Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika
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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika, 2021, Number 4, Pages 17–22 (Mi vmumm4411)  
This article is cited in 1 scientific paper (total in 1 paper)

Mathematics

An existence criterion for maximizers of convolution operators in $L_1(\mathbb{R}^n)$

G. V. Kalacheva, S. Yu. Sadov

a Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Full-text PDF (760 kB) Citations (1)
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Abstract: The operator of convolution 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 convolution, is given. Analysis of measurable solutions of Pexider's functional equation defined on subsets of positive measure in $\mathbb{R}^n$ plays the key role.
Key words: convolution operator, $L_1$ space, maximizer, Pexider's equation, Cauchy's functional equation, measurable solution.
Received: 13.12.2019
English version:
Moscow University Mathematics Bulletin, 2021, Volume 76, Issue 4, Pages 161–167
DOI: https://doi.org/10.3103/S0027132221040033
Bibliographic databases:
Document Type: Article
UDC: 517.51, 517.965
Language: Russian
Citation: G. V. Kalachev, S. Yu. Sadov, “An existence criterion for maximizers of convolution operators in $L_1(\mathbb{R}^n)$”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2021, no. 4, 17–22; Moscow University Mathematics Bulletin, 76:4 (2021), 161–167
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Full-text PDF :25
    References:22
    First page:13
     
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