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Sibirskii Matematicheskii Zhurnal, 2012, Volume 53, Number 5, Pages 1027–1047 (Mi smj2328)  

This article is cited in 2 scientific papers (total in 2 papers)

Interpolation of analytic functions with finitely many singularities

A. G. Lipchinskiĭ

P. P. Ershov Ishim State Pedagogical Institute, Ishim, Tyumen reg.
Full-text PDF (356 kB) Citations (2)
References:
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.
Keywords: analytic function, singularity of a function, interpolation process, rational fraction, uniform convergence, convergence conditions.
Received: 12.04.2011
English version:
Siberian Mathematical Journal, 2012, Volume 53, Issue 5, Pages 821–838
DOI: https://doi.org/10.1134/S0037446612050084
Bibliographic databases:
Document Type: Article
UDC: 517.53
Language: Russian
Citation: A. G. Lipchinskiǐ, “Interpolation of analytic functions with finitely many singularities”, Sibirsk. Mat. Zh., 53:5 (2012), 1027–1047; Siberian Math. J., 53:5 (2012), 821–838
Citation in format AMSBIB
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\paper Interpolation of analytic functions with finitely many singularities
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\pages 1027--1047
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  • https://www.mathnet.ru/eng/smj/v53/i5/p1027
  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Сибирский математический журнал Siberian Mathematical Journal
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    Abstract page:257
    Full-text PDF :88
    References:49
    First page:1
     
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