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Preprints of the Keldysh Institute of Applied Mathematics, 2014, 103, 16 pp. (Mi ipmp1955)  

This article is cited in 1 scientific paper (total in 1 paper)

Matrix Riemann–Hilbert problems for Pade approximants of orthogonal expansions

A. I. Aptekarev, A. I. Bogolyubsky
Full-text PDF (207 kB) Citations (1)
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Abstract: The Markov-type functions generated by measures given on some interval are considered. We are constructing the Pade approximants of orthogonal expansions for their Fourier series expansion by orthogonal polynomials on some other interval. Besides, we are studying both types of such constructions: linear Frobenius–Pade approximants and nonlinear Fourier–Pade ones. We have obtained two main new results in this paper: complete set of orthogonality relations for Fourier–Pade approximants denominators, and also equivalent reformulation of the problems concerning Pade–Fourier approximants of orthogonal expansions in terms of matrix Riemann–Hilbert problems.
Keywords: Pade–Chebyshev approximants, Pade approximants of orthogonal expansions, orthogonal polynomials, Markov-type functions, matrix Riemann–Hilbert problem.
Document Type: Preprint
Language: Russian
Citation: A. I. Aptekarev, A. I. Bogolyubsky, “Matrix Riemann–Hilbert problems for Pade approximants of orthogonal expansions”, Keldysh Institute preprints, 2014, 103, 16 pp.
Citation in format AMSBIB
\Bibitem{AptBog14}
\by A.~I.~Aptekarev, A.~I.~Bogolyubsky
\paper Matrix Riemann--Hilbert problems for Pade approximants of orthogonal expansions
\jour Keldysh Institute preprints
\yr 2014
\papernumber 103
\totalpages 16
\mathnet{http://mi.mathnet.ru/ipmp1955}
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  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Препринты Института прикладной математики им. М. В. Келдыша РАН
     
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