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