Symmetry of the Point Spectrum of Infinite Dimensional Hamiltonian Operators and Its Applications  

作　　者：Hua WANG Alatancang Jun-jie HUANG 

机构地区：[1]School of Mathematical Sciences,Inner Mongolia University,Hohhot 010021,China [2]College of Sciences,Inner Mongolia University of Technology,Hohhot 010051,China

出　　处：《Acta Mathematicae Applicatae Sinica》2012年第1期149-156,共8页应用数学学报（英文版）

基　　金：Supported by the National Natural Science Foundation of China (No. 11061019, 10962004, 11101200);the Chunhui Program of Ministry of Education of China (No. Z2009-1-01010);the Natural Science Foundation of Inner Mongolia (No. 2010MS0110, 2009BS0101);the Cultivation of Innovative Talent of ‘211 Project’ of Inner Mongolia University

摘　　要：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） U σp1 （-A＊）. Using the characteristic of the set σp1（-A＊）, we divide the point spectrum σp （d） 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.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） U σp1 （-A＊）. Using the characteristic of the set σp1（-A＊）, we divide the point spectrum σp （d） 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.

关 键 词：infinite dimensional Hamiltonian operator point spectrum SYMMETRY thin plate on elasticfoundation plane elasticity problem harmonic equation 

分 类 号：O175.3[理学—数学] O177.1[理学—基础数学]