light beams Phys Rev Lett 10 277ndash279 (1963)
[571] A Suvichakorn H Ratiney A Bucur S Cavassila J-P Antoine Toward a quantitativeanalysis of in vivo magnetic resonance proton spectroscopic signals using the continuousMorlet wavelet transform Meas Sci Technol 20 (2009) Art 104029
[572] W Sweldens The lifting scheme A custom-design construction of biorthogonal waveletsApplied Comput Harmon Anal 3 1186ndash1200 (1996)
[573] W Sweldens The lifting scheme A construction of second generation wavelets SIAM JMath Anal 29 511ndash546 (1998)
[574] FH Szafraniec The reproducing kernel Hilbert space and its multiplication operatorsin Complex Analysis and Related Topics ed by E Ramirez de Arellano et al OperatorTheory Advances and Applications vol 114 (Birkhaumluser Basel 2000) pp 254ndash263
[575] FH Szafraniec Multipliers in the reproducing kernel Hilbert space subnormality andnoncommutative complex analysis in Reproducing Kernel Spaces and Applications edby D Alpay Operator Theory Advances and Applications vol 143 (Birkhaumluser Basel2003) pp 313ndash331
570 References
[576] R Takahashi Sur les repreacutesentations unitaires des groupes de Lorentz geacuteneacuteraliseacutes BullSoc Math France 91 289ndash433 (1963)
[577] MC Teich BEA Saleh Squeezed states of light Quantum Opt 1 152ndash191 (1989)[578] R Terrier L Demanet IA Grenier J-P Antoine Wavelet analysis of EGRET data in
Proceedings of the 27th International Cosmic Ray Conference (ICRC 2001) (CopernicusGesellschaft DE 2001) pp 2923ndash2926
[579] T Thiemann Gauge field theory coherent states (GCS) 1 General properties Class QuantGrav 18 2025ndash2064 (2001)
[580] T Thiemann O Winkler Gauge field theory coherent states (GCS) 2 Peakednessproperties Class Quant Grav 18 2561ndash2636 (2001)
[581] T Thiemann O Winkler Gauge field theory coherent states (GCS) 3 Ehrenfest theoremsClass Quant Grav 18 4629ndash4682 (2001)
[582] T Thiemann O Winkler Gauge field theory coherent states (GCS) 4 Infinite tensorproduct and thermodynamical limit Class Quant Grav 18 4997ndash5054 (2001)
[583] K Thirulagasanthar ST Ali Regular subspaces of a quaternionic Hilbert space fromquaternionic Hermite polynomials and associated coherent states J Math Phys 54013506 (2013)
[584] K Thirulogasanthar G Honnouvo A Krzyzak Coherent states and Hermite polynomialson quaternionic Hilbert spaces J Phys A Math Theor 43 385205 (2010)
[585] Tokamak see Wikipedia httpenwikipediaorgwikiTokamak[586] B Torreacutesani Wavelets associated with representations of the affine Weyl-Heisenberg
group J Math Phys 32 1273ndash1279 (1991)[587] B Torreacutesani Time-frequency representation Wavelet packets and optimal decomposition
Ann Inst H Poincareacute 56 215ndash234 (1992)[588] B Torreacutesani Position-frequency analysis for signals defined on spheres Signal Proc 43
341ndash346 (2005)[589] DA Trifonov Generalized intelligent states and squeezing J Math Phys 35 2297ndash2308
(1994)[590] AS Trushechkin IV Volovich Localization properties of squeezed quantum states in
nanoscale space domains preprint (2013) arXiv13046277v1 [quant-ph][591] M Unser N Chenouard A unifying parametric framework for 2D steerable wavelet
transforms SIAM J Imaging Sci 6 102ndash135 (2013)[592] P Vandergheynst J-F Gobbers Directional dyadic wavelet transforms Design and
algorithms IEEE Trans Image Proc 11 363ndash372 (2002)[593] P Vandergheynst J-P Antoine E Van Vyve A Goldberg I Doghri Modelling and
simulation of an impact test using wavelets analytical and finite element models Int JSolids Struct 38 5481ndash5508 (2001)
[594] L Vanhamme RD Fierro S Van Huffel R de Beer Fast removal of residual water inproton spectra J Magn Reson 132 197ndash203 (1998)
[595] J Ville Theacuteorie et applications de la notion de signal analytique Cacircbles et Trans 2 61ndash74(1948)
[596] J Voisin On some unitary representations of the Galilei group I Irreducible representa-tions J Math Phys 6 1519ndash1529 (1965)
