Les fonctions de Lévy existent ! (Lévy\(functions\) do exist !)
We give a complete solution of the open problem of existence of a Lévy function L on a \({}^*\)-semigroup \((S,+,^*)\). For this we bring back the problem to the case of a group \(S=G\), solved by \textit{K. R. Parthasarathy}, \textit{R. Ranga Rao} and \textit{S. R. S. Varadhan} [Ill. J. Math. 7, 337-369 (1963; Zbl 0129.109)], with the help of the canonical group \(G=G_ S\) associated to S by the author [Math. Ann. 271, 619-639 (1985; Zbl 0547.39002)].
scientific article; zbMATH DE number 3912977