메뉴 건너뛰기




Volumn 1863, Issue , 2005, Pages 1-201

Abstract harmonic analysis of continuous wavelet transforms

Author keywords

[No Author keywords available]

Indexed keywords


EID: 23944464346     PISSN: 00758434     EISSN: None     Source Type: Book Series    
DOI: None     Document Type: Article
Times cited : (127)

References (119)
  • 2
    • 0034356779 scopus 로고    scopus 로고
    • The Wigner function for general Lie groups and the wavelet transform
    • S.T. Ali, N.M. Atakishiyev, S.M. Chumakov and K.B. Wolf, The Wigner function for general Lie groups and the wavelet transform. Ann. H. Poincaré 1 (2000), 685-714.
    • (2000) Ann. H. Poincaré , vol.1 , pp. 685-714
    • Ali, S.T.1    Atakishiyev, N.M.2    Chumakov, S.M.3    Wolf, K.B.4
  • 3
    • 0038442247 scopus 로고    scopus 로고
    • Wigner functions from the two-dimensional wavelets group
    • S.T.Ali, A.E. Krasowska and R. Murenzi, Wigner functions from the two-dimensional wavelets group, J. Opt. Soc. Am. A17 (2000), 1-11.
    • (2000) J. Opt. Soc. Am. , vol.A17 , pp. 1-11
    • Ali, S.T.1    Krasowska, A.E.2    Murenzi, R.3
  • 4
    • 1642436849 scopus 로고    scopus 로고
    • Plancherel inversion as unified approach to wavelet transforms and Wigner functions
    • S.T. Ali, H. Führ and A. Krasowska, Plancherel inversion as unified approach to wavelet transforms and Wigner functions, Ann. Henri Poincare 4 (2003), 1015-1050.
    • (2003) Ann. Henri Poincare , vol.4 , pp. 1015-1050
    • Ali, S.T.1    Führ, H.2    Krasowska, A.3
  • 6
    • 0000249728 scopus 로고
    • Classification of connected unimodular Lie groups with discrete series
    • N. H. Anh, Classification of connected unimodular Lie groups with discrete series. Ann. Inst. Fourier 30 (1980), 159-192.
    • (1980) Ann. Inst. Fourier , vol.30 , pp. 159-192
    • Anh, N.H.1
  • 7
    • 0032380062 scopus 로고    scopus 로고
    • Wavelet transforms and discrete frames associated to semidirect products
    • P. Aniello, G. Cassinelli, E. De Vito and A. Levrero, Wavelet transforms and discrete frames associated to semidirect products, J. Math. Phys. 39 (1998), 3965-3973.
    • (1998) J. Math. Phys. , vol.39 , pp. 3965-3973
    • Aniello, P.1    Cassinelli, G.2    De Vito, E.3    Levrero, A.4
  • 8
    • 0032222042 scopus 로고    scopus 로고
    • Square-integrability of induced, representations of semidirect products
    • P. Aniello, G. Cassinelli, E. De Vito and A. Levrero, Square-integrability of induced, representations of semidirect products, Rev. Math. Phys. 10 (1998), 301-313.
    • (1998) Rev. Math. Phys. , vol.10 , pp. 301-313
    • Aniello, P.1    Cassinelli, G.2    De Vito, E.3    Levrero, A.4
  • 9
    • 0037989856 scopus 로고    scopus 로고
    • Discrete frames of Poincaré coherent states in 1+3 dimension
    • J.-P. Antoine and A.L. Hohouéto, Discrete frames of Poincaré coherent states in 1+3 dimension, J. Fourier Anal, and Appl. 9 (2003), 141-173.
    • (2003) J. Fourier Anal, and Appl. , vol.9 , pp. 141-173
    • Antoine, J.-P.1    Hohouéto, A.L.2
  • 10
    • 0002266096 scopus 로고
    • Nilpotent Fourier transfonn and applications
    • D. Arnal and J.C. Cortet, Nilpotent Fourier transfonn and applications. Lett. Math. Phys. 9 (1985), 25-34.
    • (1985) Lett. Math. Phys. , vol.9 , pp. 25-34
    • Arnal, D.1    Cortet, J.C.2
  • 11
    • 0009218539 scopus 로고
    • Lie groups whose coadjoint orbits are of dimension smaller or equal to two
    • D. Arnal, M. Cahen and J. Ludwig, Lie groups whose coadjoint orbits are of dimension smaller or equal to two, Lett. Math. Phys. 33 (1995), 183-186.
