Timeline for The dual of the space of smooth functions that vanish at infinity
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| Sep 24, 2015 at 4:17 | comment | added | TaQ | The dual spaces of the first two suggested spaces are just certain spaces of distributions on $U\,$. What is "convenient to work with", depends on what one aims to work for. This does not become clear enough from the question, and so there is no proper answer. | |
| Sep 24, 2015 at 3:11 | comment | added | Alex M. | @JohannesHahn: Indeed, maybe this is what I should look for. Nevertheless, even though the compatification of $U$ might turn out to be a manifold itself, it will not be a Riemannian one, since the restriction of the Euclidean metric does not vanish at infinity on $U$. | |
| Sep 23, 2015 at 21:29 | comment | added | Johannes Hahn | I think a better choice would be the space of functions which not only vanish at infinity themselves but also have all their derivatives vanishing at infinity. Then this becomes a certain subspace of the usual $C^\infty$-space of the one-point-compactification of $U$ (which is a manifold in many interesting cases so it makes sense to talk about its $C^\infty$ space) | |
| Sep 23, 2015 at 19:59 | history | asked | Alex M. | CC BY-SA 3.0 |