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Volumn 11, Issue 3, 2005, Pages 245-287

Continuous frames, function spaces, and the discretization problem

Author keywords

Atomic decompositions; Banach algebras of kernels; Banach frames; Continuous frames; Coorbit spaces; Discrete frames; Function spaces; General sampling methods; Localization of frames

Indexed keywords


EID: 23944499554     PISSN: 10695869     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00041-005-4053-6     Document Type: Article
Times cited : (141)

References (54)
  • 2
    • 0002410060 scopus 로고
    • Continuous frames in Hilbert spaces
    • Ali, S. T., Antoine, J. P., and Gazeau, J. P. (1993). Continuous frames in Hilbert spaces, Ann. Physics 222, 1-37.
    • (1993) Ann. Physics , vol.222 , pp. 1-37
    • Ali, S.T.1    Antoine, J.P.2    Gazeau, J.P.3
  • 3
    • 0043242765 scopus 로고    scopus 로고
    • Wavelets on the 2-sphere: A group-theoretical approach
    • Antoine, J. P. and Vandergheynst, P. (1999). Wavelets on the 2-sphere: A group-theoretical approach, Appl. Comp. Harm. Anal. 7, 262-291.
    • (1999) Appl. Comp. Harm. Anal. , vol.7 , pp. 262-291
    • Antoine, J.P.1    Vandergheynst, P.2
  • 4
    • 0002221121 scopus 로고
    • The spectrum of integral operators on Lebesgue spaces
    • Barnes, B. A. (1987). The spectrum of integral operators on Lebesgue spaces, J. Oper. Theory 18, 115-132.
    • (1987) J. Oper. Theory , vol.18 , pp. 115-132
    • Barnes, B.A.1
  • 6
    • 0010047426 scopus 로고
    • Decomposition of functions as sums of elementary functions
    • Bonsall, F. F. (1986). Decomposition of functions as sums of elementary functions, Quart. J. Math. Oxford 37(2), 129-136.
    • (1986) Quart. J. Math. Oxford , vol.37 , Issue.2 , pp. 129-136
    • Bonsall, F.F.1
  • 7
    • 23944519282 scopus 로고    scopus 로고
    • Pseudodifferential operators on α-modulation spaces
    • Borup, L. (2004). Pseudodifferential operators on α-modulation spaces, J. Func. Spaces Appl. 2, 107-123.
    • (2004) J. Func. Spaces Appl. , vol.2 , pp. 107-123
    • Borup, L.1
  • 9
    • 0000340841 scopus 로고
    • Some new function spaces and their applications to harmonic analysis
    • Coifman, R. R., Meyer, Y., and Stein, E. M. (1985). Some new function spaces and their applications to harmonic analysis, J. Funct. Anal. 62, 304-335.
    • (1985) J. Funct. Anal. , vol.62 , pp. 304-335
    • Coifman, R.R.1    Meyer, Y.2    Stein, E.M.3
  • 10
    • 0001670086 scopus 로고
    • Wave packets and Fourier integral operators
    • Cordoba, A. and Fefferman, C. (1978). Wave packets and Fourier integral operators, Comm. Part. Diff. Eq. 3, 979-1005.
    • (1978) Comm. Part. Diff. Eq. , vol.3 , pp. 979-1005
    • Cordoba, A.1    Fefferman, C.2
  • 11
    • 23944437340 scopus 로고    scopus 로고
    • Adaptive frame methods for elliptic operator equations
    • Bericht Nr. 2004-3, Fachbereich Mathematik und Informatik, Philipps-Universität Marburg, to appear
    • Dahlke, S., Fornasier, M., and Raasch, T. Adaptive frame methods for elliptic operator equations, Bericht Nr. 2004-3, Fachbereich Mathematik und Informatik, Philipps-Universität Marburg, 2004, to appear in Adv. Comp. Math.
    • (2004) Adv. Comp. Math.
    • Dahlke, S.1    Fornasier, M.2    Raasch, T.3
  • 12
    • 4043157765 scopus 로고    scopus 로고
    • Coorbit spaces and Banach frames on homogeneous spaces with applications to the sphere
    • Dahlke, S., Steidl, G., and Teschke, G. (2004). Coorbit spaces and Banach frames on homogeneous spaces with applications to the sphere, Adv. Comp. Math. 21, 147-180.
    • (2004) Adv. Comp. Math. , vol.21 , pp. 147-180
    • Dahlke, S.1    Steidl, G.2    Teschke, G.3
