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

Markus Faulhuber, Stefan Steinerberger

Veröffentlichungen: Beitrag in FachzeitschriftArtikelPeer Reviewed

Abstract

We study sharp frame bounds of Gabor frames 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 $\theta_4$.
OriginalspracheEnglisch
Seiten (von - bis)407-422
Seitenumfang16
FachzeitschriftJournal of Mathematical Analysis and Applications
Jahrgang445
Ausgabenummer1
DOIs
PublikationsstatusVeröffentlicht - 1 Jan. 2017

ÖFOS 2012

  • 101002 Analysis

Zitationsweisen