Surjective partial differential operators on real analytic functions defined on open convex sets

Let P(D) be a partial differential operator with constant coefficients whic h is surjective on the space A(Omega) of real analytic functions on a cover open set Omega subset of R-n. Let L(P-m) denote the localizations at infin ity (in the sense of Hormander) of the principal part P-m. Then Q(x + i tau N) not equal 0 for (x, tau) is an element of R-n x (R\{0}) for any Q is an element of L(P-m) if N is a normal to partial derivative Omega which is non characteristic for Q. Under additional assumptions this implies that P-m mu st be locally hyperbolic.