2014/10/17 by Murray Marshall, Marshall, Murray
Mathematics · #14P99 #44A60 #Algebraic Geometry (math.AG) #FOS: Mathematics #Functional Analysis (math.FA) #math.AG #math.FA #msc:14P99 #msc:44A60
paper · pdf · doi:10.48550/arxiv.1410.4609
5 pages
arxiv created 2014/10/17 · arxiv updated 2014/10/20
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.