The multidimensional truncated moment problem: The moment cone

Let A = { a 1 , … m } ? N be measurable functions on space ( X ) . If ? is positive measure such that ? i d < ? for all then the sequence called truncated moment sequence. By Richter's Theorem each has k -atomic representing with ? The set S of sequences cone. aim this paper to analyze various structures main results concern facial structure (exposed faces, dimensions) and lower upper bounds Carathéodory number (that is, smallest atoms which suffices sequences) convex cone In case when ? R n C differential map regularity/singularity properties are analyzed. maximal mass problem considered some applications other problems sketched.