Weighted polynomials and weighted pluripotential theory

Author:
Thomas Bloom

Journal:
Trans. Amer. Math. Soc. **361** (2009), 2163-2179

MSC (2000):
Primary 32U20, 32U35

DOI:
https://doi.org/10.1090/S0002-9947-08-04607-2

Published electronically:
November 14, 2008

MathSciNet review:
2465832

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let be a compact subset of and an admissible weight function on . To we associate a canonical circular set . We obtain precise relations between the weighted pluricomplex Green function and weighted equilibrium measure of and the pluricomplex Green function and equilibrium measure of . 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 .

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Additional Information

**Thomas Bloom**

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

Email:
bloom@math.utoronto.ca

DOI:
https://doi.org/10.1090/S0002-9947-08-04607-2

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.