Orthogonal trigonometric polynomials: Riemann-Hilbert analysis and relations with OPUC

被引：3

作者：

Du, Zhihua ^{[1
]}

Du, Jinyuan ^{[2
]}

机构：

[1] Jinan Univ, Dept Math, Guangzhou 510632, Guangdong, Peoples R China

[2] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Peoples R China

来源：

ASYMPTOTIC ANALYSIS | 2012年 / 79卷 / 1-2期

关键词：

orthogonal trigonometric polynomials; Riemann-Hilbert approach; orthogonal polynomials on the unit circle; Christoffel-Darboux; recurrence; zeros; CMV MATRICES; JACOBI; ASYMPTOTICS;

D O I：

10.3233/ASY-2012-1096

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the theory of orthogonal trigonometric polynomials (OTPs). We obtain asymptotics of OTPs with positive and analytic weight functions by Riemann-Hilbert approach and find that they have relations with orthogonal polynomials on the unit circle (OPUC). By the relations and the theory of OPUC, we also get four-terms recurrent formulae, Christoffel-Darboux formula and some algebraic and asymptotic properties of zeros for orthogonal trigonometric polynomials.

引用

页码：87 / 132

页数：46

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