}}a_{-n-0-j}(y,\omega)\omega^\alpha d\omega=0,&& \forall \alpha\in {\mathbb{N}}_0^{n+0}\textrm{ with }  |\alpha|=j\end{aligned}$$ for all $j\in{\mathbb{N}}_0$. Conversely, if $K\in C^{-\infty}({\overline}{X}{\times}{\overline}{