Lévy-Khintchine formulas independency of a Lévy function (Q1378392)

The author gives a new proof of the integral representation for negative definite functions on abelian semigroups with involution, with lower bounded real part. He doesn't make use of Lévy functions, but uses instead in a clever way a result related to Choquet's representation theorem for positive functionals on adapted spaces. The same ``trick'' is also used for continuous negative definite functions on the group \(R^n\).