One Description Of The Spectrum For A Class Of The Indefinite Dimensional Hamiltonian Operator

The spectrum of the linear operators is a important part of modern functional anal-ysis, which is meaningful in theory research and applications. In this thesis, we mainlystudy the spectrum of the infinite dimensional Hamiltonian operator, and give a completedescription of the spectrum of this class of operators. First of all, we study the pointspectrum,the continuous spectrum and the residual spectrum of the infinite dimensionalHamiltonian operator with diagonal domain, and give a description about them, using theentries operators of the infinite dimensional Hamiltonian operator. Secondly, we firstlystudy the essential spectrum of the infinite dimensional Hamiltonian operator, and obtaina necessary and sufficient condition of the essential spectrum of the infinite dimensionalHamiltonian operator.