DECOMPOSITION OF SUPPORT OF MICROFUNCTIONS AT THE BOUNDARY ALONG C-R MANIFOLDS AND REPRESENTATION BY HOLOMORPHIC-FUNCTIONS

Two are the contents of the paper. A theorem of representation of microfunctions over open sets OMEGA of CR submanifolds M less-than-or-equal-to X congruent-to C(n). A theorem of decomposition of their support along the fibres of pi: T* X --> X. The main tools are the following. A result of <<flabbiness>> for microfunctions along generic manifolds due to [T-Z] (that we adapt hem to microfunctions on OMEGA). This entails our decomposition criterion for SS(OMEGA) (cf. [S1, 2]). A theorem due to [Z2] on vanishing of cohomology in degree other than 0, s- of O(X) over C2-polyhedrons W subset-of X such that on the regular part of the exterior conormal bundle N(W)-degrees(a) the <<microlocal>> Levi form of partial derivative W has a constant number s- of negative eigenvalues. We prove here that if partial derivative OMEGA is generic, then OMEGA has a fundamental system of neighbourhoods W with cone property which enter the hypotheses of [Z2]. This implies our representation theorem.