, Volume 94, Issue 2, pp 163-192
Date: 05 Oct 2006

Asymptotics and Zeros of Sobolev Orthogonal Polynomials on Unbounded Supports

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Abstract

In this paper we present a survey about analytic properties of polynomials orthogonal with respect to a weighted Sobolev inner product such that the vector of measures has an unbounded support. In particular, we focus on the asymptotic behaviour of such polynomials as well as in the distribution of their zeros. Some open problems as well as some directions for future research are formulated.

Research of Francisco Marcellán was partially supported by Dirección General de Investigación (Ministerio de Ciencia y Tecnología) of Spain under grant BFM2003-06335-C03-02 and INTAS Research Network NeCCA INTAS 03-51-6637.
Research of Juan José Moreno Balcázar was partially supported by Ministerio de Educación y Ciencia of Spain under grant MTM2005-08648-C02-01 and Junta de Andalucía (FQM 229 and FQM 481).