A zoo of diffeomorphism groups on ℝn

Abstract

We consider the groups DiffB(ℝn), DiffH∞(ℝn) and DiffS(ℝn) of smooth diffeomorphisms on ℝn which differ from the identity by a function which is in either B (bounded in all derivatives), H∞ = ∩k≥ 0Hk S (rapidly decreasing). We show that all these groups are smooth regular Lie groups. © 2013 Springer Science+Business Media Dordrecht.