Gabor frames for functions supported on a semi-axis
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912542982406144 |
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| author | Belov, Yurii Kulikov, Aleksei |
| author_facet | Belov, Yurii Kulikov, Aleksei |
| contents | Let $g\in L^2(\mathbb{R})$ be a strictly decreasing continuous function supported on $\mathbb{R}_+$ such that for all $t > 0$ we have $g(x+t)\le q(t)g(x)$ for some $q(t)<1$. We prove that the Gabor system $$\mathcal{G}(g;α,β):=\{g_{m,n}\}_{m,n\in\mathbb{Z}}=\{e^{2πi βm x}g(x-αn)\}_{m,n\in\mathbb{Z}}$$ always forms a frame in $L^2(\mathbb{R})$ for all lattice parameters $α$,$β$, $αβ\leq 1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_14207 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Gabor frames for functions supported on a semi-axis Belov, Yurii Kulikov, Aleksei Functional Analysis Let $g\in L^2(\mathbb{R})$ be a strictly decreasing continuous function supported on $\mathbb{R}_+$ such that for all $t > 0$ we have $g(x+t)\le q(t)g(x)$ for some $q(t)<1$. We prove that the Gabor system $$\mathcal{G}(g;α,β):=\{g_{m,n}\}_{m,n\in\mathbb{Z}}=\{e^{2πi βm x}g(x-αn)\}_{m,n\in\mathbb{Z}}$$ always forms a frame in $L^2(\mathbb{R})$ for all lattice parameters $α$,$β$, $αβ\leq 1$. |
| title | Gabor frames for functions supported on a semi-axis |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2505.14207 |