Perturbations of Banach frames and atomic decompositions

Mathematische Nachrichten

Volumn 185, Issue , 1997, Pages 33-47

  Christensen, Ole ^a   Heil, Christopher ^b  

^a TECHNICAL UNIVERSITY OF DENMARK   (Denmark)

^b GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Atomic decompositions; Banach frames; Frames; Gabor systems; Perturbations

Indexed keywords

EID: 0031446789     PISSN: 0025584X     EISSN: None     Source Type: Journal    
DOI: 10.1002/mana.3211850104     Document Type: Article

References (29)

1. BENEDETTO, J. J., HEIL, C., and WALNUT, D.: Differentiation and the Balian-Low Theorem, J. Fourier Anal. Appl. 1 (1995), 355-402
2. 2 and Related Spaces, in: Wavelets: Mathematics and Applications, J. J. BENEDETTO, M. W. FRAZIER (Eds.), 97-162, CRC Press, Boca Raton, FL, 1994
3. CHRISTENSEN, O.: Frames and the Projection Method, Appl. Comp. Harm. Anal. 1 (1993), 50-53
4. CHRISTENSEN, O.: A Paley-Wiener Theorem for Frames, Proc. Amer. Math. Soc. 123 (1995), 2199-2202
5. CHRISTENSEN, O.: Moment Problems and Stability Results for Frames, Appl. Comp. Harm. Anal. 3 (1996), 82-86
6. CHUI, C. K., and SHI, X.: Bessel Sequences and Affine Frames, Appl. Comp. Harm. Anal. 1 (1993), 29-49
7. DAUBECHIES, I.: The Wavelet Transform, Time-Frequency Localization and Signal Analysis, IEEE Trans. Inform. Theory 39 (1990), 961-1005
8. DAUBECHIES, I.: Ten Lectures on Wavelets, SIAM Press, Philadelphia, 1992
9. DAUBECHIES, I., GROSSMANN, A., and MEYER, Y.: Painless Nonorthogonal Expansions, J. Math. Phys. 27 (1986), 1271-1283
10. DUFFIN, R. J., and SCHAEFFER, A. C.: A Class of Nonharmonic Fourier Series, Trans. Amer. Math. Soc. 72 (1952), 341-366
11. FAVIER, S. J. and ZALIK, R. A.: On the Stability of Frames and Riesz Bases, Appl. Comp. Harm. Anal. 2 (1995), 160-173
12. FEICHTINGER, H. G.: Banach Convolution Algebras of Wiener Type, in: Functions, Series, Operators, Proc. Conf. Budapest 35, Colloq. Math. Soc. János Bolyai, B. Sz.-NAGY. J. SZABADOS (Eds.), 509-524, North Holland, Amsterdam, 1983
13. FEICHTINGER, H. G.: Atomic Characterizations of Modulation Spaces through Gabor-Type Representations, Rocky Mountain J. Math. 19 (1989), 113-126
14. FEICHTINGER, H. G., and GRÖCHENIG, K.: Banach Spaces Related to Integrable Group Representations and Their Atomic Decompositions, I, J. Funct. Anal. 86 (1989), 307-340
15. FEICHTINGER, H. G., and GRÖCHENIG, K.: Banach Spaces Related to Integrable Group Representations and Their Atomic Decompositions, II, Monatshefte für Mathematik 108 (1989), 129-148
16. FRAZIER, M., and JAWERTH, B.: Decompositions of Besov Spaces, Indiana Univ. Math. J. 34 (1985), 777-799
17. GRÖCHENIG, K.: Describing Functions: Atomic Decompositions versus Frames, Monatshefte für Mathematik 112 (1991), 1-41
18. HEIL, C:: Wiener Amalgam Spaces in Generalized Harmonic Analysis and Wavelet Theory, Ph. D. Thesis, University of Maryland, College Park, MD, 1990
19. HEIL, C., and WALNUT, D.: Continuous and Discrete Wavelet Transforms, SIAM Review 31 (1989), 628-666
20. HIGGINS, J. R.: Completeness and Basis Properties of Sets of Special Functions, Cambridge University Press, 1976
21. HOLUB, J. R.: Pre-Frame Operators, Besselian Frames, and Near-Riesz Bases in Hilbert Spaces, Proc. Amer. Math. Soc. 122 (1994), 779-785
22. KATO, T.: Perturbation Theory for Linear Operators, Second Edition, Springer-Verlag, New York, 1976
23. LINDENSTRAUSS, J., and TZAFRIRI, L.: Classical Banach Spaces, I, Springer-Verlag, New York, 1977
24. MEYER, Y.: Principe d'Incertitude, Bases Hilbertiennes et Algèbres d'Opérateurs, Séminaire Bourbaki 662, 1985-1986
25. PALEY, R. E. A. C., and WIENER, N.: Fourier Transforms in the Complex Domain, American Mathematical Society Colloquium Publications Vol. 19, American Mathematical Society, New York, 1934
26. RETHERFORD, J. R. and Holub, J. R.: The Stability of Bases in Banach and Hilbert Spaces, J. Reine Angew. Math. 246 (1971), 136-146
27. RUDIN, W.: Functional Analysis, Second Edition, McGraw-Hill, New York, 1991
28. WALNUT, D.: Weyl-Heisenberg Wavelet Expansions: Existence and Stability in Weighted Spaces, Ph. D. thesis, University of Maryland, College Park, MD, 1989
29. YOUNG, R.: An Introduction to Nonharmonic Fourier Series, Academic Press, New York, 1980