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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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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Bernstein–Walsh inequalities and the exponential curve in $\mathbb {C}^2$
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by Dan Coman and Evgeny A. Poletsky PDF
Proc. Amer. Math. Soc. 131 (2003), 879-887 Request permission

Abstract:

It is shown that for the pluripolar set $K=\{(z,e^z): |z|\leq 1\}$ in ${\Bbb C}^2$ there is a global Bernstein–Walsh inequality: If $P$ is a polynomial of degree $n$ on ${\Bbb C}^2$ and $|P|\leq 1$ on $K$, this inequality gives an upper bound for $|P(z,w)|$ which grows like $\exp (\frac 12n^2\log n)$. The result is used to obtain sharp estimates for $|P(z,e^z)|$.
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Additional Information
  • Dan Coman
  • Affiliation: Department of Mathematics, Syracuse University, Syracuse, New York 13244-1150
  • MR Author ID: 325057
  • Email: dcoman@syr.edu
  • Evgeny A. Poletsky
  • Affiliation: Department of Mathematics, Syracuse University, Syracuse, New York 13244-1150
  • MR Author ID: 197859
  • Email: eapolets@syr.edu
  • Received by editor(s): June 8, 2001
  • Received by editor(s) in revised form: October 18, 2001
  • Published electronically: June 12, 2002
  • Additional Notes: The second author was partially supported by NSF Grant DMS-9804755
  • Communicated by: Juha M. Heinonen
  • © Copyright 2002 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 131 (2003), 879-887
  • MSC (2000): Primary 41A17; Secondary 30D15, 30D20
  • DOI: https://doi.org/10.1090/S0002-9939-02-06571-1
  • MathSciNet review: 1937426