Dubovoy V. Unilateral shifts generated by contractions and their ap-plication to analysis problems

Objects - functions, which are contractive and holomorphic in the unit disk (Schur functions), contractions in the Hilbert space; goals - the matricial interpolation Schur problem, defect functions of Schur function, the scattering suboperator through the inner channels of system, pseudocontinuation of Schur functions; methods of function theory and the operator theory; new results - a constructive solving of the degenerate matricial Schur problem is proposed, for investigation of Schur problem is proposed the new method, which is synthesis of theories of J-expanding and characteristic functions, the scattering suboperator through the inner channels of a system is defined and its properties are obtained, a new method of investigations of pseudocontinuation of Schur functions is proposed; employment - the results are important in operator theory, function theory and scattering theory