Localizations of partial differential operators and surjectivity on real analytic functions

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 an open set Omega subset of R-n. Then P(D) admits shifted (generalized) elementary solutions which are real analytic on an arbitrary relatively compact open set omega subset of subset of Omega. This implies that any localization P-m ,P-Theta of the principal part P-m is hyperbolic w.r.t. any normal vector N of partial derivative Omega which is noncharacteristic for P-m,P-Theta. Un der additional assumptions P-m must be locally hyperbolic.