Localized frames are finite unions of Riesz sequences

Advances in Computational Mathematics

Volumn 18, Issue 2-4, 2003, Pages 149-157

  Gröchenig, Karlheinz ^a  

^a UNIVERSITY OF CONNECTICUT   (United States)

Author keywords

Frame; Gabor frame; Localization; Nonuniform sampling

Indexed keywords

EID: 0346494950     PISSN: 10197168     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1021368609918     Document Type: Article

References (8)

1. A. Aldroubi and K. Gröchenig, Nonuniform sampling and reconstruction in shift-invariant spaces, SIAM Rev. 43(4) (2001) 585-620.
2. J.J. Benedetto and W. Heller, Irregular sampling and the theory of frames. I, Note Mat. 10 (1990), suppl. 1 (1992) 103-125.
3. P. Casazza, O. Christensen and A. Lindner, Writing bounded frames as finite unions of Riesz basic sequences, Res. Notes (2001).
4. P. Casazza, O. Christensen, A. Lindner and R. Vershynin, Hilbert space frames, restricted invertibility, and the paving conjecture, Preprint (2002).
5. O. Christensen, Frames, Riesz bases, and discrete Gabor/wavelet expansions, Bull. Amer. Math. Soc. 38(3) (2001) 273-291.
6. K. Gröchenig, Foundations of Time-Frequency Analysis (Birkhäuser, Boston, 2001).
7. K. Gröchenig, Localization of frames, Banach frames, and the invertibility of the frame operator, to appear in J. Fourier Anal. Appl.
8. Y. Meyer, Ondelettes et Opérateurs. II. Opérateurs de Calderón-Zygmund (Hermann, Paris, 1990).