Approximating Positive Polynomials Using Sums of Squares

The paper considers the relationship between positive polynomials, sums of squares and the multidimensional moment problem in the general context of basic closed semi-algebraic sets in real n-space. The emphasis is on the non-compact case and on quadratic module representations as opposed to quadratic preordering presentations. The paper clarifies the relationship between known results on the algebraic side and on the functional-analytic side and extends these results in a variety of ways.