The Essential Spectrum Of The Infinite Dimensional Hamiltonian Operators And Symmetry

In this thesis, we mainly study the essential spectrum and symmetry of the essential spectrum of infinite dimensional Hamiltonian operators, and give a characterization of the essential spectrum and weyl spectrum of a class of infinite dimensional Hamiltonian operators.On essential spectrum, we mainly discuss the essential spectrum of the infinite dimensional Hamiltonian operators. According to Frobenius-Schur factorization of operators matrix, we obtain a necessary and sufficient condition, which is to judge a complex number whether belonging to the essential spectrum. At the same time, some examples also have been constructed to show the correctness and effectiveness of results. On symmetry of essential spectrum, we obtain a necessary and sufficient condition about the symmetry of essential spectrum with respect to real axis. Secondly, we find a characterization about essential spectrum and weyl spectrum of a class of triangular infinite dimensional Hamiltionian operators. Finally, specific examples are given to illustrate the effectiveness of the above conclusions.