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On a System of Rational Chebyshev–Markov Fractions

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Abstract

In the present paper an orthogonal system of Chebyshev–Markov rational fractions is considered. We introduce the corresponding Fourier series and find the Dirichlet integral. We obtain the decomposition of the function |x| into Fourier series with respect to the considered system in explicit form and an asymptotic estimate of the uniform approximation of this function by partial sums of the rational Fourier–Chebyshev series.

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Authors and Affiliations

  1. Yanka Kupala State University of Grodno, Grodno, Belarus

    Y. Rouba, P. Patseika & K. Smatrytski

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  1. Y. Rouba
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  2. P. Patseika
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  3. K. Smatrytski
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Correspondence to Y. Rouba.

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Rouba, Y., Patseika, P. & Smatrytski, K. On a System of Rational Chebyshev–Markov Fractions. Anal Math 44, 115–140 (2018). https://doi.org/10.1007/s10476-018-0110-7

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  • DOI: https://doi.org/10.1007/s10476-018-0110-7

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