Self-adjoint extensions for singular linear Hamiltonian systems

摘要

This paper is concerned with self-adjoint extensions for singular linear Hamiltonian systems. The domain of the closure of the corresponding minimal Hamiltonian operator is described by the properties of its elements at the endpoints of the discussed interval, and two different decompositions of the domain of the corresponding maximal Hamiltonian operator are provided. Based on them, complete and direct characterizations of all the self-adjoint extensions for a Hamiltonian system are obtained in terms of square integrable solutions. As a consequence, the characterizations of all the self-adjoint extensions are given for systems in the two special cases: the limit point case and limit circle case.