INTERSECTION-PROPERTIES OF GEVREY-CLASSES AND CERTAIN OTHER CLASSES

It is well-known that, in the case of Gevrey classes as in the case of C-k classes, a loss of regularity cannot be avoided in the division b y a generic polynomial. We show here that the intersection of Gevrey c lasses inherits the same good properties as the C-infinity class. Inde ed, we prove here a Whitney extension theorem, a Lojasiewicz theorem o n regular situation, some theorems of division and preparation and a W hitney spectral theorem. In fact, this work deals with more general no n-quasianalytic classes. (C) Elsevier, Paris.