    • (1995) Lett. Math. Phys. , vol.33 , pp. 183-186
    • Arnal, D.1    Cahen, M.2    Ludwig, J.3
  • 12
    • 1642563396 scopus 로고
    • Moyal product and representations of solvable Lie groups
    • D. Arnal, J.C. Cortet and J. Ludwig, Moyal product and representations of solvable Lie groups, J. Funct. Anal. 133 (1995), 402-424.
    • (1995) J. Funct. Anal. , vol.133 , pp. 402-424
    • Arnal, D.1    Cortet, J.C.2    Ludwig, J.3
  • 13
    • 1642522480 scopus 로고
    • 2 (G) et transformation de Fourier adaptée pour un groupe G nilpotent
    • Série I
    • 2 (G) et transformation de Fourier adaptée pour un groupe G nilpotent, C.R. Acad. Sci. Paris, t, 306, Série I (1988), 25-28.
    • (1988) C.R. Acad. Sci. Paris , vol.306 , pp. 25-28
    • Arnal, D.1    Gutt, S.2
  • 14
    • 21744443524 scopus 로고    scopus 로고
    • Q.U.P. and Paley-Wiener property of unimodular, especially nilpotent, Lie groups
    • D. Arnal and J. Ludwig, Q.U.P. and Paley-Wiener property of unimodular, especially nilpotent, Lie groups. Proc. Am. Math. Soc. 125, (1997), 1071-1080.
    • (1997) Proc. Am. Math. Soc. , vol.125 , pp. 1071-1080
    • Arnal, D.1    Ludwig, J.2
  • 16
    • 0001587550 scopus 로고
    • Continuous representation theory using the affine group
    • E.W. Aslaksen and J.R. Klauder, Continuous representation theory using the affine group, J. Math. Phys. 10, 2267-2275 (1969).
    • (1969) J. Math. Phys. , vol.10 , pp. 2267-2275
    • Aslaksen, E.W.1    Klauder, J.R.2
  • 17
    • 0003245081 scopus 로고
    • Unitary representations of solvable Lie groups
    • L. Auslander and C.C. Moore: Unitary representations of solvable Lie groups. Mem. Am. Math. Soc. 62, 1966.
    • (1966) Mem. Am. Math. Soc. , vol.62
    • Auslander, L.1    Moore, C.C.2
  • 18
    • 0010173161 scopus 로고
    • Processing a radar signal and representations of the discrete Heisenberg group
    • L. Baggett, Processing a radar signal and representations of the discrete Heisenberg group. Colloq. Math., LX/LXI (1), 1990, pp. 195-203.
    • (1990) Colloq. Math. , vol.60-61 , Issue.1 , pp. 195-203
    • Baggett, L.1
  • 19
    • 0001876907 scopus 로고    scopus 로고
    • An abstract interpretation of the wavelet dimension function using group representations
    • L.W. Baggett, An abstract interpretation of the wavelet dimension function using group representations, J. Funct. Anal. 173 (2000) 1-20.
    • (2000) J. Funct. Anal. , vol.173 , pp. 1-20
    • Baggett, L.W.1
  • 20
    • 0007090103 scopus 로고    scopus 로고
    • n
    • L. W. Baggett (ed.) et al., The functional and harmonic analysis of wavelets and frames. Proceedings of the AMS special session. San Antonio. TX, USA. January 13-14, 1999. Providence, RI: American Mathematical Society
    • n, in L. W. Baggett (ed.) et al., The functional and harmonic analysis of wavelets and frames. Proceedings of the AMS special session. San Antonio. TX, USA. January 13-14, 1999. Providence, RI: American Mathematical Society. Contemp. Math. 247 (1999) 17-27.
    • (1999) Contemp. Math. , vol.247 , pp. 17-27
    • Baggett, L.W.1    Merrill, K.D.2
  • 21
    • 0010801646 scopus 로고    scopus 로고
    • Density and redundancy of the noncoherent Weyl-Heisenberg superframes
    • R. Balan, Density and redundancy of the noncoherent Weyl-Heisenberg superframes. Cont. Mathematics 247 (1999), 29-41.
