A Chevalley's theorem in class C^r

Details A Chevalley's theorem in class C^r A Chevalley's theorem in class C^r

2008-08-26

arxiv.org/abs/0808.3513v1

Proc.R.Soc.Edinb. A139 (2009), 743-758

Mathematics

Functional Analysis

13 pages

Scientific paper

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.There exists a linear mapping from (C^r(R^n))^W to C^[r/h](R^n), f\mapsto F such that f=F \circ P, continuous for the natural Fr\'echet topologies. A general counterexample shows that this result is the best possible. The proof uses techniques of division by linear forms and a study of compensation phenomenons. An extension to P^{-1}(R^n) of invariant formally holomorphic regular fields is needed.

Affiliated with

Also associated with

No associations

Rating

A Chevalley's theorem in class C^r does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A Chevalley's theorem in class C^r, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Chevalley's theorem in class C^r will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-281683