On the transcendentality condition for Gaussian Gabor frames and Hermite super/multiwindow frames
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866918055954612224 |
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| author | Luef, Franz Testorf, Johannes Wang, Xu |
| author_facet | Luef, Franz Testorf, Johannes Wang, Xu |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_08415 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the transcendentality condition for Gaussian Gabor frames and Hermite super/multiwindow frames Luef, Franz Testorf, Johannes Wang, Xu Functional Analysis Classical Analysis and ODEs Complex Variables 42C15(Primary) 32Q99 (Secondary) 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. |
| title | On the transcendentality condition for Gaussian Gabor frames and Hermite super/multiwindow frames |
| topic | Functional Analysis Classical Analysis and ODEs Complex Variables 42C15(Primary) 32Q99 (Secondary) |
| url | https://arxiv.org/abs/2405.08415 |