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
Copyright Status
Unknown
Socpus ID
0242433429 (Scopus)
Source API URL
https://api.elsevier.com/content/abstract/scopus_id/0242433429
STARS Citation
Gröchenig, Karlheinz; Han, Deguang; and Heil, Christopher, "The Balian-Low Theorem For Symplectic Lattices In Higher Dimensions" (2002). Scopus Export 2000s. 2757.
https://stars.library.ucf.edu/scopus2000/2757