Completeness Of Generalized Eigenfunction Systems For Two Types Of Hamiltonian Operator Family

Using division with remainder of matrix polynomials and structural features of unbounded Hamiltonian operator,the plate bending problems arising from elasticity and two kinds of un-bounded Hamiltonian operator families are considered,the eigenvalues and the corresponding generalized eigenfunctions of those two kinds of unbounded Hamiltonian operators are calculat-ed,and the properties generalized eigenfunctions are studied.The completeness of the eigen-functions is proved in the sense of Cauchy principal value.This method is also extended to a class of 4th PDEs with constant coefficients,and the completeness theorem is obtained,and the general solutions of two kinds of Hamiltonian systems are given.