On the multilinear trigonometric problem of moments

Abstract

A multilinear generalization of the trigonometric problem of moments is presented and discussed. The moments c(k), k is an element of Z(n) of a regular Borel polymeasure gamma on T(n) are characterized by means of a norm parallel to . parallel to(omega) on functions on Z(n). Some properties of this norm are analyzed and various examples are presented showing that it is strictly weaker than the Frechet norms and the absolute convergence norm. The convolution product of multilinear functionals is defined and an inverse theorem is proved.