Gabor orthogonal bases and convexity

IF 1 3区数学 Q1 MATHEMATICS

Discrete Analysis Pub Date : 2017-08-01 DOI:10.19086/DA.5952

A. Iosevich, A. Mayeli

引用次数: 5

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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Gabor正交基与凸性

设$g(x)=\chi_B(x)$为$\Bbb R^d$, $d\geq 2$中有界凸集的指示函数，该凸集边界光滑，处处具有不消失的高斯曲率。用组合方法证明了如果$d \neq 1 \mod 4$，则不存在$S \subset {\Bbb R}^{2d}$使得${ \{g(x-a)e^{2 \pi i x \cdot b} \}}_{(a,b) \in S}$是$L^2({\Bbb R}^d)$的正交基。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Discrete Analysis Mathematics-Algebra and Number Theory

CiteScore

1.60

自引率

0.00%

发文量

审稿时长

17 weeks

期刊介绍： Discrete Analysis is a mathematical journal that aims to publish articles that are analytical in flavour but that also have an impact on the study of discrete structures. The areas covered include (all or parts of) harmonic analysis, ergodic theory, topological dynamics, growth in groups, analytic number theory, additive combinatorics, combinatorial number theory, extremal and probabilistic combinatorics, combinatorial geometry, convexity, metric geometry, and theoretical computer science. As a rough guideline, we are looking for papers that are likely to be of genuine interest to the editors of the journal.