Absolute convergence of the Fourier trigonometric series with gaps-Reference-Cited by-同舟云学术

Absolute convergence of the Fourier trigonometric series with gaps

Published:2022-04-28 Issue:5 Volume:29 Page:755-760
ISSN:1072-947X
Container-title:Georgian Mathematical Journal
language:en
Short-container-title:

Author:

Meskhia Rusudan¹

Affiliation:

1. Faculty of Exact and Natural Sciences , Ivane Javakhishvili Tbilisi State University , 2 University Str. , Tbilisi 0177 , Georgia

Abstract

Abstract In the present paper, the sufficient conditions are obtained for the generalized β-absolute convergence ( 0 < β < 2 )

{(0<\beta<2)}

of the Fourier trigonometric series with gaps for some classes of functions. In [8], analogous problems were considered for Fourier trigonometric series and sufficient conditions were established in terms of the δ-variation of a function; also, it was proved that these conditions are unimprovable in a certain sense. Our goal is to show that if a function f has a Fourier series with gaps, then the results obtained in [8] hold if the function f satisfies the derived conditions only on an arbitrarily small interval.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/gmj-2022-2157/pdf

Reference11 articles.

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3. translation in Sov. Math., Dokl. 15 (1974), 67-71.

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5. L. Gogoladze and R. Meskhia, On the absolute convergence of trigonometric Fourier series, Proc. A. Razmadze Math. Inst. 141 (2006), 29–40.