The problem of moments on polytopes and other bounded regions ✩

The problem of moments is considered for polytopes in Rd and other bounded regions specified piecewise by curves of the form c1x α1 1 +···+cd x αd d = c0. Necessary and sufficient conditions are suggested by a simple geometric observation. For some choices of c1, . . . , cd and α1, . . . , αd, these conditions reduce to the conditions of Hausdorff for the unit interval, of Hildebrandt and Schoenberg for the unit square and of Dale for the unit simplex in R2, whereas for other choices new conditions are required. The proofs are obtained using probabilistic techniques.  2003 Elsevier Inc. All rights reserved