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Limits of zeros of orthogonal polynomials on the circle

✍ Scribed by Barry Simon; Vilmos Totik

Publisher
John Wiley and Sons
Year
2005
Tongue
English
Weight
127 KB
Volume
278
Category
Article
ISSN
0025-584X

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✦ Synopsis

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. TurΓ‘n): 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. (Β© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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