Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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}$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 32U20, 32U35

Retrieve articles in all journals with MSC (2000): 32U20, 32U35


Additional Information

Thomas Bloom
Affiliation: Department of Mathematics, University of Toronto, Toronto, Ontario, Canada M5S 3G3
Email: bloom@math.utoronto.ca

DOI: http://dx.doi.org/10.1090/S0002-9947-08-04607-2
PII: S 0002-9947(08)04607-2
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.