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Volumn 143, Issue 4, 2004, Pages 299-331

Wavelet frames on groups and hypergroups via discretization of calderón formulas

Author keywords

Continuous square integrable representations; Frames; Hypergroups; Irregular sampling; Wavelets

Indexed keywords


EID: 11944249365     PISSN: 00269255     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00605-004-0282-z     Document Type: Article
Times cited : (6)

References (43)
  • 1
    • 0001505484 scopus 로고
    • Square integrability of group representations on homogeneous spaces. I. Reproducing triples and frames
    • Ali ST, Antoine J-P, Gazeau J-P (1991) Square integrability of group representations on homogeneous spaces. I. Reproducing triples and frames. Ann Inst Poincaré 55: 829-855
    • (1991) Ann Inst Poincaré , vol.55 , pp. 829-855
    • Ali, S.T.1    Antoine, J.-P.2    Gazeau, J.-P.3
  • 2
    • 0001505487 scopus 로고
    • Square integrability of group representations on homogeneous spaces. II. Coherent and quasi-coherent states. The case of the Poincaré group
    • Ali ST, Antoine J-P, Gazeau J-P (1991) Square integrability of group representations on homogeneous spaces. II. Coherent and quasi-coherent states. The case of the Poincaré group. Ann Inst Poincaré 55: 857-890
    • (1991) Ann Inst Poincaré , vol.55 , pp. 857-890
    • Ali, S.T.1    Antoine, J.-P.2    Gazeau, J.-P.3
  • 3
    • 0032380062 scopus 로고    scopus 로고
    • Wavelet transforms and discrete frames associated to semidirect products
    • Aniello P, Cassinelli G, De Vito E, Levrero A (1998) Wavelet transforms and discrete frames associated to semidirect products. J Math Phys 39: 3965-3973
    • (1998) J Math Phys , vol.39 , pp. 3965-3973
    • Aniello, P.1    Cassinelli, G.2    De Vito, E.3    Levrero, A.4
  • 5
    • 85088340532 scopus 로고    scopus 로고
    • Anisotropic Hardy Spaces and Wavelets
    • Bownik M (2003) Anisotropic Hardy Spaces and Wavelets. Memoirs Amer Math Society 781
    • (2003) Memoirs Amer Math Society , vol.781
    • Bownik, M.1
  • 6
    • 0030526326 scopus 로고    scopus 로고
    • Wavelets from square-integrable representations
    • Bernier D, Taylor K (1996) Wavelets from square-integrable representations. SIAM J Math Anal 27: 594-608
    • (1996) SIAM J Math Anal , vol.27 , pp. 594-608
    • Bernier, D.1    Taylor, K.2
  • 7
    • 0035998624 scopus 로고    scopus 로고
    • Characterization of tight wavelet frames with arbitrary matrix dilations and tightness preserving oversampling
    • Chui CK, Czaja W, Maggioni M, Weiss G (2002) Characterization of tight wavelet frames with arbitrary matrix dilations and tightness preserving oversampling. J Four Anal App 8: 173-200
    • (2002) J Four Anal App , vol.8 , pp. 173-200
    • Chui, C.K.1    Czaja, W.2    Maggioni, M.3    Weiss, G.4
  • 8
    • 21144467578 scopus 로고
    • Inequalities of Littlewood-Paley type for frames and wavelets
    • Chui CK, Shi X (1993) Inequalities of Littlewood-Paley type for frames and wavelets. SIAM J Math Anal 24: 263-277
    • (1993) SIAM J Math Anal , vol.24 , pp. 263-277
    • Chui, C.K.1    Shi, X.2
  • 10
    • 0003232322 scopus 로고
    • Analyse Harmonique Noncommutative sur Certains Espaces Homogenes
    • Berlin Heidelberg New York: Springer
    • Coifman R, Weiss G (1971) Analyse Harmonique Noncommutative sur Certains Espaces Homogenes. Lect Notes Math 242. Berlin Heidelberg New York: Springer
    • (1971) Lect Notes Math , vol.242
    • Coifman, R.1    Weiss, G.2
  • 13
    • 0001720260 scopus 로고
    • A boundedness criterion for generalized Calderón-Zygmund operators
    • David G, Journé JL (1984) A boundedness criterion for generalized Calderón-Zygmund operators. Annals of Math 120: 371-397
    • (1984) Annals of Math , vol.120 , pp. 371-397
    • David, G.1    Journé, J.L.2
  • 14
    • 0002350898 scopus 로고
    • Opérateurs de Calderón-Zygmund, fonctions paraaccrétives et interpolation
    • David G, Journé JL, Semmes S (1985) Opérateurs de Calderón-Zygmund, fonctions paraaccrétives et interpolation. Rev Mat Ibero 1: 1-56
    • (1985) Rev Mat Ibero , vol.1 , pp. 1-56
    • David, G.1    Journé, J.L.2    Semmes, S.3
  • 15
