# Representation of compactly supported distribution

Is this true?

Any compactly supported distribution $T\in \cal D'$ can be represented as finite sum of partial derivatives of functions.

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If $T$ is compactly supported, then $T$ can be extended to the space of infinitely differentiable function, and hence have a finite order. – Davide Giraudo May 2 '12 at 17:50
What do you mean exactly by sum of partial derivatives of functions? – Davide Giraudo May 2 '12 at 19:18
I found the answer here. people.oregonstate.edu/~peterseb/mth627/docs/…;, It is a theorem of Schwarz's. – Yimin May 2 '12 at 19:25
The link doesn't work. – Davide Giraudo May 2 '12 at 20:59
Eh...maybe you need to edit the link, just to retype the ".pdf", it is strange because the link is correct.people.oregonstate.edu/~peterseb/mth627/docs/… – Yimin May 3 '12 at 1:45