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.
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页数：25
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