ASYMPTOTICS OF ORTHOGONAL POLYNOMIALS VIA THE RIEMANN-HILBERT APPROACH  

作　　者：R．Wong 赵育求 

机构地区：[1]Department of Mathematics, City University of Hong Kong, Hong Kong, China [2]Department of Mathematics, Sun Yat-Sen University, Guangzhou 510275, China

出　　处：《Acta Mathematica Scientia》2009年第4期1005-1034,共30页数学物理学报（B辑英文版）

基　　金：supported in part by the National Natural Science Foundation of China (10471154 and 10871212)

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 Delft ＆ 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.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 Delft ＆ 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.

关 键 词：orthogonal polynomials asymptotic methods Riemann-Hilbert approach 

分 类 号：O174.41[理学—数学] O11[理学—基础数学]