This is an excercise 2.2 from Hormander, vol. I:
Does there exist a distribution $u$ on $\mathbb{R}$ with the restriction $x \rightarrow e^{1/x}$ to $\mathbb{R}_+$?
The answer, provided in the book, is "No". I am trying to "cook up" appropriate test function(s) such that $ \int \phi(x)e^{1/x} \leq C\sum_{\alpha \leq k} \sup\left|\partial^{\alpha}\phi\right|$ for no $k$, and I'm not sure at all what function(s) to take. What is the appropriate function? Is there a general method to come up with just right test functions?