The Balian-Low theorem for symplectic lattices in higher dimensions

被引：32

作者：

Gröchenig, K

Han, DG

Heil, C ^{[1
]}

Kutyniok, G

机构：

[1] Georgia Inst Technol, Sch Math, Atlanta, GA 30332 USA

[2] Univ Connecticut, Dept Math, Storrs, CT 06269 USA

[3] Univ Cent Florida, Dept Math, Orlando, FL 32826 USA

[4] Univ Gesamthsch Paderborn, Dept Math & Comp Sci, D-33095 Paderborn, Germany

来源：

APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS | 2002年 / 13卷 / 02期

基金：

奥地利科学基金会; 美国国家科学基金会;

关键词：

Balian-Low theorem; frames; Gabor systems; modulation spaces; symplectic matrices; uncertainty principles;

D O I：

10.1016/S1063-5203(02)00506-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：169 / 176

页数：8

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