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On the problem of mean periodic extension
V. V. Volchkov, Vit. V. Volchkov Donetsk National University,
24 Universitetskaya str., Donetsk 283001, Russia
Аннотация:
This paper is devoted to a study of the following version of the mean periodic extension problem:
(i) Suppose that $T\in\mathcal{E}'(\mathbb{R}^n)$, $n\geq 2$, and $E$ is a non-empty subset of $\mathbb{R}^n$. Let $f\in C(E)$. What conditions guarantee that there is an $F\in C(\mathbb{R}^n)$ coinciding with $f$ on $E$, such that $F\ast T=0$ in $\mathbb{R}^n$?
(ii) If such an extension $F$ exists, then estimate the growth of $F$ at infinity.
In this paper, we present a solution of this problem for a broad class of distributions $T$ in the case when $E$ is a segment in $\mathbb{R}^n$.
Ключевые слова:
convolution equation, mean periodicity, continuous extension, spherical transform.
Поступила в редакцию: 14.03.2020 Исправленный вариант: 23.05.2020 Принята в печать: 23.05.2020
Образец цитирования:
V. V. Volchkov, Vit. V. Volchkov, “On the problem of mean periodic extension”, Пробл. анал. Issues Anal., 9(27):2 (2020), 138–151
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/pa301 https://www.mathnet.ru/rus/pa/v27/i2/p138
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