Title: The Riemann-Hilbert approach to strong asymptotics for orthogonal polynomials on [-1,1]
Authors: Kuijlaars, Arno ×
Mclaughlin, KTR
Van Assche, Walter
Vanlessen, Maarten #
Issue Date: 2004
Publisher: Academic press inc elsevier science
Series Title: Advances in mathematics vol:188 issue:2 pages:337-398
Abstract: We consider polynomials that are orthogonal on [-1,1] with respect to a modified Jacobi weight (1-x)^alpha (1+x)^beta h(x), with alpha, beta > - 1 and h real analytic and strictly positive on [-1,1]. We obtain full asymptotic expansions for the monic and orthonormal polynomials outside the interval [-1,1], for the recurrence coefficients and for the leading coefficients of the orthonormal polynomials. We also deduce asymptotic behavior for the Hankel determinants and for the monic orthogonal polynomials on the interval [-1,1]. For the asymptotic analysis we use the steepest descent technique for Riemann-Hilbert problems developed by Deift and Zhou, and applied to orthogonal polynomials on the real line by Deift, Kriecherbauer, McLaughlin, Venakides, and Zhou. In the steepest descent method we will use the Szego function associated with the weight and for the local analysis around the endpoints +/-1 we use Bessel functions of appropriate order, whereas Deift et al. use Airy functions.
ISSN: 0001-8708
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Analysis Section
× corresponding author
# (joint) last author

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