Here I met a problem from Vasy's PDE textbook:
Show that every $u\in\mathcal{S'}(\mathbb{R}^n)$ can be approximated by elements of $\mathcal{S}(\mathbb{R}^{n})$, i.e. show that there exist $f_j\in\mathcal{S}(\mathbb{R}^n)$ such that $\iota_{f_{j}}\to u$ in $\mathcal{S'}(\mathbb{R}^n)$.
I cannot work out with the given hint in the book, or in his exam: http://web.stanford.edu/class/math173/173-f.pdf
(this was a final test in winter 2016, so please do not doubt about plagiarism)
Another question is, are there any related books or material to cover such question?