K. Schmüdgen

Given a subset $\mathcal K$ of $\mathbb R^d$ and a linear functional $L$ on the polynomials $\mathbb R^d_{2n}[\underline{x}]$ in $d$ variables and of degree at most $2n$ the truncated $\mathcal K$-moment problem asks when there is a positive Borel measure $\mu$ supported by $\mathcal K$ such that $L(p)=\int p\, d\mu$ for $p\in \mathbb R^d_{2n}[\underline{x}]$. For compact sets $\mathcal K$ we investigate the maximal mass of all representing measures at a given point of $\mathcal K$. Various characterizations of this quantity and related properties are developed and a close link to zeros of positive polynomials is established.