    • 0000653944 scopus 로고
    • On the regular representation of a nonunimodular locally compact group
    • Duflo M, Moore CC (1976) On the regular representation of a nonunimodular locally compact group. J Funct Anal 21: 209-243
    • (1976) J Funct Anal , vol.21 , pp. 209-243
    • Duflo, M.1    Moore, C.C.2
  • 16
    • 0002566774 scopus 로고    scopus 로고
    • A unified approach to atomic decompositions through integrable group representations
    • Cwikel M et al. (eds) Function Spaces and Applications. Berlin Heidelberg New York: Springer
    • Feichtinger HG, Gröchenig K-H (1998) A unified approach to atomic decompositions through integrable group representations. In: Cwikel M et al. (eds) Function Spaces and Applications. Lect Notes Math 1302: 52-73. Berlin Heidelberg New York: Springer
    • (1998) Lect Notes Math , vol.1302 , pp. 52-73
    • Feichtinger, H.G.1    Gröchenig, K.-H.2
  • 17
    • 0001242228 scopus 로고
    • Banach spaces related to integrable group representations and their atomic decompositions, I
    • Feichtinger HG, Gröchenig K-H (1989) Banach spaces related to integrable group representations and their atomic decompositions, I. J Functional Anal 86: 307-340
    • (1989) J Functional Anal , vol.86 , pp. 307-340
    • Feichtinger, H.G.1    Gröchenig, K.-H.2
  • 18
    • 0001736922 scopus 로고
    • Banach spaces related to integrable group representations and their atomic decompositions, II
    • Feichtinger HG, Gröchenig K-H (1989) Banach spaces related to integrable group representations and their atomic decompositions, II. Monatsh Math 108: 129-148
    • (1989) Monatsh Math , vol.108 , pp. 129-148
    • Feichtinger, H.G.1    Gröchenig, K.-H.2
  • 19
    • 0003292476 scopus 로고
    • Littlewood-Paley Theory and the Study of Function Spaces
    • Providence, RI: Amer Math Soc
    • Frazier M, Jawerth B, Weiss G (1991) Littlewood-Paley Theory and the Study of Function Spaces. CBMS Reg Conf Ser in Math 79. Providence, RI: Amer Math Soc
    • (1991) CBMS Reg Conf Ser in Math , vol.79
    • Frazier, M.1    Jawerth, B.2    Weiss, G.3
  • 20
    • 0036788764 scopus 로고    scopus 로고
    • Admissible vectors for the regular representation
    • Führ H (2000) Admissible vectors for the regular representation. Proc Amer Math Soc 130: 2959-2970
    • (2000) Proc Amer Math Soc , vol.130 , pp. 2959-2970
    • Führ, H.1
  • 21
    • 0030376210 scopus 로고    scopus 로고
    • Wavelet frames and admissibility in higher dimensions
    • Führ H (1996) Wavelet frames and admissibility in higher dimensions. J Math Phys 37: 6353-6366
    • (1996) J Math Phys , vol.37 , pp. 6353-6366
    • Führ, H.1
  • 23
    • 0000562670 scopus 로고
    • Decomposition of Hardy functions into square integrable wavelets of constant shape
    • Grossmann A, Morlet J (1980) Decomposition of Hardy functions into square integrable wavelets of constant shape. SIAM J Math Anal 15: 475-576
    • (1980) SIAM J Math Anal , vol.15 , pp. 475-576
    • Grossmann, A.1    Morlet, J.2
  • 24
    • 36549092519 scopus 로고
    • Transforms associated to square integrable group representations. I. General results
    • Grossmann A, Morlet J, Paul T (1985) Transforms associated to square integrable group representations. I. General results. J Math Phys 26: 2473-2479
    • (1985) J Math Phys , vol.26 , pp. 2473-2479
    • Grossmann, A.1    Morlet, J.2    Paul, T.3
  • 25
    • 0000870139 scopus 로고
    • Transforms associated to square integrable group representations. II. Examples
    • Grossmann A, Morlet J, Paul T (1986) Transforms associated to square integrable group representations. II. Examples. Ann Inst H Poincaré Phys 45: 293-309
    • (1986) Ann Inst H Poincaré Phys , vol.45 , pp. 293-309
    • Grossmann, A.1    Morlet, J.2    Paul, T.3
  • 26
    • 0009920815 scopus 로고
    • Calderón reproducing formula and the Tb theorem
    • Han YS (1994) Calderón reproducing formula and the Tb theorem. Rev Mat Ibero 10: 51-91
    • (1994) Rev Mat Ibero , vol.10 , pp. 51-91
    • Han, Y.S.1
  • 27
    • 11944256465 scopus 로고    scopus 로고
    • Discrete Calderón reproducing formula on spaces of homogeneous type
    • to appear
