Bernstein-Walsh inequalities and the exponential curve in ℂ2

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8 Scopus citations


It is shown that for the pluripolar set K = {(z, ez): |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, ez)|.

Original languageEnglish (US)
Pages (from-to)879-887
Number of pages9
JournalProceedings of the American Mathematical Society
Issue number3
StatePublished - Mar 2003

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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