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
收藏
页码：161 / 167
页数：7
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