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Sbornik: Mathematics, 2006, Volume 197, Issue 4, Pages 505–524
DOI: https://doi.org/10.1070/SM2006v197n04ABEH003768
(Mi sm1184)
 

This article is cited in 21 scientific papers (total in 21 papers)

Estimates of derivatives of simplest fractions and other questions

V. I. Danchenko

Vladimir State University
References:
Abstract: The approximation properties of simplest fractions (s.f.'s), that is, of the logarithmic derivatives of complex polynomials, have recently become a subject of intensive research. These properties of s.f.'s prove to have many similarities with those of polynomials. For instance, one has for them analogues of Mergelyan's and Jackson's classical results on uniform polynomial approximation. In connection with approximation by s.f.'s estimates of the Markov–Bernstein kind for derivatives of s.f.'s on various subsets of the complex plane arouse interest. Such estimates are obtained in this paper on circles, straight lines and their intervals, and some applications of these estimates are indicated. Several other questions relating to approximation properties of s.f.'s are also considered.
Bibliography: 28 titles.
Received: 23.08.2005
Bibliographic databases:
UDC: 517.53
MSC: 41A20, 41A17
Language: English
Original paper language: Russian
Citation: V. I. Danchenko, “Estimates of derivatives of simplest fractions and other questions”, Sb. Math., 197:4 (2006), 505–524
Citation in format AMSBIB
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\by V.~I.~Danchenko
\paper Estimates of derivatives of simplest fractions and other questions
\jour Sb. Math.
\yr 2006
\vol 197
\issue 4
\pages 505--524
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Linking options:
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  • https://doi.org/10.1070/SM2006v197n04ABEH003768
  • https://www.mathnet.ru/eng/sm/v197/i4/p33
  • This publication is cited in the following 21 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математический сборник Sbornik: Mathematics
    Statistics & downloads:
    Abstract page:901
    Russian version PDF:279
    English version PDF:21
    References:67
    First page:4
     
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