Gabor systems with Hermite functions of order n and oversampling greater than n+1 which are not frames
Functional Analysis
2025-10-01 v2 Mathematical Physics
math.MP
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.
Cite
@article{arxiv.2502.09510,
title = {Gabor systems with Hermite functions of order n and oversampling greater than n+1 which are not frames},
author = {Markus Faulhuber},
journal= {arXiv preprint arXiv:2502.09510},
year = {2025}
}
Comments
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