Asymptotics and zeros of Sobolev orthogonal polynomials on unbounded supports

Francisco Marcellan, Juan Jose Moreno-Balcazar

Published 2006-04-04, updated 2007-06-15Version 2

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 are focused in the study of the asymptotic behaviour of such polynomials as well as in the distribution of their zeros. Some open problems as well as some new directions for a future research are formulated.