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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Complex equilibrium measure and Bernstein type theorems for compact sets in $ {\bf R}\sp n$


Author: Mirosław Baran
Journal: Proc. Amer. Math. Soc. 123 (1995), 485-494
MSC: Primary 31C10; Secondary 32F05, 32F07
MathSciNet review: 1219719
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Abstract: The aim of this paper is to refine and develop further some results from a paper of Bedford and Taylor [Trans. Amer. Math. Soc. 294 (1986), 705-717]. The main result, a Bernstein type theorem, is an improvement of the classical Bernstein inequality

$\displaystyle \vert p'(x)\vert \leq (\deg p){(1 - {x^2})^{ - 1/2}}{(\left\Vert p \right\Vert _{[ - 1,1]}^2 - {p^2}(x))^{1/2}},$

from the interval $ [ - 1,1]$ to the multivariate case.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1219719-6
PII: S 0002-9939(1995)1219719-6
Keywords: Plurisubharmonic function, Monge-Ampere operator, Bernstein inequality
Article copyright: © Copyright 1995 American Mathematical Society