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 Sib. Èlektron. Mat. Izv., 2018, Volume 15, Pages 863–881 (Mi semr961)

Real, complex and functional analysis

Interpolation of analytic functions with finite number of special points by rational functions

A. G. Lipchinskij, V. N. Stolbova

a Tyumen State University, Volodarskogo st., 6, 625003, Tyumen, Russian Federation

Abstract: We consider an interpolation process for a class of functions having a finite number of singular points, using rational functions the poles of which coincide with the singular points of the interpolated function. Interpolation points form a triangular matrix where there is at least about one special point of the interpolated function having the limit of the ratio of the difference between the number of nodes of the $n$-th row associated with a singular point, and the corresponding n fraction multiplicity pole at this point to when $n$ is different from zero. The necessary and sufficient conditions of uniform convergence on any compact, which does not contain the singular points of the function; the sequence of interpolation fractions to the interpolated function were found, as well as other convergence conditions. Results on the interpolation of functions with a finite number of singular points by rational fractions and entire functions by polynomials are generalized.

Keywords: analytic function, singular point of a function, interpolation process, rational function, uniform convergence, convergence conditions.

DOI: https://doi.org/10.17377/semi.2018.15.074

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Document Type: Article
UDC: 517.53
MSC: 30E05
Received February 13, 2018, published August 15, 2018

Citation: A. G. Lipchinskij, V. N. Stolbov, “Interpolation of analytic functions with finite number of special points by rational functions”, Sib. Èlektron. Mat. Izv., 15 (2018), 863–881

Citation in format AMSBIB
\Bibitem{LipSto18} \by A.~G.~Lipchinskij, V.~N.~Stolbov \paper Interpolation of analytic functions with finite number of special points by rational functions \jour Sib. \Elektron. Mat. Izv. \yr 2018 \vol 15 \pages 863--881 \mathnet{http://mi.mathnet.ru/semr961} \crossref{https://doi.org/10.17377/semi.2018.15.074} `