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EXTREMAL POLYNOMIALS ON DISCRETE SETS

Published online by Cambridge University Press:  01 July 1999

A. B. J. KUIJLAARS  and
W. VAN ASSCHE
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Abstract

We study asymptotics for orthogonal polynomials and other extremal polynomials on infinite discrete sets, typical examples being the Meixner polynomials and the Charlier polynomials. Following ideas of Rakhmanov, Dragnev and Saff, weshow that the asymptotic behaviour is governed by a constrained extremal energy problem for logarithmic potentials, which can be solved explicitly. We give formulas for the contracted zero distributions, the $n$th root asymptotics and the asymptotics of the largest zeros.

Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 79 , Issue 1 , July 1999 , pp. 191 - 221
Copyright
London Mathematical Society 1999

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