Asymptotic behaviour of Verblunsky coefficients

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:324

Article

Alfaro, Maria Pilar ; Hernandez, Manuel Bello ; Montaner, Jesus Maria

关键词: orthogonal polynomials;    Verblunsky coefficients;   

DOI  :  10.1016/j.jmaa.2006.01.015

来源: Elsevier

【 摘 要 】

Let V(z) = Pi(m)(j=1)(z - xi(j)), xi(h) not equal xi(k), h not equal k and vertical bar xi(j)vertical bar = m, and consider the polynomials orthogonal with respect to vertical bar V vertical bar(2) d mu, psi(n)(vertical bar V vertical bar(2) d mu; z), where mu is a finite positive Borel measure on the unit circle with infinite points in its support, such that the reciprocal of its Szego function has an analytic extension beyond vertical bar z vertical bar < 1. In this paper we deduce the asymptotic behaviour of their Verblunsky coefficients. By means of this result, an asymptotic representation for these polynomials inside the unit circle is also obtained. (c) 2006 Elsevier Inc. All rights reserved.

【 授权许可】

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