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Matematicheskie Zametki, 2016, Volume 100, Issue 5, Pages 732–738
DOI: https://doi.org/10.4213/mzm11354 (Mi mzm11354) 		 
This article is cited in 7 scientific papers (total in 7 papers)

An Extremal Problem for the Derivative of a Rational Function

V. N. Dubininab

a Far Eastern Federal University, Vladivostok
b Institute for Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences, Vladivostok
Full-text PDF (475 kB) Citations (7)
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DOI: https://doi.org/10.4213/mzm11354
Abstract: Erdős' well-known problem on the maximum absolute value of the derivative of a polynomial on a connected lemniscate is extended to the case of a rational function. Moreover, under the assumption that certain lemniscates are connected, a sharp upper bound for the absolute value of the derivative of a rational function at any point in the plane different from the poles is found. The role of the extremal function is played by an appropriate Zolotarev fraction.
Keywords: rational function, Zolotarev fraction, lemniscate, Riemann surface, symmetrization.
Funding agency Grant number
Russian Science Foundation 14-11-00022
This work was supported by the Russian Science Foundation under grant no. 14-11-00022.
Received: 21.04.2016
English version:
Mathematical Notes, 2016, Volume 100, Issue 5, Pages 714–719
DOI: https://doi.org/10.1134/S0001434616110079
Bibliographic databases:
Document Type: Article
UDC: 517.54
Language: Russian
Citation: V. N. Dubinin, “An Extremal Problem for the Derivative of a Rational Function”, Mat. Zametki, 100:5 (2016), 732–738; Math. Notes, 100:5 (2016), 714–719
Citation in format AMSBIB
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    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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