[597] A Vourdas Analytic representations in quantum mechanics J Phys A Math Gen 39R65ndashR141 (2006)
[598] DF Walls Squeezed states of light Nature 306 141ndash146 (1983)[599] YK Wang FT Hioe Phase transition in the Dicke maser model Phys Rev A 7 831ndash836
(1973)[600] PSP Wang J Yang A review of wavelet-based edge detection methods Int J Patt
Recogn Artif Intell 26 1255011 (2012)[601] I Weinreich A construction of C1-wavelets on the two-dimensional sphere Appl Comput
Harmon Anal 10 1ndash26 (2001)[602] H Weyl Quantenmechanik und Gruppentheorie Z Phys 46 1ndash46 (1927)
References 571
[603] Y Wiaux L Jacques P Vandergheynst Correspondence principle between spherical andEuclidean wavelets Astrophys J 632 15ndash28 (2005)
[604] Y Wiaux L Jacques P Vielva P Vandergheynst Fast directional correlation on the spherewith steerable filters Astrophys J 652 820ndash832 (2006)
[605] Y Wiaux JD McEwen P Vandergheynst O Blanc Exact reconstruction with directionalwavelets on the sphere Mon Not R Astron Soc 388 770ndash788 (2008)
[606] WM Wieland Complex Ashtekar variables and reality conditions for Holstrsquos action AnnHenri Poincareacute 13 425ndash448 (2012)
[607] EP Wigner On the quantum correction for thermodynamic equilibrium Phys Rev 40749ndash759 (1932)
[608] RM Willette RD Nowak Platelets A multiscale approach for recovering edges andsurfaces in photon-limited medical imaging IEEE Trans Med Imaging 22 332ndash350(2003)
[609] W Wisnoe P Gajan A Strzelecki C Lempereur J-M Matheacute The use of the two-dimensional wavelet transform in flow visualization processing in Progress in WaveletAnalysis and Applications (Proc Toulouse 1992) ed by Y Meyer S Roques (EdFrontiegraveres Gif-sur-Yvette 1993) pp 455ndash458
[610] K Woacutedkiewicz On the quantum mechanics of squeezed states J Modern Optics 34 941ndash948(1987)
[611] JA Yeazell M Mallalieu CR Stroud Jr Observation of the collapse and revival of aRydberg electronic wave packet Phys Rev Lett 64 2007ndash2010 (1990)
[612] JA Yeazell CR Stroud Jr Observation of fractional revivals in the evolution of aRydberg atomic wave packet Phys Rev A 43 5153ndash5156 (1991)
[613] HP Yuen Two-photon coherent states of the radiation field Phys Rev A 13 2226ndash2243(1976)
[614] J Zak Balian-Low theorem for Landau levels Phys Rev Lett 79 533ndash536 (1997)[615] J Zak Orthonormal sets of localized functions for a Landau level J Math Phys 39 4195ndash
4200 (1998) and references quoted there[616] AA Zakharova On the properties of generalized frames Math Notes 83 190ndash200 (2008)[617] W-M Zhang DH Feng R Gilmore Coherent states Theory and some applications Rev
Mod Phys 26 867ndash927 (1990)[618] I Zlatev W-M Zhang DH Feng Possibility that Schroumldingerrsquos conjecture for the
hydrogen atom coherent states is not attainable Phys Rev A 50 R1973ndashR1975 (1994)[619] WH Zurek Decoherence einselection and the quantum origins of the classical Rev Mod
Phys 75 715ndash775 (2003)[620] WH Zurek S Habib JP Paz Coherent states via decoherence Phys Rev Lett 70 1187ndash
1190 (1993)[621] K Zyczkowski Squeezed states in a quantum chaotic system J Phys A Math Theor 22
of SU(11) 81 296 297HilbertClowast-modules 164holomorphic 140nonholomorphic 151nonlinear 146of affine Galilei group 505of affine Poincareacute group 509of affine Weyl-Heisenberg group GaWH
497of compact semisimple Lie groups 174of Euclidean group E(n) 266of Galilei group G (11) 290of isochronous Galilei group 237of non-semisimple Lie groups 179of noncompact semisimple Lie groups 177of Poincareacute group Puarr
+(11) 283massless case 288
of Poincareacute group Puarr+(13) 279
of Schroumldinger group 508quasi-coherent states 186quaternionic 164
ST Ali et al Coherent States Wavelets and Their Generalizations Theoreticaland Mathematical Physics DOI 101007978-1-4614-8535-3copy Springer Science+Business Media New York 2014
573
574 Index
coherent states (CS) (cont)spin or SU(2) 175square integrable covariant 166 180 264vector (VCS) 73 108 112 170weighted 184 523
