An endpoint Balian-Low theorem for Schauder bases

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:485

Article

Leshen, Sara¹  Powell, Alexander M.² 

[1] Rutgers Univ Camden, Dept Math Sci, Camden, NJ 08102 USA

[2] Vanderbilt Univ, Dept Math, Nashville, TN 37240 USA

关键词: Time-frequency analysis;    Gabor system;    Schauder basis;    Balian-Low theorem;   

DOI  :  10.1016/j.jmaa.2019.123774

来源: Elsevier

【 摘 要 】

We prove two new results on the validity of the Balian-Low theorem in the setting of Schauder bases. Our first main result proves an endpoint Balian-Low theorem for Gabor systems that form Schauder bases for L-2(R): if g is an element of L-2(R) is compactly supported and f|xi|(2)ck < d xi < infinity then the Gabor system G(g, 1, 1) cannot be aSchauder basis of-called type A. Our second main result proves that the classical Balian-Low theorem for orthonormal bases and Riesz bases fails in the setting of Schauder bases. In particular, given e > 0, there exists g E L2(R) such that g(g, 1, 1) is a Schauder basis for L2(R) and such that d xi no. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

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