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  • 1 Eötvös Loránd University Department of Numerical Analysis Pázmány P. sétány I/C H-1117 Budapest Hungary
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This paper is devoted to the study of Θ-summability of Fourier-Jacobi series. We shall construct such processes (using summations) that are uniformly convergent in a Banach space (
\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} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$C_{w_{\gamma ,\delta } } ,\parallel \cdot \parallel _{w_{\gamma ,\delta } }$$ \end{document}
) of continuous functions. Some special cases are also considered, such as the Fejér, de la Vallée Poussin, Cesàro, Riesz and Rogosinski summations. Our aim is to give such conditions with respect to Jacobi weights wγ,δ , wα,β and to summation matrix Θ for which the uniform convergence holds for all f
\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} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$C_{w_{\gamma ,\delta } }$$ \end{document}
. Order of convergence will also be investigated. The results and the methods are analogues to the discrete case (see [16] and [17]).
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