Prove that, for every distribution $u\in\mathcal D'(\mathbb R)$,there exists a distribution $\tilde u\in \mathcal D'(\mathbb R)$ satisfying $x\cdot\tilde u=u$.
It seems that it can be solved by Fourier Transform. But this is an exercise in the chapter which is before Fourier Transform. So can I solve this without fourier transform?
Maybe I can consider the support set of $u$, but I still cannot solve that.