The operator approach to the truncated multidimensional moment problem

Abstract

Abstract We study the truncated multidimensional moment problem with a general type of truncations. The operator approach to the moment problem is presented. The case where the associated operators form a commuting self-adjoint tuple is characterized in terms of the given moments. The case of the dimensional stability is characterized in terms of the prescribed moments as well. Some sufficient conditions for the solvability of the moment problem are presented. A construction of the corresponding solution is described by algorithms. Numerical examples of the construction are provided.