  The theory of holomorphic functions of several complex variables is applied
in proving a multidimensional variant of a theorem involving an exponential
boundedness criterion for the classical moment problem. A theorem of Petersen
concerning the relation between the multidimensional and one-dimensional moment
problems is extended for half-lines and compact subsets of the real line. These
results are used to solve the moment problem for the quantum phase space
observables generated by the number states.
