The authors investigate the completeness of the system of eigen or root vectors of the 2×2 upper triangular infinite-dimensional Hamiltonian operator H 0.First,the geometrical multiplicity and the algebraic index...The authors investigate the completeness of the system of eigen or root vectors of the 2×2 upper triangular infinite-dimensional Hamiltonian operator H 0.First,the geometrical multiplicity and the algebraic index of the eigenvalue of H0 are considered.Next,some necessary and sufficient conditions for the completeness of the system of eigen or root vectors of H0 are obtained.Finally,the obtained results are tested in several examples.展开更多
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. Fur...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.展开更多
基金supported by the National Natural Science Foundation of China (Nos. 10962004, 11061019)the Specialized Research Fund for the Doctoral Program of Higher Education of China (No. 20070126002)+1 种基金the Chunhui Program of the Ministry of Education of China (No. Z2009-1-01010)the Natural Science Foundation of Inner Mongolia (Nos. 2009BS0101, 2010MS0110)
文摘The authors investigate the completeness of the system of eigen or root vectors of the 2×2 upper triangular infinite-dimensional Hamiltonian operator H 0.First,the geometrical multiplicity and the algebraic index of the eigenvalue of H0 are considered.Next,some necessary and sufficient conditions for the completeness of the system of eigen or root vectors of H0 are obtained.Finally,the obtained results are tested in several examples.
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)+1 种基金the Natural Science Foundation of Inner Mongolia of China (No. 2010MS0110)the Cultivation of Innovative Talent of "211 Project" of Inner Mongolia University
文摘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.
