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Polynomials orthogonal in the Sobolev sense, generated by Chebyshev polynomials orthogonal on a mesh

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Abstract

We consider the problem of constructing polynomials, orthogonal in the Sobolev sense on the finite uniform mesh and associated with classical Chebyshev polynomials of discrete variable. We have found an explicit expression of these polynomials by classicalChebyshev polynomials. Also we have obtained an expansion of new polynomials by generalized powers ofNewton type. We obtain expressions for the deviation of a discrete function and its finite differences from respectively partial sums of its Fourier series on the new system of polynomials and their finite differences.

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Authors and Affiliations

  1. Dagestan State Pedagogical University, Dagestan Scientific Center of the Russian Academy of Sciences, ul. Gamidova 17, Makhachkala, 367013, Russia

    I. I. Sharapudinov

  2. Dagestan Scientific Center of the Russian Academy of Sciences, Vladikavkaz Scientific Center of the Russian Academy of Sciences, ul. Gadzhieva 45, Makhachkala, 367023, Russia

    T. I. Sharapudinov

Authors
  1. I. I. Sharapudinov
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  2. T. I. Sharapudinov
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Correspondence to I. I. Sharapudinov.

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Original Russian Text © I.I. Sharapudinov, T.I. Sharapudinov, 2017, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2017, No. 8, pp. 67–79.

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Sharapudinov, I.I., Sharapudinov, T.I. Polynomials orthogonal in the Sobolev sense, generated by Chebyshev polynomials orthogonal on a mesh. Russ Math. 61, 59–70 (2017). https://doi.org/10.3103/S1066369X17080072

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  • DOI: https://doi.org/10.3103/S1066369X17080072

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