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Sibirskii Matematicheskii Zhurnal, 2016, Volume 57, Number 1, Pages 186–198
DOI: https://doi.org/10.17377/smzh.2016.57.114
(Mi smj2737)
 

This article is cited in 11 scientific papers (total in 11 papers)

On Wiener's Theorem for functions periodic at infinity

I. I. Strukova

Voronezh State University, Voronezh, Russia
References:
Abstract: We consider the functions periodic at infinity with values in a complex Banach space. The notions are introduced of the canonical and generalized Fourier series of a function periodic at infinity. We prove an analog of Wiener's Theorem on absolutely convergent Fourier series for functions periodic at infinity whose Fourier series are summable with weight. The two criteria are given: for the function periodic at infinity to be the sum of a purely periodic function and a function vanishing at infinity and for a function to be periodic at infinity. The results of the article base on substantially use on spectral theory of isometric representations.
Keywords: Banach space, function slowly varying at infinity, function periodic at infinity, Fourier series, Wiener's Theorem.
Funding agency Grant number
Russian Foundation for Basic Research 16-01-00197
Russian Science Foundation 14-21-00066
The author was supported by the Russian Foundation for Basic Research (Grants 13-01-00378; 14-01-31196), the Russian Science Foundation (Grant 14-21-00066), and the Ministry of Science and Education in the framework of the State Tasks in Science to Institutions of Higher Education for 2014–2016 (Grant 1110).
Received: 10.02.2015
English version:
Siberian Mathematical Journal, 2016, Volume 57, Issue 1, Pages 145–154
DOI: https://doi.org/10.1134/S0037446616010146
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: Russian
Citation: I. I. Strukova, “On Wiener's Theorem for functions periodic at infinity”, Sibirsk. Mat. Zh., 57:1 (2016), 186–198; Siberian Math. J., 57:1 (2016), 145–154
Citation in format AMSBIB
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  • This publication is cited in the following 11 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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