On linear summation methods for Jacobi series in the case of half integer α

с. кАльНЕИ

doi:10.1007/bf02342337

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Analysis Mathematica

Volume/Issue:: Volume 22: Issue 1

On linear summation methods for Jacobi series in the case of half integer α

Author: с. кАльНЕИ¹

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¹ МОс кОВскИИ гОсУДАРстВЕ ННыИ ИНстИтУт ЁлЕктР ОННОИ тЕхНИкИ 103 498 МОскВА РОссИь 103 498 МОскВА РОссИь

DOI:: https://doi.org/10.1007/bf02342337

Page Count:: 35–50

Publication Date:: 10 Mar 1996

Online Publication Date:: 10 Apr 2006

Article Category:: Research Article

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Abstract

An upper estimate is proved for the Lebesgue function with respect to Jacobi polynomials

\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$P_m^{(\alpha ,\beta )} (x)$$ \end{document}

in the case of half integerα and it is expressed in terms of the matrix coefficients determining the linear summation method. The author also proves the analogue of the well-known theorem by S. M. Nikol'skii on the necessary and sufficient condition for the summability of trigonometric Fourier series.