ASYMPTOTICS OF ORTHOGONAL POLYNOMIALS VIA THE RIEMANN-HILBERT APPROACH

被引：10

作者：

Wong, R. ^{[1
]}

Zhao Yuqiu ^{[2
]}

机构：

[1] City Univ Hong Kong, Dept Math, Hong Kong, Hong Kong, Peoples R China

[2] Sun Yat Sen Univ, Dept Math, Guangzhou 510275, Guangdong, Peoples R China

来源：

ACTA MATHEMATICA SCIENTIA | 2009年 / 29卷 / 04期

基金：

中国国家自然科学基金;

关键词：

orthogonal polynomials; asymptotic methods; Riemann-Hilbert approach; MEIXNER-POLLACZEK POLYNOMIALS; LINEAR DIFFERENCE-EQUATIONS; UNIFORM ASYMPTOTICS; JACOBI-POLYNOMIALS; GLOBAL ASYMPTOTICS; KRAWTCHOUK POLYNOMIALS; LAGUERRE-POLYNOMIALS; EXPONENTIAL WEIGHTS; EXPANSIONS; RESPECT;

D O I：

10.1016/S0252-9602(09)60084-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this survey we give a brief introduction to orthogonal polynomials, including a short review of classical asymptotic methods. Then we turn to a discussion of the Riemann-Hilbert formulation of orthogonal polynomials, and the Deift & Zhou method of steepest descent. We illustrate this new approach, and a modified version, with the Hermite polynomials. Other recent progress of this method is also mentioned, including applications to discrete orthogonal polynomials, orthogonal polynomials on curves, multiple orthogonal polynomials, and certain orthogonal polynomials with singular behavior.

引用

页码：1005 / 1034

页数：30

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