An extremal problem for the derivative of a rational function |
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Authors: | V N Dubinin |
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Institution: | 1.Far-Eastern Federal University,Vladivostok,Russia;2.Institute for Applied Mathematics, Far-Eastern Branch,Russian Academy of Sciences,Vladivostok,Russia |
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Abstract: | Erd?s’ 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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