Weighted polynomials and weighted pluripotential theory
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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 $\mathbb {R}^{N}$.References
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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
- 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.
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2465832