5
$\begingroup$

On $\mathbb{R}^n$, the Schwartz space is an incredibly nice space of functions, and in many ways is more natural than $C_c^\infty (\mathbb{R}^n)$. On a manifold $M$, it of course still makes sense to talk about $C_c^\infty(M)$, but what about $\mathcal{S}(M)$, the Schwartz space on $M$? Is there a way we can define this on a general smooth manifold $M$?

  • 0
    It probably makes sense for a manifold which is flat outside of a compact set.2011-11-02
  • 0
    You should probably post a link to MO, in case someone stops by here later2011-11-05
  • 1
    @YemonChoi Good idea. I have asked this question on MO as well: http://mathoverflow.net/questions/80094/the-schwartz-space-on-a-manifold2011-11-05

0 Answers 0