Completing Invertible Infinite Dimensional Hamiltonian Operator

This paper investigates invertibility of a class of non-self-adjoint operator that is infinite dimension Hamiltonian operator which is discovered when we extend Fourier method. First, the conditions for partial matrix car completing invertible infinite dimension Hamiltonian operator with one entry of its inverse are specified and all solution of the problem are obtained; Then,the conditions for partial matrix can completing invertible infinite dimension Hamiltonian operator and all solution of the problem are obtained.