Abstract
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 language | English (US) |
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Pages (from-to) | 879-887 |
Number of pages | 9 |
Journal | Proceedings of the American Mathematical Society |
Volume | 131 |
Issue number | 3 |
DOIs | |
State | Published - Mar 2003 |
ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics