Limits of Zeros of Orthogonal Polynomials on the Circle

2004/04/29 by Barry Simon, Simon, Barry, Vilmos Totik +2 · 1 citation
Mathematics · #42C05 #Analytic Number Theory Research #Analytic and geometric function theory #FOS: Mathematics #Mathematical functions and polynomials #Spectral Theory (math.SP) #math.SP #msc:42C05

paper · pdf · doi:10.48550/arxiv.math/0404535

arxiv created 2004/04/29 · openalex publication_date 2004/04/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 Turán): namely, for n

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