Moment problems related to intrinsic characterizations of the moment functionals

In this paper, we consider linear functionals defined on an unital commutative real algebra A and establish characterizations for moment functionals on compact sets of characters that depend only on the given functional. For example, we obtain a characterization of a moment functional on a product of symmetric intervals, in which we do not assume that the functional is positive semidefinite but positive on a semiring of A, and a characterization of a moment functional that is a solution to the moment problem on a product of arbitrary intervals. We also prove a Positivstellensatz for an archimedean cone, which is neither a quadratic module nor a semiring.