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Limits of zeros of orthogonal polynomials on the circle

Simon, Barry and Totik, Vilmos (2005) Limits of zeros of orthogonal polynomials on the circle. Mathematische Nachrichten, 278 (12-13). pp. 1615-1620. ISSN 1522-2616. doi:10.1002/mana.200410326. https://resolver.caltech.edu/CaltechAUTHORS:20170408-133653793

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Abstract

We prove that there is a universal measure on the unit circle such that any probability measure on the unit disk is the limit distribution of some subsequence of the corresponding orthogonal polynomials. This follows from an extension of a result of Alfaro and Vigil (which answered a question of P. Turán): namely, for n < N , one can freely prescribe the n -th polynomial and N – n zeros of the N -th one. We shall also describe all possible limit sets of zeros within the unit disk.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1002/mana.200410326DOIArticle
http://onlinelibrary.wiley.com/doi/10.1002/mana.200410326/abstractPublisherArticle
https://arxiv.org/abs/math/0404535arXivDiscussion Paper
ORCID:
AuthorORCID
Simon, Barry0000-0003-2561-8539
Additional Information:© 2005 WILEY-VCH. Received 8 April 2004, accepted 9 August 2004. Published online 8 September 2005. Dedicated to the memory of F. V. Atkinson. Acknowledgements The first named author was supported in part by NSF grant DMS-0140592 and the second named author was supported by NSF grant DMS-0097484 and by OTKA T/034323, TS44782.
Funders:
Funding AgencyGrant Number
NSFDMS-0140592
NSFDMS-0097484
Hungarian Scientific Research Fund (OTKA)T/034323
Hungarian Scientific Research Fund (OTKA)TS44782
Subject Keywords:Orthogonal polynomials, unit circle, zeros, density of zeros, universal measure, degree theory
Issue or Number:12-13
Classification Code:MSC (2000) 42C05
DOI:10.1002/mana.200410326
Record Number:CaltechAUTHORS:20170408-133653793
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170408-133653793
Official Citation:Simon, B. and Totik, V. (2005), Limits of zeros of orthogonal polynomials on the circle. Math. Nachr., 278: 1615–1620. doi:10.1002/mana.200410326
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:75867
Collection:CaltechAUTHORS
Deposited By: 1Science Import
Deposited On:13 Apr 2017 20:02
Last Modified:15 Nov 2021 16:55

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