We consider in Rn a differential operator P(D), P a polynomial, with constant coefficients. Let U be an open set in Rn and A(U) be the space of real analytic functions on U. We consider the equation P(D)u=f, for f in A(U) and look for a solution in A(U). Hormander proved a necessary and sufficient condition for the solution to exist in the case U is convex. From this theorem one derives the fact that if a cone W admits a Phragmen-Lindeloff principle then at each of its non-zero real points the real part of W is pure dimensional of dimension n-1. The Phragmen-Lindeloff principle is reduced to...