a1 Département de mathématiques et d'informatique Université de Sherbrooke Sherbrooke Québec Canada J1K 2R1
In this paper we deal with classes of infinitely differentiable functions known in the literature as Carleman classes. Our main result is a characterisation of those Carleman classes that are closed under superposition. This result enables us to give a complete solution to a problem that has been considered by Gevrey, Cartan and Bang.
(Received August 23 1988)