Abstract
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), \(H^\infty = \bigcap _{k\ge 0}H^k\), or \(\mathcal{S }\) (rapidly decreasing). We show that all these groups are smooth regular Lie groups.
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Michor, P.W., Mumford, D. A zoo of diffeomorphism groups on \(\mathbb{R }^{n}\) . Ann Glob Anal Geom 44, 529–540 (2013). https://doi.org/10.1007/s10455-013-9380-2
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DOI: https://doi.org/10.1007/s10455-013-9380-2