    • (1999) Cont. Mathematics , vol.247 , pp. 29-41
    • Balan, R.1
  • 22
    • 0030526326 scopus 로고    scopus 로고
    • Wavelets from square-integrable representations
    • D. Bernier and K. Taylor, Wavelets from square-integrable representations. SIAM J. Math. Anal. 27 (1996), 594-608.
    • (1996) SIAM J. Math. Anal. , vol.27 , pp. 594-608
    • Bernier, D.1    Taylor, K.2
  • 24
    • 0032384695 scopus 로고    scopus 로고
    • Symbolic calculus on the time-frequency half-plane
    • J. Bertrand, and P. Bertrand, Symbolic calculus on the time-frequency half-plane, J. Math. Phys. 39 (1998), 4071-4090.
    • (1998) J. Math. Phys. , vol.39 , pp. 4071-4090
    • Bertrand, J.1    Bertrand, P.2
  • 25
    • 0000736893 scopus 로고
    • Treillis d'ondelettes aux groupes de Lorentz
    • G. Bohnke, Treillis d'ondelettes aux groupes de Lorentz. Annales de l'Institut Henri Poincaré 54 (1991), 245-259.
    • (1991) Annales de l'Institut Henri Poincaré , vol.54 , pp. 245-259
    • Bohnke, G.1
  • 26
    • 0010038364 scopus 로고    scopus 로고
    • Distributions sur un groupe localement compact et applications à l'étude des représentations des groupes p-adiques
    • F. Bruhat, Distributions sur un groupe localement compact et applications à l'étude des représentations des groupes p-adiques. Bull. Soc. math. France 89 (89), 43-75.
    • Bull. Soc. Math. France , vol.89 , Issue.89 , pp. 43-75
    • Bruhat, F.1
  • 27
    • 0001142946 scopus 로고
    • Intermediate spaces and interpolation, the complex method
    • A.P. Calderón, Intermediate spaces and interpolation, the complex method. Studia Math. 24 (1964), 113-190.
    • (1964) Studia Math. , vol.24 , pp. 113-190
    • Calderón, A.P.1
  • 29
    • 0000786587 scopus 로고
    • Group representations in reproducing kernel Hilberts spaces
    • A.L. Carey, Group representations in reproducing kernel Hilberts spaces. Reports in Math. Phys. 14 (1978), 247-259
    • (1978) Reports in Math. Phys. , vol.14 , pp. 247-259
    • Carey, A.L.1
  • 31
    • 33748949056 scopus 로고
    • The Plancherel for a group not of type I
    • M. Cowling, The Plancherel for a group not of type I, Boll. Unione Mat. Ital., V. Ser., A 15 (1978), 616-623.
    • (1978) Boll. Unione Mat. Ital., V. Ser., A , vol.15 , pp. 616-623
    • Cowling, M.1
  • 32
    • 0039324214 scopus 로고
    • An explicit Plancherel formula for completely solvable Lie groups
    • B.N. Currey, An explicit Plancherel formula for completely solvable Lie groups. Mich. Math. J. 38 (1991), 75-87.
    • (1991) Mich. Math. J. , vol.38 , pp. 75-87
    • Currey, B.N.1
  • 33
    • 0025482241 scopus 로고
    • The wavelet transform, time-frequency localization and signal analysis
    • I. Daubechies, The wavelet transform, time-frequency localization and signal analysis. IEEE Trans. Inform. Theory 34 (1988), 961-1005.
    • (1988) IEEE Trans. Inform. Theory , vol.34 , pp. 961-1005
    • Daubechies, I.1
  • 34
    • 0000352005 scopus 로고
    • L'application exponentielle dans les groupes de Lie résolubles
    • J. Dixmier, L'application exponentielle dans les groupes de Lie résolubles. Bull. Soc. Math. Fr. 85 (1957), 113-121.
    • (1957) Bull. Soc. Math. Fr. , vol.85 , pp. 113-121
    • Dixmier, J.1
  • 35
    • 0003421383 scopus 로고
    • North Holland, Amsterdam
    • J. Dixmier: C*-Algebras. North Holland, Amsterdam, 1977.
    • (1977) C*-algebras
    • Dixmier, J.1
  • 37
    • 1842605024 scopus 로고
    • A nonabelian version of the Shannon sampling theorem
    • A.H. Dooley, A nonabelian version of the Shannon sampling theorem. SIAM J. Math. Anal. 20 (1989), 624-633.
