I want to show, that for $u' \in \mathcal{D}'(\mathbb{R}^n)$
supp $u$ = $\{ 0 \}$ iff there exist numbers $m \in \mathbb{N}, c_{\alpha} \in \mathbb{K}$ such that $u = \sum_{|\alpha| \le m} c_{\alpha} D^{\alpha} \delta_0$
($\mathbb{K}$ equals $\mathbb{R}$ or $\mathbb{C}$). One direction is simple, but I find the other difficult.