of affine Weyl-Heisenberg group GaWH497
of Poincareacute group Puarr+(11) 284
cohomology group 393 403coboundaries 403cochains 402cocycle 403
algebraic 387Cauchy 418Cauchy-Paul 354 419 425conical 418difference 417 462directional 416 440kinematical 499local 488metabolite-based 355 374minimal uncertainty 425multiselective 440on a graph 493on the sphere S
2 458on the sphere S
n 479on the torus T2 481steerable 439von Mises 440
wedgelet transform 455Wigner function 322Wigner-Ville transform 349Windowed Fourier or Gabor transform 349
ZZak transform 518
References
A Books and Theses
B Articles
Index
References 569
[552] E Schroumldinger Der stetige Uumlbergang von der Mikro- zur Makromechanik Naturwiss 14664ndash666 (1926)
[553] S Scodeller Oslash Rudjord FK Hansen D Marinucci D Geller A Mayeli IntroducingMexican needlets for CMB analysis Issues for practical applications and comparison withstandard needlets Astrophys J 733 (2011) Art 121
[554] H Scutaru Coherent states and induced representations Lett Math Phys 2 101ndash107(1977)
[555] B Simon Distributions and their Hermite expansions J Math Phys 12 140ndash148 (1971)[556] B Simon The classical moment problem as a self-adjoint finite difference operator Adv
Math 137 82ndash203 (1998)[557] R Simon ECG Sudarshan N Mukunda Gaussian pure states in quantum mechanics
and the symplectic group Phys Rev A37 3028ndash3038 (1988)[558] S Sivakumar Studies on nonlinear coherent states J Opt B Quant Semiclass Opt 2
R61ndashR75 (2000)[559] E Slezak A Bijaoui G Mars Identification of structures from galaxy counts Use of the
wavelet transform Astron Astroph 227 301ndash316 (1990)[560] A Solomon A characteristic functional for deformed photon phenomenology Phys Lett
A 196 29ndash34 (1994)[561] SB Sontz Paragrassmann algebras as quantum spaces Part I Reproducing kernels in
Geometric Methods in Physics XXXI Workshop 2012 (Trends in Mathematics ed byP Kielanowski et al Birkhaumluser Verlag Basel 2013) pp 47ndash63
[562] SB Sontz Paragrassmann algebras as quantum spaces Part II Toeplitz operators J OperTh (2013 to appear) arXiv12055493
[563] SB Sontz A reproducing kernel and Toeplitz operators in the quantum plane Preprint(2013) arXiv13056986 [math-ph]
[564] SB Sontz Toeplitz quantization of an algebra with conjugation Preprint (2013)arXiv13085454 [math-ph]
[565] M Spera On a generalized Uncertainty Principle coherent states and the moment mapJ Geom Phys 12 165ndash182 (1993)
[566] J-L Starck EJ Candegraves DL Donoho The curvelet transform for image denoising IEEETrans Image Proc 11 670ndash684 (2002)
[567] J-L Starck DL Donoho E J Candegraves Astronomical image representation by the curvelettransform Astron Astroph 398 785ndash800 (2003)
[568] J-L Starck Y Moudden P Abrial M Nguyen Wavelets ridgelets and curvelets on thesphere Astron Astroph 446 1191ndash1204 (2006)
[569] MB Stenzel The Segal-Bargmann transform on a symmetric space of compact type JFunct Analysis 165 44ndash58 (1994)
[570] ECG Sudarshan Equivalence of semiclassical and quantum mechanical descriptions ofstatistical light beams Phys Rev Lett 10 277ndash279 (1963)
[571] A Suvichakorn H Ratiney A Bucur S Cavassila J-P Antoine Toward a quantitativeanalysis of in vivo magnetic resonance proton spectroscopic signals using the continuousMorlet wavelet transform Meas Sci Technol 20 (2009) Art 104029
[572] W Sweldens The lifting scheme A custom-design construction of biorthogonal waveletsApplied Comput Harmon Anal 3 1186ndash1200 (1996)
[573] W Sweldens The lifting scheme A construction of second generation wavelets SIAM JMath Anal 29 511ndash546 (1998)
[574] FH Szafraniec The reproducing kernel Hilbert space and its multiplication operatorsin Complex Analysis and Related Topics ed by E Ramirez de Arellano et al OperatorTheory Advances and Applications vol 114 (Birkhaumluser Basel 2000) pp 254ndash263
