On a class of equilibrium problems in the real axis

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:235

Article; Proceedings Paper

Orive, Ramon¹  Garcia, Zebenzui² 

[1] Univ La Laguna, Dept Anal Matemat, Tenerife 38271, Canary Islands, Spain

[2] Univ La Laguna, Dept Econ Aplicada, Tenerife 38071, Canary Islands, Spain

关键词: Heine-Stieltjes polynomials;    Lame equation;    Equilibrium measures;    External fields;   

DOI  :  10.1016/j.cam.2010.05.027

来源: Elsevier

【 摘 要 】

In a series of seminal papers, Thomas J. Stieltjes (1856-1894) gave an elegant electrostatic interpretation for the zeros of classical families of orthogonal polynomials, such as Jacobi, Hermite and Laguerre polynomials. More generally, he extended this approach to the zeros of polynomial solutions of certain second-order linear differential equations (Lame equations), the so-called Heine-Stieltjes polynomials. In this paper, a class of electrostatic equilibrium problems in R, where the free unit charges x(1),..., x(n) is an element of R are in presence of a finite family of attractors (i.e., negative charges) z(1),..., z(m) is an element of C\R, is considered and its connection with certain class of Lame-type equations is shown. In addition, we study the situation when both n -> infinity and m -> infinity, by analyzing the corresponding (continuous) equilibrium problem in presence of a certain class of external fields. (C) 2010 Elsevier B.V. All rights reserved.

【 授权许可】

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