I was reading Sogge's Fourier Integrals in Classical analysis and I came across the following statement:
Let $u,v\in \mathcal{E}'$, then we can write $û=û_1+û_0$ and $\hat{v}=\hat{v}_0+\hat{v}_1 $ where $û_0,\hat{v}_0\in\mathcal{S}$ and $ û_1, \hat{v}_1$ vanish outside of small conic neighborhoods of $\Gamma(u)$ and $\Gamma(v)$, respectively. Here, $\Gamma(u)$ is the projection of the Wave Front Set of u, $WF(u)$, onto the frequency component.
How can I do this "separation" of $u$ and $v$?