Sampling in quasi shift-invariant spaces and Gabor frames generated by ratios of exponential polynomials
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910848752025600 |
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| author | Ulanovskii, Alexander Zlotnikov, Ilya |
| author_facet | Ulanovskii, Alexander Zlotnikov, Ilya |
| contents | We introduce two families of generators (functions) $\mathcal{G}$ that consist of entire and meromorphic functions enjoying a certain periodicity property and contain the classical Gaussian and hyperbolic secant generators. Sharp results are proved on the density of separated sets that provide non-uniform sampling for the shift-invariant and quasi shift-invariant spaces generated by elements of these families. As an application, we obtain new sharp results on the density of semi-regular lattices for the Gabor frames generated by elements from these families. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2402_03090 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sampling in quasi shift-invariant spaces and Gabor frames generated by ratios of exponential polynomials Ulanovskii, Alexander Zlotnikov, Ilya Functional Analysis Classical Analysis and ODEs Complex Variables 42C15, 42C40, 94A20 We introduce two families of generators (functions) $\mathcal{G}$ that consist of entire and meromorphic functions enjoying a certain periodicity property and contain the classical Gaussian and hyperbolic secant generators. Sharp results are proved on the density of separated sets that provide non-uniform sampling for the shift-invariant and quasi shift-invariant spaces generated by elements of these families. As an application, we obtain new sharp results on the density of semi-regular lattices for the Gabor frames generated by elements from these families. |
| title | Sampling in quasi shift-invariant spaces and Gabor frames generated by ratios of exponential polynomials |
| topic | Functional Analysis Classical Analysis and ODEs Complex Variables 42C15, 42C40, 94A20 |
| url | https://arxiv.org/abs/2402.03090 |