    • (1989) SIAM J. Math. Anal. , vol.20 , pp. 624-633
    • Dooley, A.H.1
  • 38
    • 0000653944 scopus 로고
    • On the regular representation of a nonunimodular locally compact group
    • M. Duflo and C.C. Moore, On the regular representation of a nonunimodular locally compact group, J. Funct. Anal. 21 (1976), 209-243.
    • (1976) J. Funct. Anal. , vol.21 , pp. 209-243
    • Duflo, M.1    Moore, C.C.2
  • 39
    • 0000753977 scopus 로고
    • Sur l'analyse harmonique sur les groupes de Lie résolubles
    • M. Duflo and M. Raïs, Sur l'analyse harmonique sur les groupes de Lie résolubles. Ann. Sci. Ecole Norm. Sup. 9 (1976), 107-144.
    • (1976) Ann. Sci. Ecole Norm. Sup. , vol.9 , pp. 107-144
    • Duflo, M.1    Raïs, M.2
  • 40
    • 84968465416 scopus 로고
    • Global structure in von Neumann algebras
    • E.G. Effros, Global structure in von Neumann algebras. Trans. Am. Math. Soc. 121 (1966), 434-454.
    • (1966) Trans. Am. Math. Soc. , vol.121 , pp. 434-454
    • Effros, E.G.1
  • 41
    • 0000724626 scopus 로고
    • L'algébre de Fourier d'un groupe localement compact
    • P. Eymard, L'algébre de Fourier d'un groupe localement compact. Bull. Soc. Math. Fr. 92 (1964), 181-236.
    • (1964) Bull. Soc. Math. Fr. , vol.92 , pp. 181-236
    • Eymard, P.1
  • 42
    • 0011326789 scopus 로고
    • La transformation de Fourier et son inverse sur le groupe des ax+b d'un corps local
    • Analyse harmonique sur les groupes de Lie II, Semin. Nancy-Strasbourg 1976-78
    • P. Eymard and M. Terp, La transformation de Fourier et son inverse sur le groupe des ax+b d'un corps local, in Analyse harmonique sur les groupes de Lie II, Semin. Nancy-Strasbourg 1976-78, Lect. Notes Math. 739 (1979), 207-248.
    • (1979) Lect. Notes Math. , vol.739 , pp. 207-248
    • Eymard, P.1    Terp, M.2
  • 43
    • 0002566774 scopus 로고
    • A unified approach to atomic decompositions through integrable group representations
    • Function spaces and applications. Hrsg. M. Cwikel et al. Springer, Berlin
    • H.G. Feichtinger and K.-H. Gröchenig, A unified approach to atomic decompositions through integrable group representations. 52-73 in Function spaces and applications. Hrsg. M. Cwikel et al., Lecture Notes in Mathematics 1302. Springer, Berlin, 1988.
    • (1988) Lecture Notes in Mathematics , vol.1302 , pp. 52-73
    • Feichtinger, H.G.1    Gröchenig, K.-H.2
  • 44
    • 84966253677 scopus 로고
    • A Hausdorff topology for the closed subsets of a locally compact non-Hausdorff space
    • J.M.G. Fell, A Hausdorff topology for the closed subsets of a locally compact non-Hausdorff space. Proc. Am. Math. Soc. 13 (1962), 472-476.
    • (1962) Proc. Am. Math. Soc. , vol.13 , pp. 472-476
    • Fell, J.M.G.1
  • 48
    • 0030376210 scopus 로고    scopus 로고
    • Wavelet frames and admissibility in higher dimensions
    • H. Führ. Wavelet frames and admissibility in higher dimensions, J. Math. Phys. 37 (1996), 6353-6366.
    • (1996) J. Math. Phys. , vol.37 , pp. 6353-6366
    • Führ, H.1
  • 49
    • 0040583259 scopus 로고    scopus 로고
    • Continuous wavelet transforms with abelian dilation groups
    • H. Führ, Continuous wavelet transforms with abelian dilation groups, J. Math. Phys. 39 (1998), 3974-3986.
    • (1998) J. Math. Phys. , vol.39 , pp. 3974-3986
    • Führ, H.1
  • 51
    • 33748938167 scopus 로고    scopus 로고
    • Continuous wavelet transforms from semidirect products
    • H. Führ, Continuous wavelet transforms from semidirect products. Rev. Cienc. Mat. 18 (2000), 179-190.
