Application de la th�orie des fonctions caract�ristiques de plusieurs variables � l'�tude de certains probl�mes de d�composition des fonctions caract�ristiques d'une variable

Abstract

We describe here a method showing the equivalency between the problems of decomposition for some univariate characteristic functions and some associated multivariate characteristic functions. Using this method, some new results on univariate characteristic functions are deduced from known theorems on multivariate characteristic functions (it seems very difficult to obtain a direct proof of these results). For example, we give a characterization of finite products of Poisson laws without indecomposable factors, generalizing a Paul Levy's result on lattice characteristic functions. Finally, modifying a method due to B. Ramachandran, we extend a result of I. V. Ostrovskiy on decompositions of infinitely divisible characteristic functions with independent Poisson spectrum.