Is it true that the space of hyperfunctions on $\mathbb{R}^n$ supported at 0 coincides with the space of Schwartz distributions supported at 0? 


More explicitly, is it true that any hyperfunction supported at 0 is a finite linear combination of various partial derivatives of the delta-function?


If the answer is yes, a reference would be helpful.



Hyperfunctions supported at a point
No, this is not true. Schwartz distributions with compact support inovlve only finitely many
differentiations (every such distribiution is a derivative of some order of a usual, integrable function). Hyperfunctions may involve infinitely many differentiations.
For example, in dimension $1$ you can take any entire function $f(x)=\sum a\_nx^n$,
and then $F=\sum a\_n\delta^{(n)}$ is a hyperfunction with support at $0$. 


