Continuous Mean Periodic Extension of Functions from an Interval

We study the following version of the mean periodic extension problem. (i) Suppose that , n ≥ 2, and E is a nonempty closed subset of . What conditions guarantee that, for a function f  ∈ C ( E ), there is a function coinciding with f on E such that in ? (ii) If such an extension F exists, then esti...

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Bibliographic Details
Published in:Doklady. Mathematics 2021, Vol.103 (1), p.14-18
Main Authors: Volchkov, V. V., Volchkov, Vit. V.
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Summary:We study the following version of the mean periodic extension problem. (i) Suppose that , n ≥ 2, and E is a nonempty closed subset of . What conditions guarantee that, for a function f  ∈ C ( E ), there is a function coinciding with f on E such that in ? (ii) If such an extension F exists, then estimate the growth of F at infinity. We present a solution of this problem for a broad class of distributions T in the case when E is an interval in .
ISSN:1064-5624
1531-8362
DOI:10.1134/S106456242101018X