[575] FH Szafraniec Multipliers in the reproducing kernel Hilbert space subnormality andnoncommutative complex analysis in Reproducing Kernel Spaces and Applications edby D Alpay Operator Theory Advances and Applications vol 143 (Birkhaumluser Basel2003) pp 313ndash331
570 References
[576] R Takahashi Sur les repreacutesentations unitaires des groupes de Lorentz geacuteneacuteraliseacutes BullSoc Math France 91 289ndash433 (1963)
[577] MC Teich BEA Saleh Squeezed states of light Quantum Opt 1 152ndash191 (1989)[578] R Terrier L Demanet IA Grenier J-P Antoine Wavelet analysis of EGRET data in
Proceedings of the 27th International Cosmic Ray Conference (ICRC 2001) (CopernicusGesellschaft DE 2001) pp 2923ndash2926
[579] T Thiemann Gauge field theory coherent states (GCS) 1 General properties Class QuantGrav 18 2025ndash2064 (2001)
[580] T Thiemann O Winkler Gauge field theory coherent states (GCS) 2 Peakednessproperties Class Quant Grav 18 2561ndash2636 (2001)
[581] T Thiemann O Winkler Gauge field theory coherent states (GCS) 3 Ehrenfest theoremsClass Quant Grav 18 4629ndash4682 (2001)
[582] T Thiemann O Winkler Gauge field theory coherent states (GCS) 4 Infinite tensorproduct and thermodynamical limit Class Quant Grav 18 4997ndash5054 (2001)
[583] K Thirulagasanthar ST Ali Regular subspaces of a quaternionic Hilbert space fromquaternionic Hermite polynomials and associated coherent states J Math Phys 54013506 (2013)
[584] K Thirulogasanthar G Honnouvo A Krzyzak Coherent states and Hermite polynomialson quaternionic Hilbert spaces J Phys A Math Theor 43 385205 (2010)
[585] Tokamak see Wikipedia httpenwikipediaorgwikiTokamak[586] B Torreacutesani Wavelets associated with representations of the affine Weyl-Heisenberg
group J Math Phys 32 1273ndash1279 (1991)[587] B Torreacutesani Time-frequency representation Wavelet packets and optimal decomposition
Ann Inst H Poincareacute 56 215ndash234 (1992)[588] B Torreacutesani Position-frequency analysis for signals defined on spheres Signal Proc 43
341ndash346 (2005)[589] DA Trifonov Generalized intelligent states and squeezing J Math Phys 35 2297ndash2308
(1994)[590] AS Trushechkin IV Volovich Localization properties of squeezed quantum states in
nanoscale space domains preprint (2013) arXiv13046277v1 [quant-ph][591] M Unser N Chenouard A unifying parametric framework for 2D steerable wavelet
transforms SIAM J Imaging Sci 6 102ndash135 (2013)[592] P Vandergheynst J-F Gobbers Directional dyadic wavelet transforms Design and
algorithms IEEE Trans Image Proc 11 363ndash372 (2002)[593] P Vandergheynst J-P Antoine E Van Vyve A Goldberg I Doghri Modelling and
simulation of an impact test using wavelets analytical and finite element models Int JSolids Struct 38 5481ndash5508 (2001)
[594] L Vanhamme RD Fierro S Van Huffel R de Beer Fast removal of residual water inproton spectra J Magn Reson 132 197ndash203 (1998)
[595] J Ville Theacuteorie et applications de la notion de signal analytique Cacircbles et Trans 2 61ndash74(1948)
[596] J Voisin On some unitary representations of the Galilei group I Irreducible representa-tions J Math Phys 6 1519ndash1529 (1965)
[597] A Vourdas Analytic representations in quantum mechanics J Phys A Math Gen 39R65ndashR141 (2006)
[598] DF Walls Squeezed states of light Nature 306 141ndash146 (1983)[599] YK Wang FT Hioe Phase transition in the Dicke maser model Phys Rev A 7 831ndash836
(1973)[600] PSP Wang J Yang A review of wavelet-based edge detection methods Int J Patt
Recogn Artif Intell 26 1255011 (2012)[601] I Weinreich A construction of C1-wavelets on the two-dimensional sphere Appl Comput
Harmon Anal 10 1ndash26 (2001)[602] H Weyl Quantenmechanik und Gruppentheorie Z Phys 46 1ndash46 (1927)
References 571
[603] Y Wiaux L Jacques P Vandergheynst Correspondence principle between spherical andEuclidean wavelets Astrophys J 632 15ndash28 (2005)
[604] Y Wiaux L Jacques P Vielva P Vandergheynst Fast directional correlation on the spherewith steerable filters Astrophys J 652 820ndash832 (2006)
