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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Weighted polynomials and weighted pluripotential theory

Author: Thomas Bloom
Journal: Trans. Amer. Math. Soc. 361 (2009), 2163-2179
MSC (2000): Primary 32U20, 32U35
Published electronically: November 14, 2008
MathSciNet review: 2465832
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Abstract: Let $ E$ be a compact subset of $ \mathbb{C} ^{N}$ and $ w\ge 0$ an admissible weight function on $ E$. To $ (E, w)$ we associate a canonical circular set $ Z\subset \mathbb{C} ^{N+1}$. We obtain precise relations between the weighted pluricomplex Green function and weighted equilibrium measure of $ (E, w)$ and the pluricomplex Green function and equilibrium measure of $ Z$. These results, combined with an appropriate form of the Bernstein-Markov inequality, are used to obtain asymptotic formulas for the leading coefficients of orthonormal polynomials with respect to certain exponentially decreasing weights in $ \mathbb{R}^{N}$.

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Additional Information

Thomas Bloom
Affiliation: Department of Mathematics, University of Toronto, Toronto, Ontario, Canada M5S 3G3

Received by editor(s): September 15, 2006
Received by editor(s) in revised form: May 30, 2007
Published electronically: November 14, 2008
Additional Notes: The author was supported by an NSERC of Canada Grant.
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.