Abstract
In this paper, a discontinuous non-self-adjoint (dissipative) Dirac operator with eigenparameter dependent boundary condition, and with two singular endpoints is studied. The interface conditions are imposed on the discontinuous point. Firstly, we pass the considered problem to a maximal dissipative operator Lh by using operator theoretic formulation. The self-adjoint dilation Th of Lh in the space H is constructed, furthermore, the incoming and outgoing representations of Th and functional model are also constructed, hence in light of Lax–Phillips theory, we derive the scattering matrix. Using the equivalence between scattering matrix and characteristic function, completeness theorem on the eigenvectors and associated vectors of this dissipative operator is proved.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
