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Dal'nevostochnyi Matematicheskii Zhurnal, 2011, Volume 11, Number 1, Pages 28–36 (Mi dvmg208)  
This article is cited in 2 scientific papers (total in 2 papers)

On the distortion theorems for algebraic polynomials

V. N. Dubinin

Institute of Applied Mathematics, Far-Eastern Branch of the Russian Academy of Sciences
Full-text PDF (218 kB) Citations (2)
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Abstract: The applications of a boundary Schwarz lemma and the properties of the condenser capacity to some inequalities for polynomials and their derivatives are considered. We prove a new Bernstein-type inequality for the polynomials on a circle, two-sided estimates for the polynomials with constraints on their critical values, and two-sided estimates of the average distortion computed at zeros of the polynomials.
Key words: polynomials, critical points, critical values, Chebyshev polynomial, Bernstein-type inequality, distortion theorem, condenser capacity.
Received: 23.03.2011
Bibliographic databases:
Document Type: Article
UDC: 512.62, 517.54
MSC: Primary 30C10; Secondary 30C75
Language: Russian
Citation: V. N. Dubinin, “On the distortion theorems for algebraic polynomials”, Dal'nevost. Mat. Zh., 11:1 (2011), 28–36
Citation in format AMSBIB
\Bibitem{Dub11}
\by V.~N.~Dubinin
\paper On the distortion theorems for algebraic polynomials
\jour Dal'nevost. Mat. Zh.
\yr 2011
\vol 11
\issue 1
\pages 28--36
\mathnet{http://mi.mathnet.ru/dvmg208}
\elib{https://elibrary.ru/item.asp?id=16214054}
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  • https://www.mathnet.ru/eng/dvmg208
  • https://www.mathnet.ru/eng/dvmg/v11/i1/p28
    • This publication is cited in the following 2 articles:
    1. V. N. Dubinin, “Methods of geometric function theory in classical and modern problems for polynomials”, Russian Math. Surveys, 67:4 (2012), 599–684  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    2. S. I. Kalmykov, “Comparison of discrete and uniform norms of polynomials on a segment and a circle arc”, J. Math. Sci. (N. Y.), 193:1 (2013), 100–105  mathnet  crossref  mathscinet
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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