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On linear summability methods of fourier series in polynomials orthogonal in a discrete Sobolev space

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Abstract

Under study are the discrete Sobolev spaces with the inner product

$$\begin{array}{*{20}c} {\int\limits_{ - 1}^1 {f(x)g(x)w(x)dx + A_1 f(1)g(1)} } \\ { + B_1 f( - 1)g( - 1) + A_2 f'(1)g'(1) + B_2 f'( - 1)g'( - 1) = \left\langle {f,g} \right\rangle .} \\ \end{array}$$

Some results are presented on linear summation methods for Fourier series in orthonormal polynomials of discrete Sobolev spaces.

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Authors and Affiliations

  1. Moscow State University of Civil Engineering, Moscow, Russia

    B. P. Osilenker

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  1. B. P. Osilenker
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Correspondence to B. P. Osilenker.

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Moscow. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 56, No. 2, pp. 420–435, March–April, 2015.

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Osilenker, B.P. On linear summability methods of fourier series in polynomials orthogonal in a discrete Sobolev space. Sib Math J 56, 339–351 (2015). https://doi.org/10.1134/S0037446615020135

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  • DOI: https://doi.org/10.1134/S0037446615020135

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