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Keldysh Institute preprints, 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


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.

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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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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. I. Aptekarev, A. I. Bogolyubskii, M. Yattselev, “Convergence of ray sequences of Frobenius-Padé approximants”, Sb. Math., 208:3 (2017), 313–334  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
  • Препринты Института прикладной математики им. М. В. Келдыша РАН
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