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.References
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- Ch. Pommerenke, On the derivative of a polynomial, Michigan Math. J. 6 (1959), 373–375. MR 109208, DOI 10.1307/mmj/1028998284
- Paul Erdős, Some of my favourite unsolved problems, A tribute to Paul Erdős, Cambridge Univ. Press, Cambridge, 1990, pp. 467–478. MR 1117038
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