Sibirskii Matematicheskii Zhurnal
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Sibirsk. Mat. Zh.:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

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
Full-text PDF (316 kB) Citations (1)
References:
PDF
HTML
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
\Bibitem{Lip15}
\by A.~G.~Lipchinski{\v\i}
\paper Convergence conditions for interpolation rational fractions with finitely many poles
\jour Sibirsk. Mat. Zh.
\yr 2015
\vol 56
\issue 3
\pages 557--572
\mathnet{http://mi.mathnet.ru/smj2660}
\crossref{https://doi.org/10.17377/smzh.2015.56.308}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3442802}
\elib{https://elibrary.ru/item.asp?id=24795706}
\transl
\jour Siberian Math. J.
\yr 2015
\vol 56
\issue 3
\pages 442--454
\crossref{https://doi.org/10.1134/S0037446615030088}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000356826600008}
\elib{https://elibrary.ru/item.asp?id=23984651}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84934928915}
Linking options:
  • https://www.mathnet.ru/eng/smj2660
  • https://www.mathnet.ru/eng/smj/v56/i3/p557
    • This publication is cited in the following 1 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
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024