Buchwalter, Henri Semi-groupes de moments complexes. (Semigroups of complex moments). (French) Zbl 0628.43005 Am. J. Math. 108, 1089-1118 (1986). 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 Cited in 2 Documents MSC: 43A35 Positive definite functions on groups, semigroups, etc. Keywords:semigroup with involution; positive definite functions PDFBibTeX XMLCite \textit{H. Buchwalter}, Am. J. Math. 108, 1089--1118 (1986; Zbl 0628.43005) Full Text: DOI