Title

The Balian-Low Theorem For Symplectic Lattices In Higher Dimensions

Keywords

Balian-Low theorem; Frames; Gabor systems; Modulation spaces; Symplectic matrices; Uncertainty principles

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 L2(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 ℝ2d, and a strong form valid for symplectic lattices in ℝ2d. For the orthonormal basis case, we obtain a strong form valid for general non-lattice sets which are symmetric with respect to the origin. © 2002 Elsevier Science (USA). All rights reserved.

Publication Date

1-1-2002

Publication Title

Applied and Computational Harmonic Analysis

Volume

13

Issue

2

Number of Pages

169-176

Document Type

Letter

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/S1063-5203(02)00506-7

Socpus ID

0242433429 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/0242433429

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