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Fine structure of the zeros of orthogonal polynomials, I. A tale of two pictures

Simon, Barry (2006) Fine structure of the zeros of orthogonal polynomials, I. A tale of two pictures. Electronic Transactions on Numerical Analysis, 25 . pp. 328-368. ISSN 1068-9613. https://resolver.caltech.edu/CaltechAUTHORS:SIMetna06

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Abstract

Mhaskar-Saff found a kind of universal behavior for the bulk structure of the zeros of orthogonal polynomials for large n. Motivated by two plots, we look at the finer structure for the case of the Verblunsky coefficients and for what we call the BLS condition: αn = Cb^n + O ((bΔ)^n). In the former case, we describe the results of Stoiciu. In the latter case, we prove asymptotically equal spacing for the bulk of zeros.


Item Type:Article
Related URLs:
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http://www.emis.de/journals/ETNA/volumes/2001-2010/vol25/abstract_vol25_pp328-368.html?vol=25&pages=328-368PublisherArticle
ORCID:
AuthorORCID
Simon, Barry0000-0003-2561-8539
Additional Information:© 2006, Kent State University Received April 20, 2005. Accepted for publication August 23, 2005. Recommended by I. Pritsker. Supported in part by NSF grant DMS-0140592. Electronic Transactions on Numerical Analysis, Volume 25 (2006) - Special Volume on Constructive Function Theory. Dedicated to Ed Saff on the occasion of his 60th birthday. This special volume of ETNA contains selected papers presented at Constructive Functions Tech-04, a conference held at the Georgia Institute of Technology, Atlanta, November 7–9, 2004. The conference honored the sixtieth birthday of Edward B. Saff, and the twentieth anniversary of the international journal Constructive Approximation, which he founded together with Ronald DeVore. [This paper is based on the plenary talk given by Professor Barry Simon.]
Funders:
Funding AgencyGrant Number
NSFDMS-0140592
Subject Keywords:OPUC, clock behavior, Poisson zeros, orthogonal polynomials
Classification Code:AMS subject classifications 42C05, 30C15, 60G55
Record Number:CaltechAUTHORS:SIMetna06
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:SIMetna06
Alternative URL:http://etna.mcs.kent.edu/vol.25.2006/pp328-368.dir/pp328-368.html
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:8433
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:03 Aug 2007
Last Modified:02 Oct 2019 23:51

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