Acta Mathematicae Applicatae Sinica, English Series 2012, Vol. 28 Issue (1) :149-156    DOI: 10.1007/s10255-012-0130-1
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Symmetry of the Point Spectrum of Infinite Dimensional Hamiltonian Operators and Its Applications
Hua WANG1,2, Alatancang1, Jun-jie HUANG1
1. School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China;
2. College of Sciences, Inner Mongolia University of Technology, Hohhot 010051, China
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Abstract This paper studies the symmetry, with respect to the real axis, of the point spectrum of the upper triangular infinite dimensional Hamiltonian operator H. Note that the point spectrum of H can be described as σp(H) = σp(A)∪σp1(-A*). Using the characteristic of the set σp1(-A*), we divide the point spectrum σp(A) of A into three disjoint parts. Then, a necessary and sufficient condition is obtained under which σp1(-A*) and one part of σp(A) are symmetric with respect to the real axis each other. Based on this result, the symmetry of σp(H) is completely given. Moreover, the above result is applied to thin plates on elastic foundation, plane elasticity problems and harmonic equations.
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Keywordsinfinite dimensional Hamiltonian operator   point spectrum   symmetry   thin plate on elastic foundation   plane elasticity problem   harmonic equation
Abstract： This paper studies the symmetry, with respect to the real axis, of the point spectrum of the upper triangular infinite dimensional Hamiltonian operator H. Note that the point spectrum of H can be described as σp(H) = σp(A)∪σp1(-A*). Using the characteristic of the set σp1(-A*), we divide the point spectrum σp(A) of A into three disjoint parts. Then, a necessary and sufficient condition is obtained under which σp1(-A*) and one part of σp(A) are symmetric with respect to the real axis each other. Based on this result, the symmetry of σp(H) is completely given. Moreover, the above result is applied to thin plates on elastic foundation, plane elasticity problems and harmonic equations.