Asymptotics for polynomials orthogonal over the unit disk with respect to a positive polynomial weight

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:372

Article

Mina-Diaz, Erwin

关键词: Orthogonal polynomials;    Asymptotic behavior;   

DOI  :  10.1016/j.jmaa.2010.03.042

来源: Elsevier

【 摘 要 】

We derive asymptotics for polynomials orthogonal over the complex unit disk with respect to a weight of the form vertical bar h(z)vertical bar(2), with h(z) a polynomial without zeros in vertical bar z vertical bar < 1. The behavior of the polynomials is established at every point of the complex plane. The proofs are based on adapting to the unit disk a technique of J. Szabados for the asymptotic analysis of polynomials orthogonal over the unit circle with respect to the same type of weight. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free