Zagorodnyuk S. Semi-infinite matrices and polynomials orthogonal on the real and the imaginary axes

The dissertation is devoted to the solution of the inverse problem of the spectral analysis for (2N+1)-diagonal, complex, symmetric matrices, to the study of properties of polynomials connected with five-diagonal, Hermitian matrices, and to the study of corresponding moments problems. For (2N+1)-diagonal, complex, symmetric matrices the inverse problem of the spectral analysis is solved. Conditions of solvability of the moments problems connected with five-diagonal matrices, a characteristic property of the corresponding polynomials and the fundamental system of solutions of the corresponding difference equation are obtained. The methods of the investigation are similar to the classical.