Approximation by rational functions in complex regions

Name: Approximation by rational functions in complex regions
Creator: Levin, A. L.
Keywords: Polynomials and rational functions of one complex variable, 0103 physical sciences, 0101 mathematics, Approximation in the complex plane, 01 natural sciences

Levin, A. L.

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Article . 1971 . Peer-reviewed

License: Springer TDM

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Article . 1971

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https://dx.doi.org/10.1007/bf0...

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Approximation by rational functions in complex regions

descriptionPublicationkeyboard_double_arrow_right Article 01 Feb 1971 English Publisher:Springer Science and Business Media LLCJournal:Mathematical Notes of the Academy of Sciences of the USSR, volume 9, pages 72-77 (issn: 0001-4346, eissn: 1573-8876,

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Authors: Levin, A. L.;

doi: 10.1007/bf01316983

Approximation by rational functions in complex regions

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Abstract

Approximation by rational functions Rn (z) (in the C and Lp metrics) on plane compacta is investigated. The possibility is studied of the coincidence of rational and polynomial approximations for all n, and some functions are described for which this coincidence holds. Approximations on finite sets of points are investigated, and an explanation is given of why there are functions which cannot be approximated by rational functions of degree not higher than n (in the C metric).

Related Organizations

Lomonosov Moscow State University
Russian Federation

Keywords

Polynomials and rational functions of one complex variable, Approximation in the complex plane

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