Simonov K. Operator approach to the strong Hamburger moment problem

The thesis is devoted to the study of the strong matrix moment problem of Hamburger using operator methods. The strong moment problem is reduced to the problem of finding self-adjoint extensions of a model symmetric operator in a Hilbert space. The classical objects of the moment problem such as orthogonal polynomials of the first and the second kind, the Jacobi matrix and the Nevanlinna matrix, are extended to the case of the strong moment problem. The theory of representations of symmetric operators and the methods of boundary value spaces are applied for describing all the solutions in the form of a Nevanlinna-type transform both in the completely indeterminate case and in the case of the strong truncated moment problem.