A zoo of diffeomorphism groups on mathbb{R }^{n}

摘要

We consider the groups ({mathrm{Diff }}_mathcal{B }(mathbb{R }^n)), ({mathrm{Diff }}_{H^infty }(mathbb{R }^n)), and ({mathrm{Diff }}_{mathcal{S }}(mathbb{R }^n)) of smooth diffeomorphisms on (mathbb{R }^n) which differ from the identity by a function which is in either (mathcal{B }) (bounded in all derivatives), (H^infty = bigcap _{kge 0}H^k), or (mathcal{S }) (rapidly decreasing). We show that all these groups are smooth regular Lie groups.