I am working on a problem which contains the following:
Suppose that $u \in \mathcal{D}'(\mathbb{R}^n)$ satisfies $xu = 0$.
Where $\mathcal{D}'$ is the space of distributions. Now, I am not completely sure what this should mean. $x$ is a function, which is not even compactly supported, whereas $u$ is a distribution. Could someone explain what I am supposed to think of this?