[605] Y Wiaux JD McEwen P Vandergheynst O Blanc Exact reconstruction with directionalwavelets on the sphere Mon Not R Astron Soc 388 770ndash788 (2008)
[606] WM Wieland Complex Ashtekar variables and reality conditions for Holstrsquos action AnnHenri Poincareacute 13 425ndash448 (2012)
[607] EP Wigner On the quantum correction for thermodynamic equilibrium Phys Rev 40749ndash759 (1932)
[608] RM Willette RD Nowak Platelets A multiscale approach for recovering edges andsurfaces in photon-limited medical imaging IEEE Trans Med Imaging 22 332ndash350(2003)
[609] W Wisnoe P Gajan A Strzelecki C Lempereur J-M Matheacute The use of the two-dimensional wavelet transform in flow visualization processing in Progress in WaveletAnalysis and Applications (Proc Toulouse 1992) ed by Y Meyer S Roques (EdFrontiegraveres Gif-sur-Yvette 1993) pp 455ndash458
[610] K Woacutedkiewicz On the quantum mechanics of squeezed states J Modern Optics 34 941ndash948(1987)
[611] JA Yeazell M Mallalieu CR Stroud Jr Observation of the collapse and revival of aRydberg electronic wave packet Phys Rev Lett 64 2007ndash2010 (1990)
[612] JA Yeazell CR Stroud Jr Observation of fractional revivals in the evolution of aRydberg atomic wave packet Phys Rev A 43 5153ndash5156 (1991)
[613] HP Yuen Two-photon coherent states of the radiation field Phys Rev A 13 2226ndash2243(1976)
[614] J Zak Balian-Low theorem for Landau levels Phys Rev Lett 79 533ndash536 (1997)[615] J Zak Orthonormal sets of localized functions for a Landau level J Math Phys 39 4195ndash
4200 (1998) and references quoted there[616] AA Zakharova On the properties of generalized frames Math Notes 83 190ndash200 (2008)[617] W-M Zhang DH Feng R Gilmore Coherent states Theory and some applications Rev
Mod Phys 26 867ndash927 (1990)[618] I Zlatev W-M Zhang DH Feng Possibility that Schroumldingerrsquos conjecture for the
hydrogen atom coherent states is not attainable Phys Rev A 50 R1973ndashR1975 (1994)[619] WH Zurek Decoherence einselection and the quantum origins of the classical Rev Mod
Phys 75 715ndash775 (2003)[620] WH Zurek S Habib JP Paz Coherent states via decoherence Phys Rev Lett 70 1187ndash
1190 (1993)[621] K Zyczkowski Squeezed states in a quantum chaotic system J Phys A Math Theor 22
of SU(11) 81 296 297HilbertClowast-modules 164holomorphic 140nonholomorphic 151nonlinear 146of affine Galilei group 505of affine Poincareacute group 509of affine Weyl-Heisenberg group GaWH
497of compact semisimple Lie groups 174of Euclidean group E(n) 266of Galilei group G (11) 290of isochronous Galilei group 237of non-semisimple Lie groups 179of noncompact semisimple Lie groups 177of Poincareacute group Puarr
+(11) 283massless case 288
of Poincareacute group Puarr+(13) 279
of Schroumldinger group 508quasi-coherent states 186quaternionic 164
ST Ali et al Coherent States Wavelets and Their Generalizations Theoreticaland Mathematical Physics DOI 101007978-1-4614-8535-3copy Springer Science+Business Media New York 2014
573
574 Index
coherent states (CS) (cont)spin or SU(2) 175square integrable covariant 166 180 264vector (VCS) 73 108 112 170weighted 184 523
of affine Weyl-Heisenberg group GaWH497
of Poincareacute group Puarr+(11) 284
cohomology group 393 403coboundaries 403cochains 402cocycle 403
algebraic 387Cauchy 418Cauchy-Paul 354 419 425conical 418difference 417 462directional 416 440kinematical 499local 488metabolite-based 355 374minimal uncertainty 425multiselective 440on a graph 493on the sphere S
2 458on the sphere S
n 479on the torus T2 481steerable 439von Mises 440
wedgelet transform 455Wigner function 322Wigner-Ville transform 349Windowed Fourier or Gabor transform 349
ZZak transform 518
References
A Books and Theses
B Articles
Index
570 References
[576] R Takahashi Sur les repreacutesentations unitaires des groupes de Lorentz geacuteneacuteraliseacutes BullSoc Math France 91 289ndash433 (1963)
