[en] The asymptotic behaviour of tempered distributions with support in a convex, closed cone are classified by means of group theory. The notion of regulary varying distribution is introduced. An Abelian-Tauberian theorem for regulary varying tempered distributions, which generalizes the one dimensional Abelian-Tauberian theorem of Hardy-Littlewood-Karamata and the many dimensional extension due Vladimirov is proved. Applications to n-point functions are also presented. (authors)