Acta mathematica scientia,Series B ›› 2017, Vol. 37 ›› Issue (5): 1483-1496.doi: 10.1016/S0252-9602(17)30086-3

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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.

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

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