Terms Uniqueness Extent Appropriate Points in the Two-Dimensional Problem

Abstract

Background. We continue to study the properties of block Jacobi matrices corresponding to the two-dimensional real problem. Repeating the reasoning applied to probabilistic measure with compact support, we get similar matrices associated with Borel measure without limitation. The difficulty in our research is that the probability measure on compact corresponds uniquely to the block Jacobi type matrices. If the measure is arbitrary, then the same set of matrices can fit infinite number of measures.Objective. The objective of research is to find conditions under which some Borel measure without limitation corres­ponds to only one pair of block matrices.Methods. Using previous publications established the form of block Jacobi matrix type, by coefficients of these matrices one can inferred about the above mentioned bijection.Results. The result of research is a conditions on the coefficients in the form of divergent series in which the one-to-one correspondence holds true.Conclusions. Using the solution of direct and inverse spectral problems for two-dimensional real moment problem of the previous work we found its condition to be determined (unique) by the coefficients of the block Jacobi type matrix. The result is a two-dimensional analogue of the well-known case in classical Hamburger moment problem.