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Orthogonal polynomials with respect to varying weights

โœ Scribed by Vilmos Totik


Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
652 KB
Volume
99
Category
Article
ISSN
0377-0427

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โœฆ Synopsis


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) = โˆ‘ 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