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Daghestan Electronic Mathematical Reports, 2016, Issue 5, Pages 56–75 (Mi demr25)  

Polynomials, orthogonal on Sobolev, derived by the Chebyshev polynomials, orthogonal on the uniform net

I. I. Sharapudinovabc, T. I. Sharapudinovac

a Daghestan Scientific Centre of RAS
b Daghestan State Pedagogical University
c Southern Mathematical Institute of the Vladikavkaz Scientific Center of the RAS

Abstract: In this article we consider the problem of constructing polynomials, orthogonal in Sobolev sence on the finite uniform net and associated with classical Chebyshev polynomials of discrete variable. We have found an explicit expression of these polynomials by classical Chebyshev polynomials. Also we have obtained an expansion of new polynomials by generalized powers of Newton 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.

Keywords: Polynomials orthogonal in Sobolev sence, Chebyshev polynomials orthogonal on the grid, approximation of discrete functions, mixed series of Chebyshev polynomials orthogonal on a uniform grid

DOI: https://doi.org/10.31029/demr.5.6

Full text: PDF file (453 kB)
Full text: http://mathreports.ru/.../polinomy-ortogonalnye-po-sobolevu-porozhdennye-mnogochlenami-chebysheva-ortogonalnymi-na-ravnomernoy
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UDC: 517.956.4
Received: 07.04.2016
Revised: 07.06.2016
Accepted:08.06.2016
Language:

Citation: I. I. Sharapudinov, T. I. Sharapudinov, “Polynomials, orthogonal on Sobolev, derived by the Chebyshev polynomials, orthogonal on the uniform net”, Daghestan Electronic Mathematical Reports, 2016, no. 5, 56–75

Citation in format AMSBIB
\Bibitem{ShaSha16}
\by I.~I.~Sharapudinov, T.~I.~Sharapudinov
\paper Polynomials, orthogonal on Sobolev, derived by the Chebyshev polynomials, orthogonal on the uniform net
\jour Daghestan Electronic Mathematical Reports
\yr 2016
\issue 5
\pages 56--75
\mathnet{http://mi.mathnet.ru/demr25}
\crossref{https://doi.org/10.31029/demr.5.6}
\elib{http://elibrary.ru/item.asp?id=https://elibrary.ru/item.asp?id=29412581}


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