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An extremal problem for the derivative of a rational function

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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.

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Authors and Affiliations

  1. Far-Eastern Federal University, Vladivostok, Russia

    V. N. Dubinin

  2. Institute for Applied Mathematics, Far-Eastern Branch, Russian Academy of Sciences, Vladivostok, Russia

    V. N. Dubinin

Authors
  1. V. N. Dubinin
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Correspondence to V. N. Dubinin.

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Original Russian Text © V. N. Dubinin, 2016, published in Matematicheskie Zametki, 2016, Vol. 100, No. 5, pp. 732–738.

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Dubinin, V.N. An extremal problem for the derivative of a rational function. Math Notes 100, 714–719 (2016). https://doi.org/10.1134/S0001434616110079

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  • DOI: https://doi.org/10.1134/S0001434616110079

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