Abstract
The present review article contains recently published results on Markov moment problem and related approximation. The main idea is to apply theorems concerning solutions of the abstract moment problem and approximation theory to the classical moment problem on unbounded subsets of R n . We approximate some nonnegative functions of several variables by sums of tensor products of positive polynomials in each separate variables, which for the analytic expression in terms of sums of squares is known. Thus, one obtains characterizations of the solutions of multidimensional moment problem in terms of quadratic forms, similarly to the one-dimensional case. On the other hand, the case of multiplicative operator-solution is discussed in the end.
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