Title

The Balian-Low theorem for symplectic lattices in higher dimensions

Authors

Authors

K. Grochenig; D. G. Han; C. Heil;G. Kutyniok

Abbreviated Journal Title

Appl. Comput. Harmon. Anal.

Keywords

Balian-Low theorem; frames; Gabor systems; modulation spaces; symplectic; matrices; uncertainty principles; GABOR FRAMES; Mathematics, Applied; Physics, Mathematical

Abstract

The Balian-Low theorem expresses the fact that time-frequency concentration is incompatible with non-redundancy for Gabor systems that form orthonormal or Riesz bases for L-2(R). We extend the Balian-Low theorem for Riesz bases to higher dimensions, obtaining a weak form valid for all sets of time-frequency shifts which form a lattice in R-2d, and a strong form valid for symplectic lattices in R-2d. For the orthonormal basis case, we obtain a strong form valid for general non-lattice sets which are symmetric with respect to the origin. (C) 2002 Elsevier Science (USA). All rights reserved.

Journal Title

Applied and Computational Harmonic Analysis

Volume

13

Issue/Number

2

Publication Date

1-1-2002

Document Type

Article

Language

English

First Page

169

Last Page

176

WOS Identifier

WOS:000179970200006

ISSN

1063-5203

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