The multi-dimensional truncated moment problem: maximal masses - Schmüdgen, K. (Methods of Functional Analysis and Topology, 2015)
Given a subset K of R^d and a linear functional L on the polynomials R^d_2n[x] in d variables and of degree at most 2n the truncated K-moment problem asks when there is a positive Borel measure μ supported by K such that L(p)=p dμ for pR^d_2n[x]. For compact sets K we investigate the maximal mass of all representing measures at a given point of K. Various characterizations of this quantity and related properties are developed and a close link to zeros of positive polynomials is established.