The Uniform Convergence of Fourier Series in a System of Polynomials Orthogonal in the Sense of Sobolev and Associated to Jacobi Polynomials

被引：0
作者：
M. G. Magomed-Kasumov
机构：
[1] Daghestan Federal Research Center,
[2] Vladikavkaz Scientific Center,undefined
来源：
Siberian Mathematical Journal | 2023年 / 64卷
关键词：
Sobolev inner product; Jacobi polynomials; Fourier series; uniform convergence; Sobolev space; Muckenhoupt conditions; 517;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We establish that the Fourier series in the Sobolev system of polynomials \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ {\mathcal{P}}_{r}^{\alpha,\beta} $\end{document}, with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ -1<\alpha,\beta\leq 0 $\end{document}, associated to the Jacobi polynomials converge uniformly on \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ [-1,1] $\end{document} to functions in the Sobolev space \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ W^{r}_{L^{1}_{\rho(\alpha,\beta)}} $\end{document}, where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \rho(\alpha,\beta) $\end{document} is the Jacobi weight. We show also that the Fourier series converges in the norm of the Sobolev space \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ W^{r}_{L^{p}_{\rho(A,B)}} $\end{document} with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ p>1 $\end{document} under the Muckenhoupt conditions.
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页码：338 / 346
页数：8
相关论文
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