Spectrum Of A Class Of Infinite Dimensional Hamilton Operators

In this paper,the spectrum of a class of infinite dimensional Hamiltonian operators is studied and the characteristics of approximate point spectrum and essential spectrum are obtained.The paper is organized as follows. In Chapter 1,we briefly introduce the devel-opment of infinite dimensional Hamiltonian operators, In Chapter 2, the point spectrum of infinite dimensional Hamiltonian operators is divided into four parts, getting the suf-ficient and necessary condition of semmetry of each part of the point spectrum. Using structural characteristics of spectrum of infinite dimensional Hamiltonian operators, then the semmetry axis of the point spectrum is characterized by using the residual spectrum of internal elements. Some examples are constructed to illustrate the effectiveness of cri-terion. In Chapter 3, the approximate point spectrum and essential spectrum of a class of infinite dimensional Hamiltonian operators are studied. The spectrum of infinite dimen-sional Hamiltonian operators is characterized by using the spectrum of product of entries. In the end, some examples are constructed to illustrate the effectiveness of criterion.