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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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An extremal problem for polynomials
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by A. Erëmenko and L. Lempert PDF
Proc. Amer. Math. Soc. 122 (1994), 191-193 Request permission

Abstract:

Let $f(z) = {z^n} + \cdots$ be a polynomial such that the level set $E = \{ z:|f(z)| \leq 1\}$ is connected. Then $\max \{ |f’ (z)|:z \in E\} \leq {2^{(1/n) - 1}}{n^2}$, and this estimate is the best possible.
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Additional Information
  • © Copyright 1994 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 122 (1994), 191-193
  • MSC: Primary 30C10
  • DOI: https://doi.org/10.1090/S0002-9939-1994-1207536-1
  • MathSciNet review: 1207536