APPROXIMATION, MARKOV MOMENT PROBLEM AND RELATED INVERSE PROBLEMS

We give necessary and sufficient conditions for the existence of a unique solution of a multidimensional real classical Markov moment problem, in terms of quadratic forms. Next, we consider applications of a sufficient condition to solving geometrically nonlinear systems with infinite many equations and unknowns (inverse problems solved starting from the moments). Thus, one solves problems studied in the literature by some other methods. Our way of treating these problems works in several dimensions. In the end, one considers a problem not necessarily involving polynomials.