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Fine structure of the zeros of orthogonal polynomials III: Periodic recursion coefficients

Simon, Barry (2006) Fine structure of the zeros of orthogonal polynomials III: Periodic recursion coefficients. Communications on Pure and Applied Mathematics, 59 (7). pp. 1042-1062. ISSN 0010-3640. https://resolver.caltech.edu/CaltechAUTHORS:20170711-080502782

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Abstract

We discuss asymptotics of the zeros of orthogonal polynomials on the real line and on the unit circle when the recursion coefficients are periodic. The zeros on or near the absolutely continuous spectrum have a clock structure with spacings inverse to the density of zeros. Zeros away from the a.c. spectrum have limit points mod p and only finitely many of them.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1002/cpa.20106DOIArticle
http://onlinelibrary.wiley.com/doi/10.1002/cpa.20106/abstractPublisherArticle
https://arxiv.org/abs/math/0412336arXivDiscussion Paper
ORCID:
AuthorORCID
Simon, Barry0000-0003-2561-8539
Additional Information:© 2005 Wiley Periodicals, Inc. Issue online: 25 Apr 2006. Version of Record online: 5 Oct 2005. Manuscript Received: Dec 2004. This work was partially supported by NSF Grant DMS-0140592. It is a pleasure to thank Chuck Newman and Percy Deift for the hospitality of the Courant Institute, where some of this work was done.
Funders:
Funding AgencyGrant Number
NSFDMS-0140592
Courant InstituteUNSPECIFIED
Issue or Number:7
Record Number:CaltechAUTHORS:20170711-080502782
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170711-080502782
Official Citation:Simon, B. (2006), Fine structure of the zeros of orthogonal polynomials III: Periodic recursion coefficients. Comm. Pure Appl. Math., 59: 1042–1062. doi: 10.1002/cpa.20106
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:78927
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:11 Jul 2017 22:10
Last Modified:03 Oct 2019 18:13

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