  • 13
    • 11844288503 scopus 로고    scopus 로고
    • Weighted coorbit spaces and Banach frames on homogeneous spaces
    • Dahlke, S., Steidl, G., and Teschke, G. (2004). Weighted coorbit spaces and Banach frames on homogeneous spaces, J. Four. Anal, Appl. 10, 507-539.
    • (2004) J. Four. Anal, Appl. , vol.10 , pp. 507-539
    • Dahlke, S.1    Steidl, G.2    Teschke, G.3
  • 15
  • 17
    • 0000653944 scopus 로고
    • On the regular representation of a nonunimodular locally compact group
    • Duflo, M. and Moore, C. C. (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
  • 18
    • 84985400020 scopus 로고
    • Banach spaces of distributions defined by decomposition methods II
    • Feichtinger, H. G. (1987). Banach spaces of distributions defined by decomposition methods II, Math. Nachr. 132, 207-237.
    • (1987) Math. Nachr. , vol.132 , pp. 207-237
    • Feichtinger, H.G.1
  • 19
    • 84881084569 scopus 로고
    • Atomic characterization of modulation spaces through Gabor-type representations
    • Proc. Conf. Constr. Function Theory
    • Feichtinger, H. G. (1989). Atomic characterization of modulation spaces through Gabor-type representations, Proc. Conf. Constr. Function Theory, Rocky Mountain J. Math. 19, 113-126.
    • (1989) Rocky Mountain J. Math. , vol.19 , pp. 113-126
    • Feichtinger, H.G.1
  • 21
    • 84985383225 scopus 로고
    • Banach spaces of distributions defined by decomposition methods 1
    • Feichtinger, H. G. and Gröbner, P. (1985). Banach spaces of distributions defined by decomposition methods 1, Math. Nachr. 123, 97-120.
    • (1985) Math. Nachr. , vol.123 , pp. 97-120
    • Feichtinger, H.G.1    Gröbner, P.2
  • 22
    • 0002566774 scopus 로고
    • A unified approach to atomic decomposition via integrable group representations
    • Lund, 1986, Springer Lect. Notes Math.
    • Feichtinger, H. G. and Gröchenig, K. (1988). A unified approach to atomic decomposition via integrable group representations, in Proc. Conference on Functions, Spaces and Applications, Lund, 1986, Springer Lect. Notes Math., 1302, 52-73.
    • (1988) Proc. Conference on Functions, Spaces and Applications , vol.1302 , pp. 52-73
    • Feichtinger, H.G.1    Gröchenig, K.2
  • 23
    • 0001242228 scopus 로고
    • Banach spaces related to integrable group representations and their atomic decompositions I
    • Feichtinger, H. G. and Gröchenig, K. (1989). Banach spaces related to integrable group representations and their atomic decompositions I, J. Funct. Anal 86, 307-340.
    • (1989) J. Funct. Anal , vol.86 , pp. 307-340
    • Feichtinger, H.G.1    Gröchenig, K.2
  • 24
    • 0001736922 scopus 로고
    • Banach spaces related to integrable group representations and their atomic decompositions II
    • Feichtinger, H. G. and Gröchenig, K. (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.2
  • 25
    • 0003769203 scopus 로고
    • John Wiley & Sons, New York
    • Folland, G. B. (1984). Real Analysis, John Wiley & Sons, New York.
    • (1984) Real Analysis
    • Folland, G.B.1
  • 26
    • 23944503741 scopus 로고    scopus 로고
    • preprint 10/2004, Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate, Università di Roma "La Sapienza."
    • Fornasier, M. (2005). Banach frames for α-modulation spaces, preprint 10/2004, Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate, Università di Roma "La Sapienza."
    • (2005) Banach Frames for α-modulation Spaces
    • Fornasier, M.1
  • 27
    • 23944464123 scopus 로고    scopus 로고
    • Intrinsic localization of frames
    • Preprint 8/2004, Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate, Università di Roma "La Sapienza," to appear
