On The Completeness Of Eigenfunction Systems Of Infinite Dimensional Hamiltonian Operators

In this thesis, we study the completeness of eigenfunction systems of a class of opera-tor matrices under different orthogonality, and their connections are given. These results have certain importance in investigating the completeness of the function systems and expanding the types of complete function systems. Further, we study the completeness of the eigenfunction systems of a class of infinite dimensional Hamiltonian operators derived from the partial differential equations leading to Sturm-Liouville problems. In addition, we research the essential spectrum of two kinds of infinite dimensional Hamiltonian op-erators, and some necessary and sufficient conditions are given.