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Algebra i Analiz, 2007, Volume 19, Issue 2, Pages 122–130 (Mi aa116)  
This article is cited in 9 scientific papers (total in 9 papers)

Research Papers

Estimates for derivatives of rational functions and the fourth Zolotarev problem

A. L. Lukashovab

a Saratov State University named after N. G. Chernyshevsky
b Department of Mathematics, Fatih University, Istanbul, Turkey
Full-text PDF (141 kB) Citations (9)
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Abstract: An estimate is obtained for the derivatives of real rational functions that map a compact set on the real line to another set of the same kind. Many well-known inequalities (due to Bernstein, Bernstein—Szegö, V. S. Videnskii, V. N. Rusak, and M. Baran–V. Totik) are particular cases of this estimate. It is shown that the estimate is sharp. With the help of the solution of the fourth Zolotarev problem, a class of examples is constructed in which the estimates obtained turn into identities.
Keywords: Estimates of derivatives, optimal filter, Zolotarev problems.
Received: 11.10.2006
English version:
St. Petersburg Mathematical Journal, 2008, Volume 19, Issue 2, Pages 253–259
DOI: https://doi.org/10.1090/S1061-0022-08-00997-7
Bibliographic databases:
Document Type: Article
MSC: Primary 53A04; Secondary 52A40, 52A10
Language: Russian
Citation: A. L. Lukashov, “Estimates for derivatives of rational functions and the fourth Zolotarev problem”, Algebra i Analiz, 19:2 (2007), 122–130; St. Petersburg Math. J., 19:2 (2008), 253–259
Citation in format AMSBIB
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\by A.~L.~Lukashov
\paper Estimates for derivatives of rational functions and the fourth Zolotarev problem
\jour Algebra i Analiz
\yr 2007
\vol 19
\issue 2
\pages 122--130
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\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2333900}
\zmath{https://zbmath.org/?q=an:1181.26032}
\transl
\jour St. Petersburg Math. J.
\yr 2008
\vol 19
\issue 2
\pages 253--259
\crossref{https://doi.org/10.1090/S1061-0022-08-00997-7}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000267653200007}
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  • https://www.mathnet.ru/eng/aa/v19/i2/p122
    • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Алгебра и анализ St. Petersburg Mathematical Journal
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    References:62
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