    • (2000) Rev. Cienc. Mat. , vol.18 , pp. 179-190
    • Führ, H.1
  • 52
    • 0036352253 scopus 로고    scopus 로고
    • Continuous wavelet transforms from semidirect products: Cyclic representations and Plancherel measure
    • H. Führ- and M. Mayer, Continuous wavelet transforms from semidirect products: Cyclic representations and Plancherel measure, J. Fourier Anal. Appl. 8 (2002), 375-398.
    • (2002) J. Fourier Anal. Appl. , vol.8 , pp. 375-398
    • Führ, H.1    Mayer, M.2
  • 53
    • 0036788764 scopus 로고    scopus 로고
    • Admissible vectors for the regular representation
    • H. Führ, Admissible vectors for the regular representation, Proc. Am. Math. Soc. 130 (2002), 2959-2970.
    • (2002) Proc. Am. Math. Soc. , vol.130 , pp. 2959-2970
    • Führ, H.1
  • 54
    • 33748939724 scopus 로고    scopus 로고
    • Plancherel transform criteria, for Weyl-Heisenberg frames with integer oversampling
    • Allied Publishers, Chennai
    • H. Führ. Plancherel transform criteria, for Weyl-Heisenberg frames with integer oversampling. Conference Proceedings Wavelets and their applications. Allied Publishers, Chennai, 2003, 141-150.
    • (2003) Conference Proceedings Wavelets and Their Applications , pp. 141-150
    • Führ, H.1
  • 55
    • 4944235866 scopus 로고    scopus 로고
    • Admissible vectors and traces of the commuting algebra
    • JP Gazeau, R Kerner, JP Antoine, S Metens and JY Thibon (eds.) Group 24: Physical and Mathematical Aspects of Symmetries
    • H. Führ, Admissible vectors and traces of the commuting algebra, in JP Gazeau, R Kerner, JP Antoine, S Metens and JY Thibon (eds.) Group 24: Physical and Mathematical Aspects of Symmetries, Institute of Physics Conference Series 173 (2003), 867-874.
    • (2003) Institute of Physics Conference Series , vol.173 , pp. 867-874
    • Führ, H.1
  • 56
    • 0001101388 scopus 로고
    • Locally compact, transformation groups
    • J.G. Glimm, Locally compact, transformation groups. Trans. Am. Math. Soc. 101 (1961), 124-138.
    • (1961) Trans. Am. Math. Soc. , vol.101 , pp. 124-138
    • Glimm, J.G.1
  • 57
    • 84930818474 scopus 로고
    • Les fonctions de type positif et la théorie des groupes
    • R. Godement, Les fonctions de type positif et la théorie des groupes. Trans. Am. Math. Soc. 63 (1948), 1-84.
    • (1948) Trans. Am. Math. Soc. , vol.63 , pp. 1-84
    • Godement, R.1
  • 60
    • 36549092519 scopus 로고
    • Transforms associated to square integrable group representations I: General Results
    • A. Grossmann, J. Morlet and T. Paul, Transforms associated to square integrable group representations I: General Results, J. Math. Phys. 26 (1985), 2473-2479.
    • (1985) J. Math. Phys. , vol.26 , pp. 2473-2479
    • Grossmann, A.1    Morlet, J.2    Paul, T.3
  • 61
    • 33748947644 scopus 로고
    • Sur la décomposition des représentations des C*-algèbres
    • A. Guichardet, Sur la décomposition des représentations des C*-algèbres, C. R. Acad. Sci. Paris 258 (1964), 768-770.
    • (1964) C. R. Acad. Sci. Paris , vol.258 , pp. 768-770
    • Guichardet, A.1
  • 63
    • 84966224881 scopus 로고
    • Representations of semi-simple Lie groups III
    • Harish-Chandra, Representations of semi-simple Lie groups III, Trans. AMS, 75 (1953), 185-243.
    • (1953) Trans. AMS , vol.75 , pp. 185-243
    • Harish-Chandra1
  • 67
    • 79551514101 scopus 로고
    • Coherent states for n-dimensional Euclidean groups E(n) and their application
    • C.J. Isham and J.R. Klauder, Coherent states for n-dimensional Euclidean groups E(n) and their application, J. Math. Phys. 32 (1991), 607-620.
