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Asymptotics of polynomials orthogonal with respect to varying measures

✍ Scribed by Guillermo López Lagomasino

Publisher
Springer
Year
1989
Tongue
English
Weight
801 KB
Volume
5
Category
Article
ISSN
0176-4276

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In this paper we review a connection of orthogonal polynomials with respect to varying weights to weighted approximation, multipoint Pad6 approximation and to some questions of theoretical physics. (~) 1998 Elsevier Science B.V. All rights reserved.

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We consider asymptotics of orthogonal polynomials with respect to weights w(x)dx = e -Q(x) dx on the real line, where Q(x) = ∑ 2m k=0 q k x k , q 2m > 0, denotes a polynomial of even order with positive leading coefficient. The orthogonal polynomial problem is formulated as a Riemann-Hilbert problem