|
Archivo Abierto Institucional de la Universidad Carlos III de Madrid >
Investigación >
Departamentos >
Departamento de Matemáticas >
Grupo de Análisis Matemático Aplicado (GAMA) >
DM - GAMA - Artículos de Revistas >
Please use this identifier to cite or link to this item:
http://hdl.handle.net/10016/5921
|
| Title: | Electrostatic models for zeros of polynomials: Old, new, and some open problems |
| Author(s): | Marcellán, Francisco
Martínez-Finkelshtein, Andrei
Martínez-González, P. |
| Publisher: | Elsevier |
| Issued date: | 15-Oct-2007 |
| Citation: | Journal of Computational and Applied Mathematics, 2007, vol. 207, n. 2, p. 258-272 |
| URI: | http://hdl.handle.net/10016/5921 |
| ISSN: | 0377-0427 |
| DOI: | 10.1016/j.cam.2006.10.020 |
| Description: | 15 pages, 2 figures.-- MSC2000 codes: Primary, 30C15; Secondary, 34C10; 33C45; 42C05; 82B23.
MR#: MR2345246 (2008h:33017)
Zbl#: Zbl 1131.30002 |
| 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 degree of the polynomials tends to infinity. The leading role is played by the differential equation satisfied by these polynomials. Some new developments, applications and open problems are presented. |
| 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 |
| Rights: | © Elsevier |
| Appears in Collections: | DM - GAMA - Artículos de Revistas
|
Items in E-Archivo are protected by copyright, with all rights reserved, unless otherwise indicated.
|
