Microlocalisation simultanée et problème de Cauchy ramifié
Given an embeddable manifold and a non-characteristic hypersurface we present a necessary condition for the tangential Cauchy-Riemann operator on to be locally solvable near a point in one of the sidesdetermined by .
The Penrose transform gives an isomorphism between the kernel of the -Dirac operator over an affine subset and the third sheaf cohomology group on the twistor space. In the paper we give an integral formula which realizes the isomorphism and decompose the kernel as a module of the Levi factor of the parabolic subgroup. This gives a new insight into the structure of the kernel of the operator.