Spectrum Of Diagonal Inifinite-Dimensional Anti-Hamiltonian Operators

In this thesis,the spectrum of diagonal infinite-dimensional anti-Hamiltonian operators is studied.The meticulous characteristics of its point spectrum are given,and the sufficient and necessary condition is obtained for the point spectrum on the real line.In chapter 1,we mainly introduce the research background and research progress of infinite-dimensional Hamiltonian operators.In chapter 2,four types of point spectrum and two types of residual spectrum of diagonal infinite-dimensional anti-Hamiltonian operators are described.Then the symmetry of the point spectrum of the operators with respect to real line is characterized by using the spectrum of its entries.In chapter 3,by discussing the ?(A,A*)and ?(A*,A),the point spectrum of diagonal infinite-dimensional anti-Hamiltonian operators is divided into five disjoint subsets,and the sufficient and necessary condition is studied for the point spectrum on the real line.