Gabor systems with Hermite functions of order n and oversampling greater than n+1 which are not frames

Abstract

We show that a sufficient density condition for Gabor systems with Hermite functions over lattices is not sufficient in general. This follows from a result on how zeros of the Zak transform determine the frame property of integer over-sampled Gabor systems.

Version 2 contains an extended introduction and a section with open problems and new examples. 16 pages, 7 figures. To appear in Sampling Theory, Signal Processing, and Data Analysis

References in corpus (2)

• On the non-frame property of Gabor systems with Hermite generators and the frame set conjecture
• On the frame property of Hermite functions and exploration of their frame sets

Cited by in corpus (1)

• On a fundamental barrier of the Wirtinger criterion for Gabor systems with odd functions