Perturbations of the normalization matrices of the inverse scattering problem

The paper is devoted to the question about admissible perturbations of the normalization matrices of the scattering problem on the semi-axis for the system of differential equations, which is considering in known book by Z. S. Agranovich and V. A. Marchenko [1] in Hermitian case. In matrix case the test of the necessary and sufficient conditions for the scattering data is considerably complicated than in scalar case. Both for the Hermitian case and the non-Hermitian case the theorems of the paper are established. These theorems facilitate the clearing up of the belonging of the given set of the values to the scattering data, and they generalize some of results of the paper by F. S. Rofe-Beketov and the author [2].