The boundary control method and de Branges spaces. Schrödinger equation, Dirac system and discrete Schrödinger operator

We establish the relationship between the Boundary Control method for dynamic inverse problems and the method of de Branges on the examples of dynamical systems for Schrödinger and Dirac operators on a half-line and semi-infinite discrete Schrödinger operator. For each of the system we construct the de Branges space and describe in natural dynamic terms its attributes: the set of function the space consists of, the scalar product, the reproducing kernel.