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

2025/02/13 by Faulhuber, Markus
#33C45 #42C15 #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2502.09510

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.

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