On linear summability methods of fourier series in polynomials orthogonal in a discrete Sobolev space

被引：10
作者：
Osilenker, B. P. [1 ]
机构：
[1] Moscow State Univ Civil Engn, Moscow, Russia
来源：
SIBERIAN MATHEMATICAL JOURNAL | 2015年 / 56卷 / 02期
关键词：
discrete Sobolev space; orthogonal polynomial; Fourier series; linear summation method; Cesaro method; symmetric Gegenbauer-Sobolev polynomials; ASYMPTOTICS;
D O I：
10.1134/S0037446615020135
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Under study are the discrete Sobolev spaces with the inner product Some results are presented on linear summation methods for Fourier series in orthonormal polynomials of discrete Sobolev spaces.
引用
收藏
页码：339 / 351
页数：13
相关论文
共 50 条
[41]   Approximation of classes of convolutions by linear methods of summation of Fourier series [J].
D. M. Bushev .
Ukrainian Mathematical Journal, 1997, 49 (6) :825-843
[42]   Saturation of the linear methods of summation of Fourier series in the spaces Spφ [J].
A. L. Shydlich .
Ukrainian Mathematical Journal, 2008, 60 :950-966
[43]   SATURATION OF THE LINEAR METHODS OF SUMMATION OF FOURIER SERIES IN THE SPACES Spφ [J].
Shydlich, A. L. .
UKRAINIAN MATHEMATICAL JOURNAL, 2008, 60 (06) :950-966
[44]   Approximation Properties of the Vallée-Poussin Means Similar to the Partial Sums of Fourier Series in Laguerre–Sobolev Polynomials [J].
R. M. Gadzhimirzaev .
Siberian Mathematical Journal, 2022, 63 :451-465
[45]   Approximation Properties of the Vallee-Poussin Means Similar to the Partial Sums of Fourier Series in Laguerre-Sobolev Polynomials [J].
Gadzhimirzaev, R. M. .
SIBERIAN MATHEMATICAL JOURNAL, 2022, 63 (03) :451-465
[46]   Sharp estimates for the convergence rate of Fourier series in terms of orthogonal polynomials in L 2((a, b), p(x)) [J].
Abilov, V. A. ;
Abilova, F. V. ;
Kerimov, M. K. .
COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 2009, 49 (06) :927-941
[47]   Sharp estimates for the convergence rate of Fourier series in terms of orthogonal polynomials in L2((a, b), p(x)) [J].
V. A. Abilov ;
F. V. Abilova ;
M. K. Kerimov .
Computational Mathematics and Mathematical Physics, 2009, 49 :927-941
[48]   Linear Methods for Summing Fourier Series and Approximation in Weighted Lebesgue Spaces with Variable Exponents [J].
S. Z. Jafarov .
Ukrainian Mathematical Journal, 2015, 66 :1509-1518
[49]   Approximation of Functions of the Classes <mml:semantics>Cβψ<mml:msup>Hα</mml:msup></mml:semantics> by Linear Methods Summation of Their Fourier Series [J].
Kharkevych, Yurii ;
Kal'chuk, Inna .
AXIOMS, 2023, 12 (11)
[50]   On Approximation Properties of Fourier Series in Jacobi Polynomials \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$P_n^{\alpha-r,-r}(x)$$\end{document} Orthogonal in the Sense of Sobolev [J].
R. M. Gadzhimirzaev .
Mathematical Notes, 2022, 111 (5-6) :827-840
12345