On the transcendentality condition for Gaussian Gabor frames and Hermite super/multiwindow frames

Franz Luef; Johannes Testorf; Xu Wang

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arXiv · 2405.08415

On the transcendentality condition for Gaussian Gabor frames and Hermite super/multiwindow frames

Franz Luef·Johannes Testorf·Xu Wang

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Abstract

We give a criterion for higher-dimensional Gaussian Gabor frames, which is a reformulation of one of the main results in in a previous article by the first and last authors in more explicit terms. We use this formulation in order to extend a result of Romero, Ulanovskii, and Zlotnikov to lattices given by irrational rotations. We also show that this density criterion for Gaussian Gabor frames is generic in a certain sense. In addition, we also extend the methods of the first and last named authors to the pseudoeffective threshold which gives a condition for uniqueness in the Bargmann-Fock space. We also use this viewpoint to study super and multi-window Gabor frames with Hermitian windows. In particular, we find a density criterion for transcendental lattices.

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BibTeX RIS

Franz Luef, Johannes Testorf, Xu Wang. 2024-05-14. On the transcendentality condition for Gaussian Gabor frames and Hermite super/multiwindow frames. https://arxiv.org/abs/2405.08415

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