On the zeros of orthogonal polynomials on the unit circle

JOURNAL OF APPROXIMATION THEORY

卷:170

Article; Proceedings Paper

Pilar Alfaro, Maria¹  Bello-Hernandez, Manuel²  Maria Montaner, Jesus³ 

[1] Univ Zaragoza, Dept Matemat, E-50009 Zaragoza, Spain

[2] Univ La Rioja, Dpto Matemat & Computac, Logrono 26004, Spain

[3] Univ Zaragoza, Dept Matemat Aplicada, Zaragoza 50018, Spain

关键词: Orthogonal polynomials;    Zeros;    Asymptotics;   

DOI  :  10.1016/j.jat.2012.07.006

来源: Elsevier

【 摘 要 】

Let {z(n)} be a sequence in the unit disk {z is an element of C: vertical bar z vertical bar < 1}. It is known that there exists a unique positive Borel measure on the unit circle such that their orthogonal polynomials {Phi(n)} satisfy Phi(n) (z(n)) = 0 for each n = 1, 2, .... Characteristics of the orthogonality measure and asymptotic properties of the orthogonal polynomials are given in terms of the asymptotic behavior of the sequence {z(n)}. Particular attention is paid to periodic sequences of zeros {z(n)} with periods two and three. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free