    • Fornasier, M. and Gröchenig, K. (2005). Intrinsic localization of frames, Preprint 8/2004, Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate, Università di Roma "La Sapienza," to appear in Constr. Approx.
    • (2005) Constr. Approx.
    • Fornasier, M.1    Gröchenig, K.2
  • 29
    • 0003292476 scopus 로고
    • Littlewood-Paley theory and the study of function spaces
    • Providence RI
    • Frazier, M., Jawerth, B., and Weiss, G. (1991). Littlewood-Paley theory and the study of function spaces, AMS, Providence RI.
    • (1991) AMS
    • Frazier, M.1    Jawerth, B.2    Weiss, G.3
  • 30
    • 23944464346 scopus 로고    scopus 로고
    • Abstract harmonic analysis of continuous wavelet transforms
    • Führ, H. (2005). Abstract harmonic analysis of continuous wavelet transforms, Springer Lect. Notes Math. 1863.
    • (2005) Springer Lect. Notes Math. , vol.1863
    • Führ, H.1
  • 31
    • 0037212177 scopus 로고    scopus 로고
    • Frames associated with measurable spaces
    • Gabardo, J.-P. and Han, D. (2003). Frames associated with measurable spaces, Adv. Comput. Math. 18, 127-147.
    • (2003) Adv. Comput. Math. , vol.18 , pp. 127-147
    • Gabardo, J.-P.1    Han, D.2
  • 33
    • 30844456696 scopus 로고
    • Describing functions: Atomic decompositions versus frames
    • Gröchenig, K. (1991). Describing functions: Atomic decompositions versus frames, Monatsh. Math. 112, 1-41.
    • (1991) Monatsh. Math. , vol.112 , pp. 1-41
    • Gröchenig, K.1
  • 35
    • 2442697562 scopus 로고    scopus 로고
    • Localization of frames, Banach frames, and the invertibility of the frame operator
    • Gröchenig, K. (2004). Localization of frames, Banach frames, and the invertibility of the frame operator, J. Four. Anal. Appl. 10(2), 105-132.
    • (2004) J. Four. Anal. Appl. , vol.10 , Issue.2 , pp. 105-132
    • Gröchenig, K.1
  • 36
    • 23944503700 scopus 로고    scopus 로고
    • Symmetry and inverse-closedness of matrix algebras and symbolic calculus and symbolic calculus for infinite matrices
    • to appear
    • Gröchenig, K. and Leinert, M. (2003). Symmetry and inverse-closedness of matrix algebras and symbolic calculus and symbolic calculus for infinite matrices, to appear in Trans. Amer. Math. Soc.
    • (2003) Trans. Amer. Math. Soc.
    • Gröchenig, K.1    Leinert, M.2
  • 37
    • 36549092519 scopus 로고
    • Transforms associated to square integrable group representation, I
    • Grossmann, A., Morlet, J., and Paul, T. (1985). Transforms associated to square integrable group representation, I, J. Math. Phys. 26, 2473-2479.
    • (1985) J. Math. Phys. , vol.26 , pp. 2473-2479
    • Grossmann, A.1    Morlet, J.2    Paul, T.3
  • 38
    • 0000870139 scopus 로고
    • Transforms associated to square integrable group representation, II, examples
    • Grossmann, A., Morlet, J., and Paul, T. (1986). Transforms associated to square integrable group representation, II, Examples, Ann. Inst. H. Poincaré 25, 293-309.
    • (1986) Ann. Inst. H. Poincaré , vol.25 , pp. 293-309
    • Grossmann, A.1    Morlet, J.2    Paul, T.3
  • 39
    • 0007197031 scopus 로고
    • Propriétés des matrices "bien localisées" preè de leur diagonale et quelques applications
    • Jaffard, S. (1990). Propriétés des matrices "bien localisées" preè de leur diagonale et quelques applications, Ann. Inst. H. Poicaré Anal. Non Linéaire 7, 461-476.
    • (1990) Ann. Inst. H. Poicaré Anal. Non Linéaire , vol.7 , pp. 461-476
    • Jaffard, S.1
  • 40
    • 0011869412 scopus 로고    scopus 로고
    • Embeddings and uncertainty principles for generalized modulation spaces
    • Chapter 4, Benedetto, J. J. and Ferreira, P.J.S.G., Eds., Birkhäuser, Boston
