Some problems of convergence of general Fourier series-Reference-Cited by-同舟云学术

Some problems of convergence of general Fourier series

Published:2022-11-15 Issue: Volume: Page:70-80
ISSN:0002-3043
Container-title:Proceedings of NAS RA. Mathematics
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Author:

Tsagareishvili V.¹,Tutberidze G.²

Affiliation:

1. Ivane Javakhishvili Tbilisi State University, Tbilisi, Georgia

2. The University of Georgia, School of science and technology, Tbilisi, Georgia

Abstract

S. Banach [1] proved that good differential properties of function do not guarantee the a.e. convergence of the Fourier series of this function with respect to general orthonormal systems (ONS). On the other hand it is very well known that a sufficient condition for the a.e. convergence of an orthonormal series is given by the Menshov-Rademacher Theorem. The paper deals with sequence of positive numbers (dn) such that multiplying the Fourier coefficients (Cn(f)) of functions with bounded variation by these numbers one obtains a.e. convergent series of the form P∞ n=1 dnCn(f)φn(x). It is established that the resulting conditions are best possible.

Publisher

National Academy of Sciences of the Republic of Armenia

Reference22 articles.

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3. U. Goginava and L. Gogoladze, “Convergence in measure of logarithmic means of multipleFourier series”, J. Contemp. Math. Anal., 49(2), 70 – 77 (2014).

4. B.S. Kashin and A. A. Saakyan, Orthogonal Series, Izd. AFTs, Moscow, Russ. (1999).

5. L. Gogoladze and V. Tsagareishvili, “Some classes of functions and Fourier coefficients withrespect to general orthonormal systems”, English version: Proceedings of the Steklov Instituteof Mathematics, 280, 156 – 168 (2013).