Completeness of system of root vectors of upper triangular infinite-dimensional Hamiltonian operators appearing in elasticity theory |
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Authors: | Hua Wang Alatancang Jun-jie Huang |
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Institution: | 1. School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, P. R. China;College of Science, Inner Mongolia University of Technology, Hohhot 010051, P. R. China 2. School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, P. R. China |
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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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Keywords: | upper triangular infinite-dimensional Hamiltonian operator eigenvector root vector multiplicity completeness |
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