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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2512.04594 |
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| _version_ | 1866912748874498048 |
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| author | Belov, Yurii Kulikov, Aleksei |
| author_facet | Belov, Yurii Kulikov, Aleksei |
| contents | We find sufficient conditions on a compactly supported function $g$, $\supp g = [a,b]$ which guarantee that the Gabor system $$\mathcal{G}(g;α,β)=\{e^{2πi βm x}g(x-αn)\}_{m,n\in\mathbb{Z}}$$ is a frame for all $α< b-a, αβ< 1, αβ\notin\Q$. These conditions are on one hand satisfied by almost all such functions, and on the other hand are explicit enough that we can give many concrete examples of the functions $g$ which give us a frame e.g. $g(x) = \exp(\frac{1}{x^4-1})χ_{(-1,1)}(x)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_04594 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Frames for compactly supported functions with irrational density Belov, Yurii Kulikov, Aleksei Functional Analysis We find sufficient conditions on a compactly supported function $g$, $\supp g = [a,b]$ which guarantee that the Gabor system $$\mathcal{G}(g;α,β)=\{e^{2πi βm x}g(x-αn)\}_{m,n\in\mathbb{Z}}$$ is a frame for all $α< b-a, αβ< 1, αβ\notin\Q$. These conditions are on one hand satisfied by almost all such functions, and on the other hand are explicit enough that we can give many concrete examples of the functions $g$ which give us a frame e.g. $g(x) = \exp(\frac{1}{x^4-1})χ_{(-1,1)}(x)$. |
| title | Frames for compactly supported functions with irrational density |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2512.04594 |