Limits of zeros of orthogonal polynomials on the circle | Zendy

Simon Barry | Zendy; Totik Vilmos | Zendy

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Limits of zeros of orthogonal polynomials on the circle

Author(s) -

Simon Barry,

Totik Vilmos

Publication year - 2005

Publication title -

mathematische nachrichten

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.913

H-Index - 50

eISSN - 1522-2616

pISSN - 0025-584X

DOI - 10.1002/mana.200410326

Subject(s) - mathematics , subsequence , unit disk , unit circle , limit (mathematics) , measure (data warehouse) , unit (ring theory) , combinatorics , polynomial , extension (predicate logic) , longest increasing subsequence , distribution (mathematics) , probability measure , discrete mathematics , pure mathematics , mathematical analysis , mathematics education , database , computer science , bounded function , programming language

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. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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