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

作　　者：王华 阿拉坦仓 黄俊杰 

机构地区：[1]School of Mathematical Sciences,Inner Mongolia University [2]College of Sciences,Inner Mongolia University of Technology

出　　处：《Applied Mathematics and Mechanics(English Edition)》2012年第3期385-398,共14页应用数学和力学（英文版）

基　　金：supported by the National Natural Science Foundation of China (Nos. 11061019,10962004,11101200,and 11026175);the Chunhui Program of Ministry of Education of China (No. Z2009-1-01010);the Natural Science Foundation of Inner Mongolia of China (No. 2010MS0110);the Cultivation of Innovative Talent of "211 Project" of Inner Mongolia University

摘　　要：This paper deals with a class of upper triangular infinite-dimensional Hamilto- nian 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.This paper deals with a class of upper triangular infinite-dimensional Hamilto- nian 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.

关 键 词：upper triangular infinite-dimensional Hamiltonian operator EIGENVECTOR root vector MULTIPLICITY COMPLETENESS 

分 类 号：O177[理学—数学]