一类Hamilton 算子的重数和完备性及其应用

Abstract

Abstract:

In this paper, we consider the multiplicity of the eigenvalue and the completeness of the eigen and root vector system
of a class of Hamiltonian operators. The geometric multiplicity, algebraic index and algebraic multiplicity of each eigenvalue is completely determined. Based on the above properties and the symplectic orthogonality of the associated eigen and root vectors, the necessary and sufficient condition for the eigen or root vector system to be complete is obtained. Moreover, the obtained results are tested for several problems, for example, the plate bending, plane elasticity, Stokes flow.

Key words: Hamiltonian operator, Eigenvalue problem, Eigenvector, Root vector, Multiplicity Completeness

CLC Number:

47A70

WANG Hua, Alatanchang, HUANG Jun-Jie. Multiplicity and Completeness of a Class of |Hamiltonian |Operators and Its Applications[J].Acta mathematica scientia,Series A, 2014, 34(6): 1507-1517.

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Multiplicity and Completeness of a Class of |Hamiltonian |Operators and Its Applications

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