Acta mathematica scientia,Series A ›› 2011, Vol. 31 ›› Issue (5): 1266-1272.

• Articles • Previous Articles     Next Articles

Algebraic Index of Eigenvalues of Infinite-dimensional Hamiltonian Operators

 WANG Hua1,2, Alatancang1, HUANG Jun-jie1*   

  1. 1.School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021;
    2.College of Sciences, Inner Mongolia University of Technology, Hohhot 010051
  • Received:2009-11-14 Revised:2011-08-23 Online:2011-10-25 Published:2011-10-25
  • Contact: HUANG Jun-jie,hjjwh@sina.com E-mail:hjjwh@sina.com
  • Supported by:

    国家自然科学基金(10962004, 11061019)、高等学校博士学科点专项科研基金(20070126002)、教育部留学回国人员科研启动基金、教育部`春晖计划'项目(Z2009-1-01010)和内蒙古自然科学基金(2009BS0101, 2010MS0110)资助

Abstract:

This paper deals with the algebraic index of eigenvalues of infinite-dimensional Hamiltonian operators with at least one diagonal elements to be invertible. Based on certain properties of their eigenvalues and eigenvectors, it is  obtained that the algebraic index of eigenvalue  of a class of infinite-dimensional Hamiltonian operators  is 1 or 2. Moreover, some applications are presented to illustrate these results.

Key words: Infinite-dimensional Hamiltonian operator, Eigenvalue problem, Algebraic index

CLC Number: 

  • 47A75
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