The uniqueness question in the multidimensional moment problem with applications to phase space observables
Anatolij Dvurecenskij, Pekka Lahti, Kari Ylinen
Abstract
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.
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