The problem of moments on polytopes and other bounded regions. (Q1410244)

The problem of moments is considered for the bounded region in \(\mathbb{R}^d\) specified piecewise by curves of the form \[ c_1 x^{a_1}+ \cdots+ c_d x^{a_d}_d= c_0. \] The purpose of this paper is to establish necessary and sufficient conditions such that an array \[ M= \{m(i_1,\dots, i_d): i_1,\dots, i_d\in \mathbb{Z}^+\} \] corresponds to the joint moments of some probability distribution \(p\) on this region. For some choices of \(c_1,\dots, c_d\) and \(a_1,\dots, a_d\) these conditions reduce to some ones by Hausdorff, Hildebrandt and Schoenberg, Dale for corresponding sets. Probabilistic techniques are used in proving.