Analysis of the action of a pseudodifferential operator over \((C_{\Omega \mid X})_{T^*_ M X}\) (Q1177327)

The authors consider a pseudodifferential operator \(P\) on a complexification \(X\) of a real analytic manifold \(M\). For suitable open subsets \(\Omega\subset M\) they use the action of \(P\) over holomorphic functions and the representation of microfunctions at the boundary \((C_{\Omega\mid X})_{T^*_ MX}\) in order to prove that \(P\) defines a sheaf morphism of \((C_{\Omega\mid X})_{T^*_ MX}\).