Multidimensional moment problem and diagonal Schur algorithm

The multidimensional moment problem is studied in terms of the Steiltjes transform. The diagonal step-by-step algorithm is constructed for the multidimensional moment problem. The set of solutions of the full multidimensional moment problem is found in terms of the continued fractions. Moreover, the diagonal step-by-step algorithm can be applied to the special truncated multidimensional moment problem.