Polynomial Approximation on Unbounded Subsets and the Moment Problem

In the first part of this work, one proves a Markov moment problem involving - norm on a space
for a regular positive special measure .. To this end, polynomial approximation on unbounded
subsets and Hahn - Banach principle are applied. One uses approximation by sums of tensor
products of positive polynomials in each separate variable. This way, one solves the difficulty created
by the fact that there are positive polynomials, which are not writable as sums of squares in several
dimensions. Consequently, we can solve the multidimensional moment problem in terms of quadratic
mappings. We also discuss Markov moment problems in concrete spaces. These last results
represent interpolation problems with two constraints. Here the main ingredients of the proofs are
constrained extension theorems for linear operators.