Abstract
In this paper we use a Choquet type theorem on adapted spaces to obtain or reobtain some results in harmonic analysis on semigroups. Thus we give a Lévy–Khinchine formula for some negative definite functions defined on a commutative semigroup with neutral element, we prove that completely monotonic (resp. alternating) functions are completely positive (resp. negative) definite, we characterize the completely monotonic and the completely alternating functions defined on N*≔{1,2,3,…}, and we consider a Stieltjes' moment problem.
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