Kozak V. Jacobi matrices corresponding to two dimensional moment problem

Research objects: the block Jacobi type matrices and their corresponding the symmetric formal commuting operators, orthogonal polynomial systems, the corresponding Borel measure on the real plane. Subject of research: the matrices corresponding to a the strong two-dimensional real problem of moments and corresponding to the orthogonal polynomials. The basic methods are is methods of functional analysis, in particular, the theory of the linear operators and Hilbert spaces; the method of expansion by generalized own the vectors for a finite set of commuting self-directed operators. The inverse and direct spectral problems for block Jacobi matrices type of the corresponding to a strong two-dimensional real moments problem are solved - block Jacobi type matrices are constructed in a given the Borel probability measure on the real plane with compact support. The description of the internal structure of block Jacobi matrices corresponding to the strong two-dimensional real problem of moments is given, and the commutative properties of matrices corresponding to a non-strong two-dimensional problem of moments are investigated.