S-Asymptotic of Distributions

In the last thirty years many definitions of the asymptotoic behaviour of distributions have been presented. We can roughly divide them in two sets. To the first one belong those definitions which directly use the classical definition of the asymptotic behaviour of a numerical function. The distribution T has to be equal to a numerical function f or to a derivative, in the sense of distributions, of a numerical functions, DPf, in a neighbourhood of infinity. The behaviour of the distribution at infinity is in reality the behaviour of the function f or corrected by p. All of these definitions are basically given in the one dimensional case.