[577] MC Teich BEA Saleh Squeezed states of light Quantum Opt 1 152ndash191 (1989)[578] R Terrier L Demanet IA Grenier J-P Antoine Wavelet analysis of EGRET data in
Proceedings of the 27th International Cosmic Ray Conference (ICRC 2001) (CopernicusGesellschaft DE 2001) pp 2923ndash2926
[579] T Thiemann Gauge field theory coherent states (GCS) 1 General properties Class QuantGrav 18 2025ndash2064 (2001)
[580] T Thiemann O Winkler Gauge field theory coherent states (GCS) 2 Peakednessproperties Class Quant Grav 18 2561ndash2636 (2001)
[581] T Thiemann O Winkler Gauge field theory coherent states (GCS) 3 Ehrenfest theoremsClass Quant Grav 18 4629ndash4682 (2001)
[582] T Thiemann O Winkler Gauge field theory coherent states (GCS) 4 Infinite tensorproduct and thermodynamical limit Class Quant Grav 18 4997ndash5054 (2001)
[583] K Thirulagasanthar ST Ali Regular subspaces of a quaternionic Hilbert space fromquaternionic Hermite polynomials and associated coherent states J Math Phys 54013506 (2013)
[584] K Thirulogasanthar G Honnouvo A Krzyzak Coherent states and Hermite polynomialson quaternionic Hilbert spaces J Phys A Math Theor 43 385205 (2010)
[585] Tokamak see Wikipedia httpenwikipediaorgwikiTokamak[586] B Torreacutesani Wavelets associated with representations of the affine Weyl-Heisenberg
group J Math Phys 32 1273ndash1279 (1991)[587] B Torreacutesani Time-frequency representation Wavelet packets and optimal decomposition
Ann Inst H Poincareacute 56 215ndash234 (1992)[588] B Torreacutesani Position-frequency analysis for signals defined on spheres Signal Proc 43
341ndash346 (2005)[589] DA Trifonov Generalized intelligent states and squeezing J Math Phys 35 2297ndash2308
(1994)[590] AS Trushechkin IV Volovich Localization properties of squeezed quantum states in
nanoscale space domains preprint (2013) arXiv13046277v1 [quant-ph][591] M Unser N Chenouard A unifying parametric framework for 2D steerable wavelet
transforms SIAM J Imaging Sci 6 102ndash135 (2013)[592] P Vandergheynst J-F Gobbers Directional dyadic wavelet transforms Design and
algorithms IEEE Trans Image Proc 11 363ndash372 (2002)[593] P Vandergheynst J-P Antoine E Van Vyve A Goldberg I Doghri Modelling and
simulation of an impact test using wavelets analytical and finite element models Int JSolids Struct 38 5481ndash5508 (2001)
[594] L Vanhamme RD Fierro S Van Huffel R de Beer Fast removal of residual water inproton spectra J Magn Reson 132 197ndash203 (1998)
[595] J Ville Theacuteorie et applications de la notion de signal analytique Cacircbles et Trans 2 61ndash74(1948)
[596] J Voisin On some unitary representations of the Galilei group I Irreducible representa-tions J Math Phys 6 1519ndash1529 (1965)
[597] A Vourdas Analytic representations in quantum mechanics J Phys A Math Gen 39R65ndashR141 (2006)
[598] DF Walls Squeezed states of light Nature 306 141ndash146 (1983)[599] YK Wang FT Hioe Phase transition in the Dicke maser model Phys Rev A 7 831ndash836
(1973)[600] PSP Wang J Yang A review of wavelet-based edge detection methods Int J Patt
Recogn Artif Intell 26 1255011 (2012)[601] I Weinreich A construction of C1-wavelets on the two-dimensional sphere Appl Comput
Harmon Anal 10 1ndash26 (2001)[602] H Weyl Quantenmechanik und Gruppentheorie Z Phys 46 1ndash46 (1927)
References 571
[603] Y Wiaux L Jacques P Vandergheynst Correspondence principle between spherical andEuclidean wavelets Astrophys J 632 15ndash28 (2005)
[604] Y Wiaux L Jacques P Vielva P Vandergheynst Fast directional correlation on the spherewith steerable filters Astrophys J 652 820ndash832 (2006)
[605] Y Wiaux JD McEwen P Vandergheynst O Blanc Exact reconstruction with directionalwavelets on the sphere Mon Not R Astron Soc 388 770ndash788 (2008)
[606] WM Wieland Complex Ashtekar variables and reality conditions for Holstrsquos action AnnHenri Poincareacute 13 425ndash448 (2012)
[607] EP Wigner On the quantum correction for thermodynamic equilibrium Phys Rev 40749ndash759 (1932)
