Asymptotics of orthogonal polynomials via the Riemann-Hilbert approach

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

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Detail(s)

Original languageEnglish
Pages (from-to)1005-1034
Journal / PublicationActa Mathematica Scientia
Volume29
Issue number4
Publication statusPublished - Jul 2009

Abstract

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. © 2009 Wuhan Institute of Physics and Mathematics.

Research Area(s)

  • 33C45, 41A60, 42C05, asymptotic methods, orthogonal polynomials, Riemann-Hilbert approach

Citation Format(s)

Asymptotics of orthogonal polynomials via the Riemann-Hilbert approach. / Wong, R.; Yuqiu, Zhao.
In: Acta Mathematica Scientia, Vol. 29, No. 4, 07.2009, p. 1005-1034.

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review