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Weak convergence of CD kernels and applications

Simon, Barry (2009) Weak convergence of CD kernels and applications. Duke Mathematical Journal, 146 (2). pp. 305-330. ISSN 0012-7094. http://resolver.caltech.edu/CaltechAUTHORS:SIMdmj09

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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 ∫ Ι(1/n)Kn(x, x)dμs → 0 for the singular part of dμ and ∫ Ι |ρE(x) − (w(x)/n)Kn(x, x)| dx → 0, where ρE is the density of the equilibrium measure and w(x) the density of dμ.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1215/00127094-2008-067DOIArticle
http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.dmj/123117094PublisherArticle
ORCID:
AuthorORCID
Simon, Barry0000-0003-2561-8539
Additional Information:© 2009 Duke University Press. Received 19 December 2007. Revision received 1 May 2008; publication date 1 February 2009. It is a pleasure to thank Jonathan Breuer, Yoram Last, and especially Vilmos Totik for useful conversations. I also thank Ehud de Shalit and Yoram Last for the hospitality of the Einstein Institute of Mathematics of the Hebrew University during part of the preparation of this article.
Funders:
Funding AgencyGrant Number
NSFDMS-0140592
Binational Science Foundation (USA-Israel)2002068
Subject Keywords:Orthogonal polynomials; unit-circle; paraorthogonal polynomials; zeros; asymptotics; quadrature; intervals; operators; matrices
Issue or Number:2
Record Number:CaltechAUTHORS:SIMdmj09
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:SIMdmj09
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:13478
Collection:CaltechAUTHORS
Deposited By: Jason Perez
Deposited On:23 Apr 2009 18:59
Last Modified:01 May 2017 22:50

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