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1 February 2009 Weak convergence of CD kernels and applications
Barry Simon
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Duke Math. J. 146(2): 305-330 (1 February 2009). DOI: 10.1215/00127094-2008-067

Abstract

We prove a general result on equality of the weak limits of the zero counting measure, dνn, of orthogonal polynomials (defined by a measure dμ) and (1/n)Kn(x,x)dμ(x). By combining this with the asymptotic upper bounds of Máté and Nevai [16] and Totik [33] on nλn(x), we prove some general results on I(1/n)Kn(x,x)dμs0 for the singular part of dμ and I|ρE(x)(w(x)/n)Kn(x,x)|dx0, where ρE is the density of the equilibrium measure and w(x) the density of dμ

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Barry Simon. "Weak convergence of CD kernels and applications." Duke Math. J. 146 (2) 305 - 330, 1 February 2009. https://doi.org/10.1215/00127094-2008-067

Information

Published: 1 February 2009
First available in Project Euclid: 5 January 2009

zbMATH: 1158.33003
MathSciNet: MR2477763
Digital Object Identifier: 10.1215/00127094-2008-067

Subjects:
Primary: 33C45
Secondary: 05E35 , 60B10

Rights: Copyright © 2009 Duke University Press

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Vol.146 • No. 2 • 1 February 2009
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