Sharp estimates for the convergence rate of Fourier series in terms of orthogonal polynomials in L 2((a, b), p(x))

被引：8

作者：

Abilov, V. A. ^{[1
]}

Abilova, F. V. ^{[2
]}

Kerimov, M. K. ^{[3
]}

机构：

[1] Dagestan State Univ, Makhachkala 367025, Russia

[2] Dagestan State Tech Univ, Makhachkala 367015, Russia

[3] Russian Acad Sci, Dorodnicyn Comp Ctr, Moscow 119991, Russia

来源：

COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS | 2009年 / 49卷 / 06期

基金：

俄罗斯基础研究基金会;

关键词：

Fourier series; generalized modulus of continuity; width; generalized derivatives; expansions in terms of Laguerre; Hermite; Jacobi polynomials; convergence of series;

D O I：

10.1134/S0965542509060049

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Sharp estimates are given for the convergence rate of Fourier series in terms of classical orthogonal polynomials in some classes of functions characterized by a generalized modulus of continuity in the space L (2)((a, b), p(x)). Expansions in terms of Laguerre, Hermite, and Jacobi polynomials are considered.

引用

页码：927 / 941

页数：15

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