Electrostatic models for zeros of polynomials: Old, new, and some open problems

Marcellán Español, Francisco José; Martínez-Finkelshtein, Andrei; Martínez-González, P.

e-Archivo Home
→
Investigación
→
Departamentos
→
Departamento de Matemáticas
→
Grupo de Análisis Matemático Aplicado (GAMA)
→
DM - GAMA - Artículos de Revistas
→
View Item

Electrostatic models for zeros of polynomials: Old, new, and some open problems

Author(s): Marcellán Español, Francisco José; Martínez-Finkelshtein, Andrei; Martínez-González, P.

Publisher: Elsevier

Issued date: 2007-10-15

Citation: Journal of Computational and Applied Mathematics, 2007, vol. 207, n. 2, p. 258-272

ISSN: 0377-0427

DOI: 10.1016/j.cam.2006.10.020

Sponsor: This research was supported, in part, by a grant of Dirección General de Investigación (Ministerio de Ciencia y Tecnología) of Spain, project code BFM2003-06335-C03-02 (FM), a grant from the Ministry of Education and Science of Spain, project code MTM2005-08648-C02-01 (AMF, PMG), by Junta de Andalucía, Grupo de Investigación FQM 0229 (AMF, PMG), by “Research Network on Constructive Complex Approximation (NeCCA)”, INTAS 03-51-6637 (FM, AMF), and by NATO Collaborative Linkage Grant “Orthogonal Polynomials: Theory, Applications and Generalizations”, ref. PST.CLG.979738 (FM, AMF).

Review: PeerReviewed

Publisher version: http://dx.doi.org/10.1016/j.cam.2006.10.020

Keywords: Second order differential equation , Orthogonal polynomials , Zeros , Asymptotics , Electrostatic model , Logarithmic potential

URI: http://hdl.handle.net/10016/5921

Rights: © Elsevier

Abstract:

We give a survey concerning both very classical and recent results on the electrostatic interpretation of the zeros of some well-known families of polynomials, and the interplay between these models and the asymptotic distribution of their zeros when the degre [+]