MARKOV MOMENT PROBLEM AND RELATED APPROXIMATION

We apply approximation results of certain functions of several variables by means of sums of tensor products of positive polynomials on the real line, in each separate variable, which are sums of squares. This leads to characterizations of the existence of the solutions of the multidimensional Markov moment problem in terms of quadratic forms or mappings, similarly to the one-dimensional case. From this point of view, one solves the difficulty created by the existence of positive polynomials that are not sums of squares in several dimensions. On the other hand, applications of general results to concrete spaces are considered. The continuity of the dominating operator seems to be essential in proving the properties of the solution.