[608] RM Willette RD Nowak Platelets A multiscale approach for recovering edges andsurfaces in photon-limited medical imaging IEEE Trans Med Imaging 22 332ndash350(2003)
[609] W Wisnoe P Gajan A Strzelecki C Lempereur J-M Matheacute The use of the two-dimensional wavelet transform in flow visualization processing in Progress in WaveletAnalysis and Applications (Proc Toulouse 1992) ed by Y Meyer S Roques (EdFrontiegraveres Gif-sur-Yvette 1993) pp 455ndash458
[610] K Woacutedkiewicz On the quantum mechanics of squeezed states J Modern Optics 34 941ndash948(1987)
[611] JA Yeazell M Mallalieu CR Stroud Jr Observation of the collapse and revival of aRydberg electronic wave packet Phys Rev Lett 64 2007ndash2010 (1990)
[612] JA Yeazell CR Stroud Jr Observation of fractional revivals in the evolution of aRydberg atomic wave packet Phys Rev A 43 5153ndash5156 (1991)
[613] HP Yuen Two-photon coherent states of the radiation field Phys Rev A 13 2226ndash2243(1976)
[614] J Zak Balian-Low theorem for Landau levels Phys Rev Lett 79 533ndash536 (1997)[615] J Zak Orthonormal sets of localized functions for a Landau level J Math Phys 39 4195ndash
4200 (1998) and references quoted there[616] AA Zakharova On the properties of generalized frames Math Notes 83 190ndash200 (2008)[617] W-M Zhang DH Feng R Gilmore Coherent states Theory and some applications Rev
Mod Phys 26 867ndash927 (1990)[618] I Zlatev W-M Zhang DH Feng Possibility that Schroumldingerrsquos conjecture for the
hydrogen atom coherent states is not attainable Phys Rev A 50 R1973ndashR1975 (1994)[619] WH Zurek Decoherence einselection and the quantum origins of the classical Rev Mod
Phys 75 715ndash775 (2003)[620] WH Zurek S Habib JP Paz Coherent states via decoherence Phys Rev Lett 70 1187ndash
1190 (1993)[621] K Zyczkowski Squeezed states in a quantum chaotic system J Phys A Math Theor 22
of SU(11) 81 296 297HilbertClowast-modules 164holomorphic 140nonholomorphic 151nonlinear 146of affine Galilei group 505of affine Poincareacute group 509of affine Weyl-Heisenberg group GaWH
497of compact semisimple Lie groups 174of Euclidean group E(n) 266of Galilei group G (11) 290of isochronous Galilei group 237of non-semisimple Lie groups 179of noncompact semisimple Lie groups 177of Poincareacute group Puarr
+(11) 283massless case 288
of Poincareacute group Puarr+(13) 279
of Schroumldinger group 508quasi-coherent states 186quaternionic 164
ST Ali et al Coherent States Wavelets and Their Generalizations Theoreticaland Mathematical Physics DOI 101007978-1-4614-8535-3copy Springer Science+Business Media New York 2014
573
574 Index
coherent states (CS) (cont)spin or SU(2) 175square integrable covariant 166 180 264vector (VCS) 73 108 112 170weighted 184 523
of affine Weyl-Heisenberg group GaWH497
of Poincareacute group Puarr+(11) 284
cohomology group 393 403coboundaries 403cochains 402cocycle 403
algebraic 387Cauchy 418Cauchy-Paul 354 419 425conical 418difference 417 462directional 416 440kinematical 499local 488metabolite-based 355 374minimal uncertainty 425multiselective 440on a graph 493on the sphere S
2 458on the sphere S
n 479on the torus T2 481steerable 439von Mises 440
wedgelet transform 455Wigner function 322Wigner-Ville transform 349Windowed Fourier or Gabor transform 349
ZZak transform 518
References
A Books and Theses
B Articles
Index
References 571
[603] Y Wiaux L Jacques P Vandergheynst Correspondence principle between spherical andEuclidean wavelets Astrophys J 632 15ndash28 (2005)
[604] Y Wiaux L Jacques P Vielva P Vandergheynst Fast directional correlation on the spherewith steerable filters Astrophys J 652 820ndash832 (2006)
[605] Y Wiaux JD McEwen P Vandergheynst O Blanc Exact reconstruction with directionalwavelets on the sphere Mon Not R Astron Soc 388 770ndash788 (2008)
[606] WM Wieland Complex Ashtekar variables and reality conditions for Holstrsquos action AnnHenri Poincareacute 13 425ndash448 (2012)
