数学物理学报(英文版) ›› 2017, Vol. 37 ›› Issue (5): 1483-1496.doi: 10.1016/S0252-9602(17)30086-3

• 论文 • 上一篇    下一篇

THE ENERGY FUNCTION WITH RESPECT TO THE ZEROS OF THE EXCEPTIONAL HERMITE POLYNOMIALS

Ágota P. HORVÁTH   

  1. Department of Analysis, Budapest University of Technology and Economics, Egry J. u1-3, Budapest, Hungary
  • 收稿日期:2015-10-08 修回日期:2016-10-20 出版日期:2017-10-25 发布日期:2017-10-25
  • 作者简介:Ágota P. HORV ÁTH,E-mail:g.horvath.agota@renyi.mta.hu
  • 基金资助:

    Supported by Hungarian National Foundation for Scientific Research, Grant No. K-100461.

THE ENERGY FUNCTION WITH RESPECT TO THE ZEROS OF THE EXCEPTIONAL HERMITE POLYNOMIALS

Ágota P. HORVÁTH   

  1. Department of Analysis, Budapest University of Technology and Economics, Egry J. u1-3, Budapest, Hungary
  • Received:2015-10-08 Revised:2016-10-20 Online:2017-10-25 Published:2017-10-25
  • Supported by:

    Supported by Hungarian National Foundation for Scientific Research, Grant No. K-100461.

摘要:

We examine the energy function with respect to the zeros of exceptional Hermite polynomials. The localization of the eigenvalues of the Hessian is given in the general case. In some special arrangements we have a more precise result on the behavior of the energy function. Finally we investigate the energy function with respect to the regular zeros of the exceptional Hermite polynomials.

关键词: exceptional Hermite polynomials, system of minimal energy, energy function, partitioned matrices

Abstract:

We examine the energy function with respect to the zeros of exceptional Hermite polynomials. The localization of the eigenvalues of the Hessian is given in the general case. In some special arrangements we have a more precise result on the behavior of the energy function. Finally we investigate the energy function with respect to the regular zeros of the exceptional Hermite polynomials.

Key words: exceptional Hermite polynomials, system of minimal energy, energy function, partitioned matrices