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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.14207 |
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Table of 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 $α$,$β$, $αβ\leq 1$.