    • Han YS (1999) Discrete Calderón reproducing formula on spaces of homogeneous type. Acta Math Sinica (to appear)
    • (1999) Acta Math Sinica
    • Han, Y.S.1
  • 28
    • 29044434383 scopus 로고    scopus 로고
    • Inhomogeneous Calderón reproducing formula on spaces of homogeneous type
    • Han YS (1997) Inhomogeneous Calderón reproducing formula on spaces of homogeneous type. J Geometric Anal 7: 259-284
    • (1997) J Geometric Anal , vol.7 , pp. 259-284
    • Han, Y.S.1
  • 30
    • 0001971392 scopus 로고
    • Littlewood-Paley theory on spaces of homogeneous type and the classical function spaces
    • Han YS, Sawyer ET (1994) Littlewood-Paley theory on spaces of homogeneous type and the classical function spaces. Mem Amer Math Soc 530
    • (1994) Mem Amer Math Soc , vol.530
    • Han, Y.S.1    Sawyer, E.T.2
  • 32
    • 79551514101 scopus 로고
    • Coherent States for n-dimensional Euclidean Groups E(n) and their application
    • Isham CJ, Klauder JR (1991) Coherent States for n-dimensional Euclidean Groups E(n) and their application. J Math Phys 32: 607-620
    • (1991) J Math Phys , vol.32 , pp. 607-620
    • Isham, C.J.1    Klauder, J.R.2
  • 33
    • 0000651893 scopus 로고
    • Intertwining operators for semisimple groups
    • Knapp AW, Stein EM (1971) Intertwining operators for semisimple groups. Ann Math 93: 489-578
    • (1971) Ann Math , vol.93 , pp. 489-578
    • Knapp, A.W.1    Stein, E.M.2
  • 35
    • 0000651893 scopus 로고
    • Intertwining operators for semi-simple groups
    • Knapp AW, Stein EM (1991) Intertwining operators for semi-simple groups. Ann Math 93: 489-578
    • (1991) Ann Math , vol.93 , pp. 489-578
    • Knapp, A.W.1    Stein, E.M.2
  • 36
    • 84867922891 scopus 로고    scopus 로고
    • Characterization of higher dimensional groups associated with continuous wavelets
    • Laugesen RS, Weaver N, Wilson E, Weiss G (2000) Characterization of higher dimensional groups associated with continuous wavelets. J Geom Analysis 12: 89-102
    • (2000) J Geom Analysis , vol.12 , pp. 89-102
    • Laugesen, R.S.1    Weaver, N.2    Wilson, E.3    Weiss, G.4
  • 37
    • 0013512144 scopus 로고
    • Base d'Ondelettes sur les groupes de Lie stratifiés
    • Lemarié PG (1989) Base d'Ondelettes sur les groupes de Lie stratifiés. Bull Soc Math France 117: 211-232
    • (1989) Bull Soc Math France , vol.117 , pp. 211-232
    • Lemarié, P.G.1
  • 38
    • 0039176205 scopus 로고    scopus 로고
    • Admissible wavelets associated with the Heisenberg group
    • Liu H, Peng L (1997) Admissible wavelets associated with the Heisenberg group. Pacific J Math 180: 101-123
    • (1997) Pacific J Math , vol.180 , pp. 101-123
    • Liu, H.1    Peng, L.2
  • 39
    • 0001533989 scopus 로고
    • Lipschitz functions on spaces of homogeneous type
    • Macias RC, Segovia C (1979) Lipschitz functions on spaces of homogeneous type. Adv Math 33: 254-257
    • (1979) Adv Math , vol.33 , pp. 254-257
    • Macias, R.C.1    Segovia, C.2
  • 41
    • 0003295738 scopus 로고
    • Theory of function spaces
    • Triebel H (1987) Theory of function spaces. Monographs in Math 3: 163-189
    • (1987) Monographs in Math , vol.3 , pp. 163-189
    • Triebel, H.1
  • 42
    • 0041126378 scopus 로고
    • Laguerre polynomials, Whittaker functions and representations of groups of bordered matrices
    • Vilenkin NJa (1968) Laguerre polynomials, Whittaker functions and representations of groups of bordered matrices. Math USSR Sb 4: 399-410
    • (1968) Math USSR Sb , vol.4 , pp. 399-410
    • Vilenkin, N.Ja.1
  • 43
    • 1242339429 scopus 로고    scopus 로고
    • The mathematical theory of wavelets
    • Byrnes JS (ed) Twentieth Century Harmonic Analysis - A Celebration. Proc of the NATO Advanced Study Institute, II Ciocco, Italy, 2000, NATO Sci Ser II, Dordrecht: Kluwer
    • Wilson E, Weiss G (2001) The mathematical theory of wavelets. In: Byrnes JS (ed) Twentieth Century Harmonic Analysis - A Celebration. Proc of the NATO Advanced Study Institute, II Ciocco, Italy, 2000, NATO Sci Ser II, Math Phys Chem 33: 329-366. Dordrecht: Kluwer
    • (2001) Math Phys Chem , vol.33 , pp. 329-366
    • Wilson, E.1    Weiss, G.2


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