    • Hogan, J. A. and Lakey, J. D. (2000). Embeddings and uncertainty principles for generalized modulation spaces, Chapter 4 in Modern Sampling Theory: Mathematics and Applications, Benedetto, J. J. and Ferreira, P.J.S.G., Eds., Birkhäuser, Boston, 73-105.
    • (2000) Modern Sampling Theory: Mathematics and Applications , pp. 73-105
    • Hogan, J.A.1    Lakey, J.D.2
  • 41
    • 0345149768 scopus 로고    scopus 로고
    • Coherent states lattices and square integrability of representations
    • Hohouéto, A. L., Kengatharam, T., Ali, S. T., and Antoine. J. P. (2003). Coherent states lattices and square integrability of representations, J. Phys. A 36, 11817-11835.
    • (2003) J. Phys. A , vol.36 , pp. 11817-11835
    • Hohouéto, A.L.1    Kengatharam, T.2    Ali, S.T.3    Antoine, J.P.4
  • 42
    • 31144440283 scopus 로고    scopus 로고
    • An interpolation family between Gabor and wavelet transformations. Application to differential calculus and construction of anisotropic Banach spaces
    • Albeverio, Demuth, Schrohe, and Schulze, Eds., Wiley
    • Holschneider, M. and Nazaret, B. (2003). An interpolation family between Gabor and wavelet transformations. Application to differential calculus and construction of anisotropic Banach spaces, in Adv. In Partial Diff. Eq., Nonlinear Hyperbolic Equations, Spectral Theory, and Wavelet Transformations, Albeverio, Demuth, Schrohe, and Schulze, Eds., Wiley, 363-394.
    • (2003) Adv. in Partial Diff. Eq., Nonlinear Hyperbolic Equations, Spectral Theory, and Wavelet Transformations , pp. 363-394
    • Holschneider, M.1    Nazaret, B.2
  • 45
    • 0010050587 scopus 로고
    • Paracommutators and minimal spaces
    • Powers, S.C., Ed., NATO ASI Series, Reidel, Dordrecht
    • Peetre, J. (1985). Paracommutators and minimal spaces, in Operators and Function Theory, Powers, S.C., Ed., NATO ASI Series, Reidel, Dordrecht.
    • (1985) Operators and Function Theory
    • Peetre, J.1
  • 47
    • 23944517673 scopus 로고    scopus 로고
    • Wavelet transforms associated to group representations and functions invariant under symmetry groups
    • to appear
    • Rauhut, H. (2005). Wavelet transforms associated to group representations and functions invariant under symmetry groups, to appear in Int. J. Wavelets, Multisc. Inf. Proc.
    • (2005) Int. J. Wavelets, Multisc. Inf. Proc.
    • Rauhut, H.1
  • 48
    • 11844256923 scopus 로고    scopus 로고
    • Banach frames in coorbit spaces consisting of elements which are invariant under symmetry groups
    • Rauhut, H. (2005). Banach frames in coorbit spaces consisting of elements which are invariant under symmetry groups, Appl. Comput. Harm. Anal. 18, 94-122.
    • (2005) Appl. Comput. Harm. Anal. , vol.18 , pp. 94-122
    • Rauhut, H.1
  • 50
    • 0001343343 scopus 로고
    • Wavelets associated with representations of the Affine Weyl-Heisenberg group
    • Torresani, B. (1991). Wavelets associated with representations of the Affine Weyl-Heisenberg group, J. Math. Phys. 32, 1273-1279.
    • (1991) J. Math. Phys. , vol.32 , pp. 1273-1279
    • Torresani, B.1
  • 51
    • 2342655157 scopus 로고
    • Time-frequency representation, wavelet packets and optimal decomposition
    • Torresani, B. (1992). Time-frequency representation, wavelet packets and optimal decomposition, Ann. Inst. H. Poincaré 56, 215-234.
    • (1992) Ann. Inst. H. Poincaré , vol.56 , pp. 215-234
    • Torresani, B.1
  • 52
    • 0005209640 scopus 로고
    • Position-frequency analysis for signals defined on spheres
    • Torresani, B. (1995). Position-frequency analysis for signals defined on spheres, Signal Process, 43, 341-346.
    • (1995) Signal Process , vol.43 , pp. 341-346
    • Torresani, B.1


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