Optimal Gabor frame bounds for separable lattices and estimates for Jacobi theta functions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:445

Article

Faulhuber, Markus¹  Steinerberger, Stefan² 

[1] Univ Vienna, Fac Math, NuHAG, Oskar Morgenstern Pl 1, A-1090 Vienna, Austria

[2] Yale Univ, Dept Math, 10 Hillhouse Ave, New Haven, CT 06510 USA

关键词: Gabor frame;    Frame bounds;    Jacobi theta functions;    Log-convexity;    Log-concavity;   

DOI  :  10.1016/j.jmaa.2016.07.074

来源: Elsevier

【 摘 要 】

We study sharp frame bounds of Gabor frames for integer redundancy with the standard Gaussian window and prove that the square lattice optimizes both the lower and the upper frame bound among all rectangular lattices. This proves a conjecture of Floch, Alard & Berrou (as reformulated by Strohmer & Beaver). The proof is based on refined log-convexity/concavity estimates for the Jacobi theta functions theta(3) and theta(4). (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free