Completeness of the System of Root Vectors of Upper Triangular Infinite Dimensional Hamiltonian Operators Appearing in Elasticity Theory

WANG Hua; Alatancang; HUANG Jun-jie

doi:10.3879/j.issn.1000-0887.2012.03.010

Volume 33 Issue 3

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WANG Hua, Alatancang, HUANG Jun-jie. Completeness of the System of Root Vectors of Upper Triangular Infinite Dimensional Hamiltonian Operators Appearing in Elasticity Theory[J]. Applied Mathematics and Mechanics, 2012, 33(3): 366-378. doi: 10.3879/j.issn.1000-0887.2012.03.010

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Completeness of the System of Root Vectors of Upper Triangular Infinite Dimensional Hamiltonian Operators Appearing in Elasticity Theory

doi: 10.3879/j.issn.1000-0887.2012.03.010

¹School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, P.R.China;²College of Sciences, Inner Mongolia University of Technology, Hohhot 010051, P.R.China

Received Date: 2011-05-04
Rev Recd Date: 2011-12-22
Publish Date: 2012-03-15

Abstract

Abstract

A class of upper triangular infinite dimensional Hamiltonian operators appearing in elasticity theory was dealt with. The geometric multiplicity and algebraic index of the eigenvalue were investigated, then further the algebraic multiplicity of the eigenvalue was obtained. Based on these properties,the concrete completeness formulation of the system of eigen or root vectors of the Hamiltonian operator was proposed. It is shown that this completeness is determined by the system of eigenvectors of its operator entries. Finally, some illustrating applications from elasticity theory are presented.
- upper triangular infinite dimensional Hamiltonian operator,
- eigenvector,
- root vector,
- multiplicity,
- completeness

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References(15)

References

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