    • (1991) J. Math. Phys. , vol.32 , pp. 607-620
    • Isham, C.J.1    Klauder, J.R.2
  • 68
    • 21644490412 scopus 로고    scopus 로고
    • 2 space on the Cartan domain BDI (q = 2)
    • 2 space on the Cartan domain BDI (q = 2): Trans. Am. Math. Soc. 349 (1997), 2049-2068.
    • (1997) Trans. Am. Math. Soc. , vol.349 , pp. 2049-2068
    • Jiang, Q.1
  • 69
    • 84972541011 scopus 로고
    • Group extensions and Plancherel formulas
    • T. Kajiwara, Group extensions and Plancherel formulas, J. Math. Soc. Japan, 35 (1983), 93-115.
    • (1983) J. Math. Soc. Japan , vol.35 , pp. 93-115
    • Kajiwara, T.1
  • 70
    • 0010201513 scopus 로고
    • Der typ der regulären darstellung diskreter
    • E. Kaniuth, Der Typ der regulären Darstellung diskreter Gruppen. Math. Ann. 182 (1969), 334-339.
    • (1969) Gruppen. Math. Ann. , vol.182 , pp. 334-339
    • Kaniuth, E.1
  • 71
    • 0037907071 scopus 로고
    • Sur l'analyse harmonique du groupe affine de la droite
    • I. Khalil, Sur l'analyse harmonique du groupe affine de la droite. Stud. Math. 51 (1974), 139-167.
    • (1974) Stud. Math. , vol.51 , pp. 139-167
    • Khalil, I.1
  • 72
    • 0033419403 scopus 로고    scopus 로고
    • Merits and demerits of the orbit method
    • A. A. Kirillov, Merits and demerits of the orbit method, Bull. Am. Math. Soc. (New Ser.) 36 (1999), 433-488.
    • (1999) Bull. Am. Math. Soc. (New Ser.) , vol.36 , pp. 433-488
    • Kirillov, A.A.1
  • 74
    • 0001218146 scopus 로고
    • A wavelet transform for the Poincaré group
    • J.R. Klauder and R.F. Streater, A wavelet transform for the Poincaré group, J. Math. Phys. 32 (1991), 1609-1611.
    • (1991) J. Math. Phys. , vol.32 , pp. 1609-1611
    • Klauder, J.R.1    Streater, R.F.2
  • 75
    • 0000263185 scopus 로고
    • The Plancherel formula for group extensions, I and II
    • A. Kleppner and R.L. Lipsman, The Plancherel formula for group extensions, I and II, Ann. Sci. Ecole Norm. Sup. 5 (1972), 459-516;
    • (1972) Ann. Sci. Ecole Norm. Sup. , vol.5 , pp. 459-516
    • Kleppner, A.1    Lipsman, R.L.2
  • 76
    • 0000981812 scopus 로고
    • The Plancherel formula for group extensions, I and II
    • A. Kleppner and R.L. Lipsman, The Plancherel formula for group extensions, I and II, Ann. Sci. Ecole Norm. Sup. ibid. 6 (1973), 103-132.
    • (1973) Ann. Sci. Ecole Norm. Sup. , vol.6 , pp. 103-132
    • Kleppner, A.1    Lipsman, R.L.2
  • 77
    • 0002850312 scopus 로고
    • Sampling theorem in abstract harmonic analysis
    • I. Kluvánek, Sampling theorem in abstract harmonic analysis. Mat.-Fyz. Casopis Sloven.Akad. Vied. 15 (1965), 43-48.
    • (1965) Mat.-Fyz. Casopis Sloven.Akad. Vied. , vol.15 , pp. 43-48
    • Kluvánek, I.1
  • 78
    • 84867922891 scopus 로고    scopus 로고
    • Continuous wavelets associated with a general, class of admissible groups and their characterization
    • R.S. Laugesen, N. Weaver, G. Weiss and E.N. Wilson, Continuous wavelets associated with a general, class of admissible groups and their characterization, J. Geom. Anal. 12 (2002), 89-102.
    • (2002) J. Geom. Anal. , vol.12 , pp. 89-102
    • Laugesen, R.S.1    Weaver, N.2    Weiss, G.3    Wilson, E.N.4
  • 79
    • 0013512144 scopus 로고
    • Base d'ondelettes sur les groupes de Lie stratifiés
    • Lemarié, P.G., Base d'ondelettes sur les groupes de Lie stratifiés. Bull. Soc. Math. Fr, 117 (1989), 211-232.
