An Existence Criterion for Maximizers of Convolution Operators in L1(Rn)

被引：0

作者：

Kalachev, G., V ^{[1
]}

Sadov, S. Yu ^{[1
]}

机构：

[1] Lomonosov Moscow State Univ, Fac Mech & Math, Lab Problems Theoret Cybernet, Moscow 119992, Russia

来源：

MOSCOW UNIVERSITY MATHEMATICS BULLETIN | 2021年 / 76卷 / 04期

关键词：

convolution operator; space L-1; maximizer; Pexider's equation; Cauchy's functional equation; measurable solution;

D O I：

10.3103/S0027132221040033

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The convolution operator with a complex-valued integrable kernel in the space of integrable functions is considered; a necessary and sufficient condition for the existence of a maximizer, i.e., a norm-one function that maximizes the norm of the convolution, is given. The analysis of measurable solutions of Pexider's functional equation defined on subsets of positive measure in R-n plays the key role.

引用

页码：161 / 167

页数：7

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