Bernstein-Walsh inequalities and the exponential curve in ℂ2

Dan Coman; Evgeny A. Poletsky

doi:10.1090/S0002-9939-02-06571-1

Bernstein-Walsh inequalities and the exponential curve in ℂ²

Dan Coman, Evgeny A. Poletsky

Department of Mathematics

Research output: Contribution to journal › Article

8 Scopus citations

Abstract

It is shown that for the pluripolar set K = {(z, e^z): |z| ≤ 1} in ℂ² there is a global Bernstein-Walsh inequality: If P is a polynomial of degree n on ℂ² and |P| ≤ 1 on K, this inequality gives an upper bound for |P(z, w)| which grows like exp(1/2n² log n). The result is used to obtain sharp estimates for |P(z, e^z)|.

Original language	English (US)
Pages (from-to)	879-887
Number of pages	9
Journal	Proceedings of the American Mathematical Society
Volume	131
Issue number	3
DOIs	https://doi.org/10.1090/S0002-9939-02-06571-1
State	Published - Mar 1 2003

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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Coman, D., & Poletsky, E. A. (2003). Bernstein-Walsh inequalities and the exponential curve in ℂ². Proceedings of the American Mathematical Society, 131(3), 879-887. https://doi.org/10.1090/S0002-9939-02-06571-1

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