Gabor frames over irregular lattices

Advances in Computational Mathematics

Volumn 18, Issue 2-4, 2003, Pages 329-344

  Casazza, Peter G ^a   Christensen, Ole ^b  

^a UNIVERSITY OF MISSOURI   (United States)

^b TECHNICAL UNIVERSITY OF DENMARK   (Denmark)

Author keywords

Gabor frame; Irregular lattice

Indexed keywords

EID: 0037212716     PISSN: 10197168     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1021356503075     Document Type: Article

References (30)

1. R. Balan, Stability theorems for Fourier frames and wavelet Riesz bases, J. Fourier Anal. Appl. 3(5) (1997) 499-504.
2. K. Bittner and C.K. Chui, Gabor frames with arbitrary windows, in: Approximation Theorie, Vol. X, eds. C.K. Chui, L.L. Schumakes and J. Steckler (Vanderbilt Univ. Press, 2002).
3. 2(ℝ), Proc. Amer. Math. Soc. 129 (2001) 145-154.
4. P.G. Casazza, O. Christensen and A.J.E.M. Janssen, Weyl Heisenberg frames, translation invariant systems and the Walnut representation, J. Funct. Anal. 180 (2001) 85-147.
5. P.G. Casazza and N.J. Kalton, Roots of complex polynomials and Weyl-Heisenberg frame sets, Proc. Amer. Math. Soc. (to appear).
6. P.G. Casazza and M.C. Lammers, Analyzing the Gabor frame identity, Preprint.
7. P.G. Casazza and M.C. Lammers, Bracket products for Gabor frames, Preprint.
8. O. Christensen, A Paley Wiener theorem for frames, Proc. Amer. Math. Soc. 123 (1995) 2199-2202.
9. O. Christensen, Atomic decomposition via projective group representations, Rocky Mountain J. Math. 6(1) (1996) 1289-1312.
10. O. Christensen, Perturbations of frames and applications to Gabor frames, in: Gabor Analysis and Algorithms: Theory and Applications, eds. H.G. Feichtinger and T. Strohmer (Birkhäuser, Basel, 1997) pp. 193-209.
11. O. Christensen, C. Deng and C. Heil, Density of Gabor frames, Appl. Comput. Harmon. Anal. 7 (1999) 292-304.
12. I. Daubechies, The wavelet transform, time-frequency localization and signal analysis, IEEE Trans. Inform. Theory 36(5) (1990) 961-1005.
13. R.J. Duffin and A.C. Schaeffer, A class of nonharmonic Fourier series, Trans. Amer. Math. Soc. 72 (1952) 341-366.
14. H.G. Feichtinger, Private communication.
15. H.G. Feichtinger, Banach convolution algebras of Wiener's type, in: Proc. of Conf. on Functions, Series, Operators, Budapest, 1980, Colloqia Mathematica Societatis Janos Bolyai (North-Holland, Amsterdam, 1983) pp. 509-524.
16. H.G. Feichtinger and K. Gröchenig, Banach spaces related to integrable group representations and their atomic decomposition, J. Funct. Anal. 86 (1989) 307-340.
17. H.G. Feichtinger and A.J.E.M. Janssen, Validity of WH-frame conditions depends on lattice parameters, Appl. Comput. Harmon. Anal. 8 (2000) 104-112.
18. H.G. Feichtinger and G. Zimmermann, A Banach space of test functions for Gabor analysis, in: Gabor Analysis: Theory and Application, eds. H.G. Feichtinger and T Strohmer (1998) pp. 123-170.
19. K.H. Gröchenig, Describing functions: Atomic decompositions versus frames, Monatsh. Math. 112(1) (1991) 1-42.
20. K.H. Gröchenig, Irregular sampling of wavelet and short time Fourier transforms, Constr. Approx. 9 (1993) 283-297.
21. K.H. Gröchenig, Foundations of Time-Frequency Analysis (Birkhäuser, Basel, 2000).
22. C. Heil and D. Walnut, Continuous and discrete wavelet transforms, SIAM Rev. 31(4) (1989) 628-666.
23. S. Jaffard, A Density criterion for frames of complex exponentials, Michigan Math. J. 38 (1991) 339-348.
24. A.J.E.M. Janssen, The duality condition for Weyl-Heisenberg frames, in: Gabor Analysis: Theory and Application, eds. H.G. Feichtinger and T. Strohmer (Birkhäuser, Basel, 1998).
25. A.J.E.M. Janssen, Zak transforms with few zeroes and the tie, Preprint.
26. P.A. Olsen and K. Seip, A note on irregular discrete wavelet transforms, IEEE Trans. Inform. Theory 38(2, Part 2) (1992) 861-863.
27. J. Ramanathan and T. Steger, Incompleteness of sparse coherent states, Appl. Comput. Harmon. Anal. 2 (1995) 148-153.
28. K. Seip and R. Wallsten, Sampling and interpolation in the Bargmann-Fock space II, J. Reine Angew. Math. 429 (1995) 107-113.
29. W. Sun and X. Zhou, On the stability of Gabor frames, Adv. in Appl. Math. 26 (2001) 181-191.
30. D. Walnut, Weyl Heisenberg wavelet expansions: Existence and stability in weighted spaces, Ph.D. thesis, University of Maryland, College Park, MD (1989).