Acta Applicandae Mathematica

, Volume 94, Issue 2, pp 163–192

Asymptotics and Zeros of Sobolev Orthogonal Polynomials on Unbounded Supports

  • Francisco Marcellán
  • Juan José Moreno Balcázar
Article

DOI: 10.1007/s10440-006-9073-y

Cite this article as:
Marcellán, F. & Balcázar, J.J.M. Acta Appl Math (2006) 94: 163. doi:10.1007/s10440-006-9073-y

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.

Key words

Sobolev orthogonal polynomialsasymptoticszeros

Mathematics Subject Classifications (2000)

Primary 42C05Secondary 33C45

Copyright information

© Springer Science + Business Media B.V. 2006

Authors and Affiliations

  • Francisco Marcellán
    • 1
  • Juan José Moreno Balcázar
    • 2
    • 3
  1. 1.Departamento de MatemáticasUniversidad Carlos III de MadridLeganésSpain
  2. 2.Departamento de Estadística y Matemática AplicadaUniversidad de AlmeríaAlmeríaSpain
  3. 3.Instituto Carlos I de Física Teórica y ComputacionalUniversidad de GranadaGranadaSpain