Surjectivity of differential operators and linear topological invariants for spaces of zero solutions

We provide a sufficient condition for a linear differential operator with constant coefficients P(D) to be surjective on C(X) and D(X), respectively, where XRd is open. Moreover, for certain differential operators this sufficient condition is also necessary and thus a characterization of surjectivity for such differential operators on C(X), resp. on D(X), is derived. Additionally, we obtain for certain surjective differential operators P(D) on C(X), resp. D(X), that the spaces of zero solutions CP(X)={uC(X); resp. DP(X)={uD(X);} possess the linear topological invariant () introduced by Vogt and Wagner (Stud. Math. 68:225-240, 1980), resp. its generalization (P) introduced by Bonet and Domaski (J. Funct. Anal. 230:329-381, 2006).