    • (1989) Bull. Soc. Math. Fr. , vol.117 , pp. 211-232
    • Lemarié, P.G.1
  • 81
    • 33646834792 scopus 로고    scopus 로고
    • A direct integral, decomposition of the wavelet representation
    • L.-H. Lim, J.A. Packer and K. F. Taylor, A direct integral, decomposition of the wavelet representation. Proc. Am. Math. Soc. 129 (2001) 3057-3067.
    • (2001) Proc. Am. Math. Soc. , vol.129 , pp. 3057-3067
    • Lim, L.-H.1    Packer, J.A.2    Taylor, K.F.3
  • 82
    • 0010600509 scopus 로고
    • Non-abelian Fourier analysis
    • R.L. Lipsman, Non-abelian Fourier analysis. Bull. Sci. Math. 98 (1974), 209-233.
    • (1974) Bull. Sci. Math. , vol.98 , pp. 209-233
    • Lipsman, R.L.1
  • 83
    • 0010810704 scopus 로고
    • Group representations
    • Springer Verlag Berlin
    • R.L. Lipsman: Group Representations. Lecture Notes in Mathematics 388, Springer Verlag Berlin, 1974.
    • (1974) Lecture Notes in Mathematics , vol.388
    • Lipsman, R.L.1
  • 84
    • 0039176205 scopus 로고    scopus 로고
    • Admissible wavelets associated with the Heisenberg group
    • Liu, H. and Peng, L., Admissible wavelets associated with the Heisenberg group. Pac. J. Math. 180 (1997), 101-123.
    • (1997) Pac. J. Math. , vol.180 , pp. 101-123
    • Liu, H.1    Peng, L.2
  • 86
    • 0346234939 scopus 로고
    • 1 of a nilpotent Lie group
    • 1 of a nilpotent Lie group, Math. Ann. 273 (1986) 383-395.
    • (1986) Math. Ann. , vol.273 , pp. 383-395
    • Ludwig, J.1
  • 87
    • 0000670833 scopus 로고
    • Induced representations of locally compact groups, I
    • G. W. Mackey, Induced representations of locally compact groups, I, Ann. of Math. 55 (1952), 101-139.
    • (1952) Ann. of Math. , vol.55 , pp. 101-139
    • Mackey, G.W.1
  • 88
    • 0000056671 scopus 로고
    • Induced representations of locally compact groups, II
    • G. W. Mackey, Induced representations of locally compact groups, II, Ann. of Math. 58 (1953), 193-221.
    • (1953) Ann. of Math. , vol.58 , pp. 193-221
    • Mackey, G.W.1
  • 89
    • 84931205353 scopus 로고
    • Borel structure in groups and their duals
    • G. W. Mackey, Borel structure in groups and their duals, Trans. Am. Math. Soc. 85 (1957), 134-165.
    • (1957) Trans. Am. Math. Soc. , vol.85 , pp. 134-165
    • Mackey, G.W.1
  • 93
    • 0002971198 scopus 로고
    • Wavelet transform maxima and multiscale edges
    • M.B. Ruskai, G. Beylkin, R. Coifman, I. Daubechies, S. Mallat, Y. Meyer, and L. Raphael, eds., Jones and Bartlett, Boston
    • S. Mallat and S. Zhong, Wavelet transform maxima and multiscale edges, in Wavelets and Their Applications, M.B. Ruskai, G. Beylkin, R. Coifman, I. Daubechies, S. Mallat, Y. Meyer, and L. Raphael, eds., Jones and Bartlett, Boston, 1992, 67-104.
    • (1992) Wavelets and Their Applications , pp. 67-104
    • Mallat, S.1    Zhong, S.2
  • 97
    • 33748933191 scopus 로고
    • Matrix coefficients and a Weyl correspondence for nilpotent Lie groups
    • N. V. Pedersen, Matrix coefficients and a Weyl correspondence for nilpotent Lie groups, Invent. Math. 118 (1994), 1-36.
    • (1994) Invent. Math. , vol.118 , pp. 1-36
    • Pedersen, N.V.1
  • 99
    • 1842633361 scopus 로고    scopus 로고
    • Sampling of Paley-Wiener functions on stratified groups
    • I. Pesenson, Sampling of Paley-Wiener functions on stratified groups, J. Fourier Anal. Appl. 4 (1998), 271-281.
