Chevalley's theorem in class Cr

Let W be a finite reflection group acting orthogonally on R-n, P be the Chevalley polynomial mapping determined by an integrity basis of the algebra of W-invariant polynomials, and h be the highest degree of the coordinate polynomials in P. Let r be a positive integer and [r/h] be the integer part of r/h. There exists a linear mapping C-r (R-n)(W) (sic) f bar right arrow F is an element of C-[r/h] (R-n) such that f = F circle P, which is continuous for the natural Frechet topologies. A general counter-example shows that this results is the best possible. The proof uses techniques of division by linear forms and a study of compensation phenomena. An extension to P-1 (R-n) of invariant formally holomorphic regular fields is needed.