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In the framework of the application of the Boundary Control method to solvingthe inverse dynamical problems for the one-dimensional Schr\"odinger and Diracoperators on the half-line and semi-infinite discrete Schr\"odinger operator,we establish the connections with the method of De Branges: for each of thesystem we construct the De Branges space and give a natural dynamicalinterpretation of all its ingredients: the set of function the De Brange spaceconsists of, the scalar product, the reproducing kernel.

Boundary Control method and De Branges spaces. Schr\"odinger equation, Dirac system and Discrete Schr\"odinger operator