Hoi, consider $\displaystyle u= \frac{1}{|x|}e^{-|x|}$ for $x\in \mathbb{R}^3$, then one can see that $\Delta u = u$ for $|x|>0$ ( which one can see by transferring $u$ to spherical coordinates).
So can we then conclude: (*) $(1-\Delta)u$ is a distribution with support $= \left\{0\right\}$ and order $N=0$?
I want to either show that $((1-\Delta)u, \phi) = \phi(0)$ or show that (*) holds.
One of the 2 is enough to show that $(1-\Delta)u = \delta$. Thanks for any help.