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• ̃0 . We use the theory of microlocalization of sheaves of [K-S 2], and especially its formulation in [S] for boundary value problems, to treat the extension of regular solutions of systems of P. D. E. across 1-codimensional singular sets. Let M be a real analytic manifold, X a complexification of M, N an analytic hypersurface of M, Y a complexification of N, Q an open component of M\N at x e N. For a suitable involutive manifold V c Tag, invariant under the Hamiltonian flow of N•~M T Mx, we introduce a new complex P X of hyperfunctions in Q with real analytic parameters (of also

An application of the second microlocalization at the boundary to the extension of solutions of differential systems