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arXiv · 1511.09470

On some Hermite series identities and their applications to Gabor analysis

Jakob Lemvig
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Abstract

We prove some infinite series identities for the Hermite functions. From these identities we disprove the Gabor frame set conjecture for Hermite functions of order $4m+2$ and $4m+3$ for $m \in \{0\} \cup \mathbb{N}$. The results hold not only for Hermite functions, but for two large classes of eigenfunctions of the Fourier transform associated with the eigenvalues $-1$ and $i$, and the results indicate that the Gabor frame set of all such functions must have a rather complicated structure.

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Jakob Lemvig. 2015-11-30. On some Hermite series identities and their applications to Gabor analysis. https://arxiv.org/abs/1511.09470

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