Banach frames in coorbit spaces consisting of elements which are invariant under symmetry groups

Applied and Computational Harmonic Analysis

Volumn 18, Issue 1, 2005, Pages 94-122

  Rauhut, Holger ^a  

^a TECHNICAL UNIVERSITY OF MUNICH   (Germany)

Author keywords

Atomic decomposition; Banach frame; Coorbit space; Function spaces; Gabor frame; Radial functions; Representations of locally compact groups; Symmetry group; Wavelet frame

Indexed keywords

APPROXIMATION THEORY; FOURIER TRANSFORMS; FUNCTIONS; INTEGRAL EQUATIONS; PROBABILITY; PROBLEM SOLVING;

ATOMIC DECOMPOSITION; BANACH FRAME; COORBIT SPACE; FUNCTION SPACES; GABOR FRAME; RADIAL FUNCTIONS; REPRESENTATIONS OF LOCALLY COMPACT GROUPS; SYMMETRY GROUP; WAVELET FRAME;

WAVELET TRANSFORMS;

EID: 11844256923     PISSN: 10635203     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.acha.2004.09.002     Document Type: Article

References (20)

1. W.R. Bloom, and H. Heyer Harmonic Analysis of Probability Measures on Hypergroups 1995 de Gruyter Berlin/New York
2. S. Dahlke, G. Steidl, and G. Teschke Coorbit spaces and Banach frames on homogeneous spaces with applications to the sphere Adv. Comput. Math. 21 2004 147 180
3. S. Dahlke, G. Steidl, and G. Teschke Weighted coorbit spaces and Banach frames on homogeneous spaces J. Fourier Anal. Appl. 10 2004 507 539
4. M. Duflo, and C.C. Moore On the regular representation of a nonunimodular locally compact group J. Funct. Anal. 21 1976 209 243
5. J. Epperson, and M. Frazier An almost orthogonal radial wavelet expansion for radial distributions J. Fourier Anal. Appl. 1 1995 311 353
6. H.G. Feichtinger Banach spaces of distributions of Wiener's type and interpolation. Functional analysis and approximation (Oberwolfach, 1980) Internat. Ser. Numer. Math. vol. 60 1981 Birkhäuser Basel/Boston, MA 153 165
7. H.G. Feichtinger Banach convolution algebras of Wiener's type Proceedings, Conference on Functions, Series, Operators Budapest, 1980 Colloq. Math. Soc. János Bolyai 1983 North-Holland Amsterdam 509 524
8. H.G. Feichtinger, and K.H. Gröchenig A unified approach to atomic decompositions via integrable group representations M. Cwikel Proc. Conf. Function Spaces and Applications Lecture Notes in Mathematics vol. 1302 1988 Springer Berlin/Heidelberg/New York 52 73
9. H.G. Feichtinger, and K.H. Gröchenig Banach spaces related to integrable group representations and their atomic decompositions I J. Funct. Anal. 86 1989 307 340
10. H.G. Feichtinger, and K.H. Gröchenig Banach spaces related to integrable group representations and their atomic decompositions II Monatsh. Math. 108 1989 129 148
11. M. Fornasier, H. Rauhut, Continuous frames, function spaces, and the discretization problem, Preprint, 2004
12. K. Gröchenig Describing functions: Atomic decomposition versus frames Monatsh. Math. 112 1991 1 41
13. K. Gröchenig Foundations of Time-Frequency Analysis 2001 Birkhäuser Boston, MA
14. R.I. Jewett Spaces with an abstract convolution of measures Adv. in Math. 18 1975 1 101
15. T. Kühn, H. Leopold, W. Sickel, and L. Skrzypczak Entropy numbers of Sobolev embeddings of radial Besov spaces J. Approx. Theory 121 2003 244 268
16. P. Milnes, and J.V. Bondar A simple proof of a covering property of locally compact groups Proc. AMS vol. 73 1979 117 118
17. H. Rauhut, Wavelet transforms associated to group representations and functions invariant under symmetry groups, Int. J. Wavelets Multiresolut. Inf. Process., in press
18. H. Rauhut, Time-frequency and wavelet analysis of functions with symmetry properties, Ph.D. thesis, Technical University of Munich, 2004
19. H. Rauhut, M. Rösler, Radial multiresolution in dimension three, Construct. Approx., in press
20. H. Triebel Characterizations of Besov-Hardy-Sobolev-spaces: A unified approach J. Approx. Theory 52 1988 162 203