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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

An extremal problem for polynomials


Authors: A. Erëmenko and L. Lempert
Journal: Proc. Amer. Math. Soc. 122 (1994), 191-193
MSC: Primary 30C10
MathSciNet review: 1207536
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Abstract: Let $ f(z) = {z^n} + \cdots $ be a polynomial such that the level set $ E = \{ z:\vert f(z)\vert \leq 1\} $ is connected. Then $ \max \{ \vert f' (z)\vert:z \in E\} \leq {2^{(1/n) - 1}}{n^2}$, and this estimate is the best possible.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1994-1207536-1
PII: S 0002-9939(1994)1207536-1
Keywords: Polynomial, Chebyshev polynomials
Article copyright: © Copyright 1994 American Mathematical Society