A zoo of diffeomorphism groups on \mathbb{R }^{n} |
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Authors: | Peter W Michor David Mumford |
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Institution: | 1. Fakult?t für Mathematik, Universit?t Wien, Nordbergstrasse 15, 1090, Wien, Austria 2. Division of Applied Mathematics, Brown University, Box F, Providence, RI, 02912, USA
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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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