Recalled definitions and results

Let $X\subset {\mathbb{R}}^d$ and $V_q\subset {\mathbb{R}}^m$ be open with $0\in V_q$, let $Z\subset X$ be relatively closed, $X^{\circ }=X\setminus Z$, $U=X\times V_q$, $U^{\circ }=X^{\circ }\times V_q$. For $b\in {\mathcal{D}}^{\prime }(X)$, $\varphi \in \mathcal{D}(U)$,

and ${{\mathsf{E}}^{\circ }}_{\gamma }$ is the same on $X^{\circ }$, $U^{\circ }$. Fix $r\ge 0$, $M_r=\#\{\gamma \in {\mathbb{N}}^m:|\gamma |\le r\}$, ${{\mathcal{P}}_r}^{\mathrm{jet}}={⨁}_{|\alpha |\le r}{C}^{\infty }(U)$, and

Fix $T^{\circ }\in {\mathcal{D}}^{\prime }(X^{\circ })$. For an extension $T\in {\mathcal{D}}^{\prime }(X)$ of $T^{\circ }$,

${F_0}^T={\mathsf{Rec}}_T$, ${d_0}^T={F_0}^T{|}_H$, $\mathrm{Ann}(T^{\circ })=\{g\in C^{\infty }(X):g{|}_{X^{\circ }}{T}^{\circ }=0\}$, $\mathrm{Ann}(T)=\{g\in C^{\infty }(X):gT=0\}$. For $\psi \in \mathcal{D}(X)$, $p_k(\psi )={\max }_{|\alpha |\le k}\Vert {\partial }^{\alpha }\psi {\Vert }_{\infty }$. For $\psi \in \mathcal{D}(X)$ and $\chi \in \mathcal{D}(V_q)$ equal to one near $0$, ${\mathsf{J}}_{\gamma }\psi (x,q)=\frac{(-1{)}^{|\gamma |}}{\gamma !}{q}^{\gamma }\chi (q)\psi (x)$, so that