Unconditional Convergence of Fourier Series for Functions of Bounded Variation

被引：7

作者：

Gogoladze, L. D. ^{[1
]}

Tsagareishvili, V. Sh. ^{[1
]}

机构：

[1] Tbilisi State Univ, Tbilisi, Georgia

来源：

SIBERIAN MATHEMATICAL JOURNAL | 2018年 / 59卷 / 01期

关键词：

Fourier coefficients; function of finite variation; unconditional convergence; ABSOLUTE CONVERGENCE; RESPECT;

D O I：

10.1134/S0037446618010081

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This article concerns the unconditional convergence a.e. of Fourier series with respect to general orthonormal systems. We find certain conditions to be satisfied by the functions in the orthonormal system so that the Fourier series of each function of finite variation unconditionally converge a.e. The results are best possible.

引用

页码：65 / 72

页数：8

共 50 条

[1] Unconditional Convergence of Fourier Series for Functions of Bounded Variation
L. D. Gogoladze
V. Sh. Tsagareishvili
Siberian Mathematical Journal, 2018, 59 : 65 - 72
[2] The Nature of Convergence of the Fourier Series for Functions of Bounded Variation
Telyakovskii, S. A.
RUSSIAN MATHEMATICS, 2010, 54 (03) : 42 - 44
[3] On the rate of convergence of Fourier series of functions of bounded variation
Telyakovskii, SA
MATHEMATICAL NOTES, 2002, 72 (5-6) : 872 - 876
[4] Convergence of multiple Fourier series for functions of bounded variation
Telyakovskii, SA
Temlyakov, VN
MATHEMATICAL NOTES, 1997, 61 (3-4) : 484 - 494
[5] CONVERGENCE OF FOURIER SERIES OF FUNCTIONS OF GENERALIZED BOUNDED VARIATION
WATERMAN, D
NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1971, 18 (03): : 518 - &
[6] On the Rate of Convergence of Fourier Series of Functions of Bounded Variation
S. A. Telyakovskii
Mathematical Notes, 2002, 72 : 872 - 876
[7] Convergence of multiple fourier series for functions of bounded variation
S. A. Telyakovskii
V. N. Temlyakov
Mathematical Notes, 1997, 61 : 484 - 494
[8] Convergence of Multiple Fourier Series of Functions of Bounded Generalized Variation
U. Goginava
A. Sahakian
Ukrainian Mathematical Journal, 2015, 67 : 186 - 198
[9] Convergence of Multiple Fourier Series of Functions of Bounded Generalized Variation
Goginava, U.
Sahakian, A.
UKRAINIAN MATHEMATICAL JOURNAL, 2015, 67 (02) : 186 - 198
[10] CONVERGENCE OF FOURIER-SERIES OF FUNCTIONS OF GENERALIZED BOUNDED VARIATION
WATERMAN, D
STUDIA MATHEMATICA, 1972, 44 (02) : 107 - &

← 1 2 3 4 5 →