APPLICATION OF LOCALIZATION TO THE MULTIVARIATE MOMENT PROBLEM

It is explained how the localization technique introduced by the author in [19] leads to a useful reformulation of the multivariate moment problem in terms of extension of positive semidefinite linear functionals to positive semidefinite linear functionals on the localization of R[(x) under bar] at p = Pi(n)(i=1) (1 + x(i)(2)) or p' = Pi(n-1)(i=1) (1 + x(i)(2)). It is explained how this reformulation can be. exploited to prove new results concerning existence and uniqueness of the measure mu, and density of C[(x) under bar] in L-s (mu) and, at the same time, to give new proofs of old results of Fuglede [11], Nussbaum [21], Petersen [22] and Schmtidgen [27], results which were proved previously using the theory of strongly commuting self-adjoint operators on Hilbert space.