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Riemann-Hilbert Analysis for Orthogonal Polynomials

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Orthogonal Polynomials and Special Functions

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1817))

Abstract

This is an introduction to the asymptotic analysis of orthogonal polynomials based on the steepest descent method for Riemann-Hilbert problems of Deift and Zhou. We consider in detail the polynomials that are orthogonal with respect to the modified Jacobi weight (1-x)α(1+x)β h(x) on [-1,1] where α, β > -1 and h is real analytic and positive on [-1,1]. These notes are based on joint work with Kenneth McLaughlin, Walter Van Assche and Maarten Vanlessen.

The author’s research was supported in part by FWO research project G.0176.02, INTAS project 2000-272, and by the Ministry of Science and Technology (MCYT) of Spain and the European Regional Development Fund (ERDF) through the grant BFM2001-3878-C02-02.

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Authors and Affiliations

  1. Department of Mathematics, Katholieke Universiteit Leuven, Celestijnenlaan 200 B, 3001, Leuven, Belgium

    Arno B.J. Kuijlaars

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  1. Arno B.J. Kuijlaars
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Editor information

Editors and Affiliations

  1. Afd.Toegepaste Wiskundige Analyse, EWI-TWA,Technische Universiteit Delft, Postbus 5031, 2600, GA Delft, Netherlands

    Erik Koelink

  2. Departement Wiskunde, Katholieke Universiteit Leuven, Celestijnenlaan 200B, 3001, Leuven, Belgium

    Walter Van Assche

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Kuijlaars, A.B. (2003). Riemann-Hilbert Analysis for Orthogonal Polynomials. In: Koelink, E., Van Assche, W. (eds) Orthogonal Polynomials and Special Functions. Lecture Notes in Mathematics, vol 1817. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44945-0_5

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  • DOI: https://doi.org/10.1007/3-540-44945-0_5

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  • Print ISBN: 978-3-540-40375-3

  • Online ISBN: 978-3-540-44945-4

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