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Sibirskii Matematicheskii Zhurnal, 2015, Volume 56, Number 3, Pages 557–572
DOI: https://doi.org/10.17377/smzh.2015.56.308 (Mi smj2660) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Convergence conditions for interpolation rational fractions with finitely many poles

A. G. Lipchinskiĭ

Ishim State Pedagogical Institute, Ishim, Russia
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DOI: https://doi.org/10.17377/smzh.2015.56.308
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 the sequence 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: 15.04.2014
English version:
Siberian Mathematical Journal, 2015, Volume 56, Issue 3, Pages 442–454
DOI: https://doi.org/10.1134/S0037446615030088
Bibliographic databases:
Document Type: Article
UDC: 517.53
Language: Russian
Citation: A. G. Lipchinskiǐ, “Convergence conditions for interpolation rational fractions with finitely many poles”, Sibirsk. Mat. Zh., 56:3 (2015), 557–572; Siberian Math. J., 56:3 (2015), 442–454
Citation in format AMSBIB
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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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    		Сибирский математический журнал Siberian Mathematical Journal
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