    • (1998) J. Fourier Anal. Appl. , vol.4 , pp. 271-281
    • Pesenson, I.1
  • 100
    • 23044519949 scopus 로고    scopus 로고
    • A sampling theorem on homogeneous manifolds
    • I. Pesenson, A sampling theorem on homogeneous manifolds, Trans. Am. Math. Soc. 352 (2000), 4257-4269.
    • (2000) Trans. Am. Math. Soc. , vol.352 , pp. 4257-4269
    • Pesenson, I.1
  • 101
    • 0035616727 scopus 로고    scopus 로고
    • Sampling of band-limited vectors
    • I. Pesenson, Sampling of band-limited vectors, J. Fourier Anal. Appl. 4 (2001), 93-100.
    • (2001) J. Fourier Anal. Appl. , vol.4 , pp. 93-100
    • Pesenson, I.1
  • 103
    • 0001429894 scopus 로고
    • Square integrable representations of Hilbert algebras
    • M. Rieffel, Square integrable representations of Hilbert algebras. J. Funct. Anal. 3 (1969), 265-300.
    • (1969) J. Funct. Anal. , vol.3 , pp. 265-300
    • Rieffel, M.1
  • 104
    • 84968515966 scopus 로고
    • Square-integrable factor representations of locally compact groups
    • J. Rosenberg, Square-integrable factor representations of locally compact groups, Trans. Am. Math. Soc. 261 (1978), pp. 1-33.
    • (1978) Trans. Am. Math. Soc. , vol.261 , pp. 1-33
    • Rosenberg, J.1
  • 107
    • 0009031851 scopus 로고
    • An extension of Plancherel's formula to separable unimodular groups
    • I.E. Segal, An extension of Plancherel's formula to separable unimodular groups, Ann. Math. 52, (1950), 272-292.
    • (1950) Ann. Math. , vol.52 , pp. 272-292
    • Segal, I.E.1
  • 108
    • 84972538926 scopus 로고
    • Type analysis of the regular representation of a non-unimodular group
    • C.E. Sutherland, Type analysis of the regular representation of a non-unimodular group, Pac. J. Mathematics 79 (1978), 225-250.
    • (1978) Pac. J. Mathematics , vol.79 , pp. 225-250
    • Sutherland, C.E.1
  • 109
    • 4744346375 scopus 로고
    • Cartan subalgebras, transverse measures and non-type-I Plancherel formulae
    • C.E. Sutherland, Cartan subalgebras, transverse measures and non-type-I Plancherel formulae, J. Funct. Anal. 60 (1985), 281-308.
    • (1985) J. Funct. Anal. , vol.60 , pp. 281-308
    • Sutherland, C.E.1
  • 110
    • 33744990734 scopus 로고
    • A generalized commutation relation for the regular representation
    • M. Takesaki, A generalized commutation relation for the regular representation. Bull. Soc. Math. France 97, (1969), 289-298.
    • (1969) Bull. Soc. Math. France , vol.97 , pp. 289-298
    • Takesaki, M.1
  • 111
    • 0001531644 scopus 로고
    • Plancherel formula for non-unimodular locally compact groups
    • N. Tatsuuma, Plancherel formula for non-unimodular locally compact groups, J. Math. Kyoto Univ. 12 (1972), 179-261.
    • (1972) J. Math. Kyoto Univ. , vol.12 , pp. 179-261
    • Tatsuuma, N.1
  • 112
    • 0013199326 scopus 로고
    • Eine charakterisierung diskreter gruppen vom typ I
    • E. Thoma, Eine Charakterisierung diskreter Gruppen vom Typ I, Invent. Math. 6 (1968), 190-196.
    • (1968) Invent. Math. , vol.6 , pp. 190-196
    • Thoma, E.1
  • 115
    • 33745014742 scopus 로고
    • On the quantum correction for thermodynamic equilibrium
    • E.P. Wigner, On the quantum correction for thermodynamic equilibrium. Phys. Rev. 40 (1932), 749-759.
    • (1932) Phys. Rev. , vol.40 , pp. 749-759
    • Wigner, E.P.1
  • 116
    • 0038695694 scopus 로고    scopus 로고
    • New uncertainty principles for the continuous Gabor transform and the continuous wavelet transform
    • E. Wilczok, New uncertainty principles for the continuous Gabor transform and the continuous wavelet transform. Doc. Math. 5 (2000), 203-226.
    • (2000) Doc. Math. , vol.5 , pp. 203-226
    • Wilczok, E.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.