Invertibility And Fredholmness Of Symplectic Symmetric Hamiltonian Operators

The symplectic symmetric Hamiltonian operator plays an important role in solving some Hamiltonian systems with definite solution conditions,so it is necessary to study the properties of symplectic symmetric Hamiltonian operators.In this thesis,the invert-ibility,generalized invertibility and Fredholmness of symplectic symmetric Hamiltonian operators are studied.The first chapter is the introduction,which briefly introduces the research background of symplectic symmetric Hamiltonian operators.In the second chap-ter,we first describe the invertibility of symplectic symmetric Hamiltonian operators by using the structural properties of symplectic symmetric Hamiltonian operators and the relatively bounded perturbation theory.Secondly,some sufficient conditions for symplec-tic symmetric Hamiltonian operators to have bounded generalized inverse are obtained by the generalized inverse perturbation of the operator entries.The third chapter discusses the characterization of Fredholmness of symplectic symmetric Hamiltonian operators.