Email this article An extremal problem for the derivative of a rational function
- Authors: Dubinin V.N.1,2
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Affiliations:
- Far-Eastern Federal University
- Institute for Applied Mathematics, Far-Eastern Branch
- Issue: Vol 100, No 5-6 (2016)
- Pages: 714-719
- Section: Article
- URL: https://journals.rcsi.science/0001-4346/article/view/149847
- DOI: https://doi.org/10.1134/S0001434616110079
- ID: 149847
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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.
About the authors
V. N. Dubinin
Far-Eastern Federal University; Institute for Applied Mathematics, Far-Eastern Branch
Author for correspondence.
Email: dubinin@iam.dvo.ru
Russian Federation, Vladivostok; Vladivostok
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