Boundary Control method and De Branges spaces. Schrödinger equation, Dirac system and Discrete Schrödinger operator
In the framework of the application of the Boundary Control method to solving the inverse dynamical problems for the one-dimensional Schrödinger and Dirac operators on the half-line and semi-infinite discrete Schrödinger operator, we establish the connections with the method of De Branges: for each of the system we construct the De Branges space and give a natural dynamical interpretation of all its ingredients: the set of function the De Brange space consists of, the scalar product, the reproducing kernel.
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