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arXiv · 2605.29984

Compactly supported Gabor orthonormal bases

Lukas Liehr
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Abstract

We characterize all lattices $\Lambda \subset \mathbb{R}^2$ and all compactly supported functions $g \in L^2(\mathbb{R})$ for which the Gabor system $\left \{ e^{2\pi i s x} g(x-t) : (t,s) \in \Lambda \right \}$ forms an orthonormal basis for $L^2(\mathbb{R})$. The characterization is given in geometric terms through translation tilings and discreteness properties of lattice projections. In particular, this resolves a conjecture of Han and Wang on the non-existence of Gabor bases along specific irrational lattices. Finally, we construct Gabor bases that cannot be realized by any product set, answering a problem of Iosevich and Mayeli.

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Lukas Liehr. 2026-05-28. Compactly supported Gabor orthonormal bases. https://arxiv.org/abs/2605.29984

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