The multidimensional Moment Problem: Set of Atoms and Determinacy

This paper is about two special topics of the multi-dimensional truncated moment problem. First we investigate the determinacy problem, that is, the question of when a truncated moment sequence has a unique representing measure. Then we define the moment cone on $\mathbb{R}^n$ and characterize inner points and boundary points of this cone. Finally, we study the set of all possible atoms of representing measures for a truncated moment sequence.