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<p>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.</p>

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Gabor systems with Hermite functions of order \(N\) and oversampling greater than \(N+1\) which are not frames

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年9月9日

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  • Markus Faulhuber

摘要

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.