Dynamical systems with boundary control: models and characterization of inverse data

An abstract version of the BC method is proposed as a chapter of the linear system theory dealing with dynamical systems with boundary control (DSBCs). A characterization of the response operator of DSBCs is given; a set of models (realizations) of DSBCs determined by the response operator is presented. As an application, a conditional existence theorem characterizing the dynamical Dirichlet-to-Neumann map of the Riemannian manifold is obtained. An abstract analogue of the Gelfand-Levitan-Krein-Marchenko equations is derived.