Weyl-heisenberg frames and riesz bases in L2(IRd)

Duke Mathematical Journal

Volumn 89, Issue 2, 1997, Pages 237-282

  Ron, Amos ^a   Shen, Zuowei ^b  

^a University of Wisconsin Madison   (United States)

^b NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000371437     PISSN: 00127094     EISSN: None     Source Type: Journal    
DOI: 10.1215/S0012-7094-97-08913-4     Document Type: Article

References (22)

1. 2 and related spaces” in Wavelets: Mathematics and Applications, ed. J. Benedetto and M. Frazier, CRC Press, Boca Raton, Fla., 1994, 97-162.
2. C. K. Chui, An Introduction to Wavelets, Wavelet Analysis and its Application 1, Academic Press, Boston, 1992.
3. I. Daubechies, The wavelet transform, time-frequency localization and signal analysis, IEEE Trans. Inform. Theory 36 (1990), 961-1005.
4. I. Daubechies, Ten Lectures on Wavelets, CBMS-NSF Regional Conf. Ser. in Appl. Math. 61, SIAM, Philadelphia, 1992.
5. I. Daubechies, A. Grossmann, and Y. Meyer, Painless nonorthogonal expansions, J. Math. Phys. 27 (1986), 1271-1283.
6. I. Daubechies, H. J. Landau, and Z. Landau, Gabor time-frequency lattices and the Wexler-Raz identity, J. Fourier Anal. Appl. 1 (1995), 437-478.
7. d), J. Funct. Anal. 119 (1994), 37-78; FTP site anonymous@stolp.cs.wisc.edu, file name several.ps.
8. R. J. Duffin and A. C. Schaeffer, A class of nonharmonic Fourier series, Trans. Amer. Math. Soc. 72 (1952), 341-366.
9. H. G. Feichtinger and K. Gröchenig, Banach spaces related to integrable group representation and their atomic decomposition, I, J. Funct. Anal. 86 (1989), 307-340.
10. C. Heil and D. Walnut, Continuous and discrete wavelet transforms, SIAM Rev. 31 (1989), 628-666.
11. H. Helson, Lectures on Invariant Subspaces, Academic Press, New York, 1964.
12. A. J. E. M. Janssen, Duality and biorthogonality for Weyl-Heisenberg frames, J. Fourier Anal. Appl. 1 (1995), 403-436.
13. J. Ramanathan and T. Steger, Incompleteness of sparse coherent states, Appl. Comput. Harmon. Anal. 2 (1995), 148-153.
14. M. Rieffel, von Neumann algebras associated with pairs of lattices in Lie groups, Math. Ann. 257 (1981), 403-418.
15. d), Canad. J. Math. 47 (1995), 1051-1094; FTP site anonymous@stolp.cs.wisc.edu, file name framel.ps.
16. d): The duality principle of Weyl-Heisenberg sets” in Proceedings of the Lanczos International Centenary Conference, Raleigh, N.C., 1993, ed. D. Brown et al., SIAM, Philadelphia, 1994,422-425.
17. d): The analysis of the analysis operator, to appear in J. Funct. Anal.; FTP site anonymous@stolp. cs.wisc.edu, file name affine.ps.
18. R. Tolimieri and R. S. Orr, Characterization of Weyl-Heisenberg frames via Poisson summation relationships, Proc. ICASSP 92-4 (1992), 277-280.
19. R. Tolimieri and R. S. Orr, Poisson Summation, the ambiguity function, and the theory of Weyl-Heisenberg frames, J. Fourier Anal. Appl. 1 (1995), 233-247.
20. J. Wexler and S. Raz, Discrete Gabor expansions, Signal Processing 21 (1990), 207-220.
21. M. Zibulski and Y. Y. Zeevi, Matrix algebra approach to Gabor-scheme analysis, EE Pub. 856, Technion Israel Inst, of Tech, September 1992;
22. M. Zibuslski and Y. Y. Zeevi, “Gabor representation with oversampling”, in Conf on Visual Communication and Image Processing, Proc. SPIE 1818 1992, 976-984.