A remark on the multidimensional moment problem

@article{Berg1979ARO,
  title={A remark on the multidimensional moment problem},
  author={Christian Berg and Jens Peter Reus Christensen and Christian U. Jensen},
  journal={Mathematische Annalen},
  year={1979},
  volume={243},
  pages={163-169}
}
To mot ivate the following results let us recall some definitions and results with relation to the m o m e n t problem. Let (S, + ) be an abelian semigroup with neutral element 0. A real-valued function f : S ~ I R is called positive definite, if for any finite set of elements sl . . . . . s, s S the matr ix f(s~ + s) is positive semidefinite. The set ~ = ~ ( S ) of positive definite functions is easily seen to be a closed convex cone in the vector space i f (S) of all functions f : S--.IR with… 
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