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
![]() |
PDF
- Submitted Version
See Usage Policy. 146kB |
Use this Persistent URL to link to this item: https://resolver.caltech.edu/CaltechAUTHORS:20170408-133653793
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: |
| ||||||||||||
ORCID: |
| ||||||||||||
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: |
| ||||||||||||
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 |
Repository Staff Only: item control page