Application of localization to the multivariate moment problem II

The paper is a sequel to the paper "Application of localization to the multivariate moment problem" by the same author. A new criterion is presented for a positive semidefinite linear functional on the real polynomial algebra to correspond to a positive Borel measure on real n-space. The criterion is stronger than Nussbaum's criterion and is similar in nature to a criterion of Schmudgen. It is also explained how the criterion allows one to understand the support of the associated measure in terms of the non-negativity of the linear functional on a quadratic module of the real polynomial algebra. This latter result extends a result of Lasserre. The techniques employed are the same localization techniques employed already in two earlier papers by the same author.