Ivasiuk I. Spectral theory of generalized Jacobi Hermitian matrices

The thesis is devoted to investigation of spectral theory of Jacobi matrices of some types. Direct spectral problem for generalized Jacobi Hermitian matrices is solved and spectral measure is constructed. Inverse spectral problem is solved for some type of generalied Jacobi Hermitian matrices and necessary and sufficient conditions, which guarantee that some infinite dimentional matrix valued measure is the spectral measure of generalized Jacobi Hermitian matrices, are found. It is shown that Szego recursion is nothing else but system of equations for finding of polynomials of first order, which correspond to the three-diagonal block Jacobi unitary matrices.