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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.10503 |
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| _version_ | 1866908300227903488 |
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| author | Faulhuber, Markus Shafkulovska, Irina Zlotnikov, Ilya |
| author_facet | Faulhuber, Markus Shafkulovska, Irina Zlotnikov, Ilya |
| contents | We study Gabor frames with Hermite window functions. Gröchenig and Lyubarskii provided a sufficient density condition for their frame sets, which leads to what we call the "safety region". For rectangular lattices and Hermite windows of order 4 and higher, we enlarge this safety region by providing new points on the boundary of this region. For this purpose, we employ the Janssen representation of the frame operator to compare its distance to the identity in the operator norm. The calculations lead to estimates on series involving Laguerre polynomials with Gaussian weight functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_10503 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the frame property of Hermite functions and exploration of their frame sets Faulhuber, Markus Shafkulovska, Irina Zlotnikov, Ilya Functional Analysis 42C15, 33C45 We study Gabor frames with Hermite window functions. Gröchenig and Lyubarskii provided a sufficient density condition for their frame sets, which leads to what we call the "safety region". For rectangular lattices and Hermite windows of order 4 and higher, we enlarge this safety region by providing new points on the boundary of this region. For this purpose, we employ the Janssen representation of the frame operator to compare its distance to the identity in the operator norm. The calculations lead to estimates on series involving Laguerre polynomials with Gaussian weight functions. |
| title | On the frame property of Hermite functions and exploration of their frame sets |
| topic | Functional Analysis 42C15, 33C45 |
| url | https://arxiv.org/abs/2403.10503 |