TY - JOUR
T1 - Bernstein-Walsh inequalities and the exponential curve in ℂ2
AU - Coman, Dan
AU - Poletsky, Evgeny A.
PY - 2003/3
Y1 - 2003/3
N2 - 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)|.
AB - 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)|.
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U2 - 10.1090/S0002-9939-02-06571-1
DO - 10.1090/S0002-9939-02-06571-1
M3 - Article
AN - SCOPUS:0037374571
VL - 131
SP - 879
EP - 887
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
SN - 0002-9939
IS - 3
ER -