Markov Moment Problems on Special Closed Subsets of Rn

First, this paper provides characterizing the existence and uniqueness of linear operator solution T for large classes full Markov moment problems on closed subsets F Rn. One uses approximation by special nonnegative polynomials. The case when is compact studied. Then cases F=Rn F=R+n are under attention. Here, main findings consist in proving applying density polynomials, which sums squares, positive cone Lν1(Rn), respectively Lν1(R+n), a class measures ν. solves important difficulty created fact that Rn, n≥2, there exist polynomials not expressible terms squares. This second aim paper. On other hand, two types symmetry outlined. Both these properties appear naturally from thematic mentioned above. third They lead to new statements, illustrated corollaries, supported few examples.