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arXiv · 1708.06397

Gabor orthogonal bases and convexity

Alex Iosevich·Azita Mayeli
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Abstract

Let $g(x)=\chi_B(x)$ be the indicator function of a bounded convex set in $\Bbb R^d$, $d\geq 2$, with a smooth boundary and everywhere non-vanishing Gaussian curvature. Using a combinatorial appraoch we prove that if $d \neq 1 \mod 4$, then there does not exist $S \subset {\Bbb R}^{2d}$ such that ${ \{g(x-a)e^{2 \pi i x \cdot b} \}}_{(a,b) \in S}$ is an orthonormal basis for $L^2({\Bbb R}^d)$.

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Alex Iosevich, Azita Mayeli. 2017-08-21. Gabor orthogonal bases and convexity. https://arxiv.org/abs/1708.06397

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