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Semi-groupes de moments complexes. (Semigroups of complex moments). (French) Zbl 0628.43005

Let S be a discrete semigroup with involution, and let \(S^\wedge\) denote the set of bounded *-semicharacters of S. This paper is concerned with bounded positive definite functions on S. The contents consist of a lengthly proof of a theorem establishing necessary and sufficient conditions for a function \(\psi: S\to {\mathbb{C}}\) to have the property that the functions \(\exp(t\psi)\) \((t>0)\) are bounded, positive definite functions. The condition is in terms of moments on \(S^\wedge\). The originality derives from not requiring the existence of a Lévy function for S.
Reviewer: J.W.Baker

MSC:

43A35 Positive definite functions on groups, semigroups, etc.
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