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Interpolation of analytic functions with finitely many singularities

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Abstract

We consider an interpolation process for the class of functions with finitely many singular points by means of rational functions whose poles coincide with the singular points of the function under interpolation. The interpolation nodes form a triangular matrix. We find necessary and sufficient conditions for the uniform convergence of sequences of interpolation fractions to the function under interpolation on every compact set disjoint from the singular points of the function and other conditions for convergence. We generalize and improve the familiar results on the interpolation of functions with finitely many singular points by rational fractions and of entire functions by polynomials.

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Authors and Affiliations

  1. P. P. Ershov Ishim State Pedagogical Institute, Ishim, Tyumen’ Region, Russia

    A. G. Lipchinskiĭ

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  1. A. G. Lipchinskiĭ
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Correspondence to A. G. Lipchinskiĭ.

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Original Russian Text Copyright © 2012 Lipchinskiĭ A.G.

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Ishim. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 53, No. 5, pp. 1027–1047, September–October, 2012.

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Lipchinskiĭ, A.G. Interpolation of analytic functions with finitely many singularities. Sib Math J 53, 821–838 (2012). https://doi.org/10.1134/S0037446612050084

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  • DOI: https://doi.org/10.1134/S0037446612050084

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