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Applied Mathematics and Mechanics (English Edition) ›› 2012, Vol. 33 ›› Issue (3): 385-398.doi: https://doi.org/10.1007/s10483-012-1558-x

• 论文 • 上一篇    

Completeness of system of root vectors of upper triangular infinitedimensional Hamiltonian operators appearing in elasticity theory

王华1,2 ALATANCANG1 黄俊杰1   

  1. 1. School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, P. R. China;
    2. College of Sciences, Inner Mongolia University of Technology, Hohhot 010051, P. R. China
  • 收稿日期:2011-05-04 修回日期:2011-11-22 出版日期:2012-03-02 发布日期:2012-03-01

Completeness of system of root vectors of upper triangular infinitedimensional Hamiltonian operators appearing in elasticity theory

 WANG Hua1,2, ALATANCANG1, HUANG Jun-Jie1   

  1. 1. School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, P. R. China;
    2. College of Sciences, Inner Mongolia University of Technology, Hohhot 010051, P. R. China
  • Received:2011-05-04 Revised:2011-11-22 Online:2012-03-02 Published:2012-03-01

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被引次数

42

摘要： This paper deals with a class of upper triangular infinite-dimensional Hamiltonian operators appearing in the elasticity theory. The geometric multiplicity and algebraic index of the eigenvalue are investigated. Furthermore, the algebraic multiplicity of the eigenvalue is obtained. Based on these properties, the concrete completeness formulation of the system of eigenvectors or root vectors of the Hamiltonian operator is proposed. It is shown that the completeness is determined by the system of eigenvectors of the operator entries. Finally, the applications of the results to some problems in the elasticity theory are presented.

Abstract: This paper deals with a class of upper triangular infinite-dimensional Hamiltonian operators appearing in the elasticity theory. The geometric multiplicity and algebraic index of the eigenvalue are investigated. Furthermore, the algebraic multiplicity of the eigenvalue is obtained. Based on these properties, the concrete completeness formulation of the system of eigenvectors or root vectors of the Hamiltonian operator is proposed. It is shown that the completeness is determined by the system of eigenvectors of the operator entries. Finally, the applications of the results to some problems in the elasticity theory are presented.

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