On the l4 : l2 ratio of functions with restricted Fourier support

被引：1

作者：

Kirshner, Naomi ^{[1
]}

Samorodnitsky, Alex ^{[1
]}

机构：

[1] Hebrew Univ Jerusalem, Sch Engn & Comp Sci, IL-91904 Jerusalem, Israel

来源：

JOURNAL OF COMBINATORIAL THEORY SERIES A | 2020年 / 172卷

关键词：

Fourier spectrum; Hypercontractivity; Additive combinatorics; Uncertainty principle; Krawchouk polynomials; THEOREM;

D O I：

10.1016/j.jcta.2019.105202

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Given a subset A subset of {0,1}(n), let mu(A) be the maximal ratio between l(4) and l(2) norms of a function whose Fourier support is a subset of A.(1) We make some simple observations about the connections between mu(A) and the additive properties of A on one hand, and between mu(A) and the uncertainty principle for A on the other hand. One application obtained by combining these observations with results in additive number theory is a stability result for the uncertainty principle on the discrete cube. Our more technical contribution is determining mu(A) rather precisely, when A is a Hamming sphere S(n, k) for all 0 <= k <= n. (C) 2020 Elsevier Inc. All rights reserved.

引用

页数：25

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