[607] EP Wigner On the quantum correction for thermodynamic equilibrium Phys Rev 40749ndash759 (1932)
[608] RM Willette RD Nowak Platelets A multiscale approach for recovering edges andsurfaces in photon-limited medical imaging IEEE Trans Med Imaging 22 332ndash350(2003)
[609] W Wisnoe P Gajan A Strzelecki C Lempereur J-M Matheacute The use of the two-dimensional wavelet transform in flow visualization processing in Progress in WaveletAnalysis and Applications (Proc Toulouse 1992) ed by Y Meyer S Roques (EdFrontiegraveres Gif-sur-Yvette 1993) pp 455ndash458
[610] K Woacutedkiewicz On the quantum mechanics of squeezed states J Modern Optics 34 941ndash948(1987)
[611] JA Yeazell M Mallalieu CR Stroud Jr Observation of the collapse and revival of aRydberg electronic wave packet Phys Rev Lett 64 2007ndash2010 (1990)
[612] JA Yeazell CR Stroud Jr Observation of fractional revivals in the evolution of aRydberg atomic wave packet Phys Rev A 43 5153ndash5156 (1991)
[613] HP Yuen Two-photon coherent states of the radiation field Phys Rev A 13 2226ndash2243(1976)
[614] J Zak Balian-Low theorem for Landau levels Phys Rev Lett 79 533ndash536 (1997)[615] J Zak Orthonormal sets of localized functions for a Landau level J Math Phys 39 4195ndash
4200 (1998) and references quoted there[616] AA Zakharova On the properties of generalized frames Math Notes 83 190ndash200 (2008)[617] W-M Zhang DH Feng R Gilmore Coherent states Theory and some applications Rev
Mod Phys 26 867ndash927 (1990)[618] I Zlatev W-M Zhang DH Feng Possibility that Schroumldingerrsquos conjecture for the
hydrogen atom coherent states is not attainable Phys Rev A 50 R1973ndashR1975 (1994)[619] WH Zurek Decoherence einselection and the quantum origins of the classical Rev Mod
Phys 75 715ndash775 (2003)[620] WH Zurek S Habib JP Paz Coherent states via decoherence Phys Rev Lett 70 1187ndash
1190 (1993)[621] K Zyczkowski Squeezed states in a quantum chaotic system J Phys A Math Theor 22
of SU(11) 81 296 297HilbertClowast-modules 164holomorphic 140nonholomorphic 151nonlinear 146of affine Galilei group 505of affine Poincareacute group 509of affine Weyl-Heisenberg group GaWH
497of compact semisimple Lie groups 174of Euclidean group E(n) 266of Galilei group G (11) 290of isochronous Galilei group 237of non-semisimple Lie groups 179of noncompact semisimple Lie groups 177of Poincareacute group Puarr
+(11) 283massless case 288
of Poincareacute group Puarr+(13) 279
of Schroumldinger group 508quasi-coherent states 186quaternionic 164
ST Ali et al Coherent States Wavelets and Their Generalizations Theoreticaland Mathematical Physics DOI 101007978-1-4614-8535-3copy Springer Science+Business Media New York 2014
573
574 Index
coherent states (CS) (cont)spin or SU(2) 175square integrable covariant 166 180 264vector (VCS) 73 108 112 170weighted 184 523
of affine Weyl-Heisenberg group GaWH497
of Poincareacute group Puarr+(11) 284
cohomology group 393 403coboundaries 403cochains 402cocycle 403
of SU(11) 81 296 297HilbertClowast-modules 164holomorphic 140nonholomorphic 151nonlinear 146of affine Galilei group 505of affine Poincareacute group 509of affine Weyl-Heisenberg group GaWH
497of compact semisimple Lie groups 174of Euclidean group E(n) 266of Galilei group G (11) 290of isochronous Galilei group 237of non-semisimple Lie groups 179of noncompact semisimple Lie groups 177of Poincareacute group Puarr
+(11) 283massless case 288
of Poincareacute group Puarr+(13) 279
of Schroumldinger group 508quasi-coherent states 186quaternionic 164
ST Ali et al Coherent States Wavelets and Their Generalizations Theoreticaland Mathematical Physics DOI 101007978-1-4614-8535-3copy Springer Science+Business Media New York 2014
573
574 Index
coherent states (CS) (cont)spin or SU(2) 175square integrable covariant 166 180 264vector (VCS) 73 108 112 170weighted 184 523
of affine Weyl-Heisenberg group GaWH497
of Poincareacute group Puarr+(11) 284
cohomology group 393 403coboundaries 403cochains 402cocycle 403