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 X⊆Rd 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)={u∈C∞(X);P(D)u=0}, resp. DP′(X)={u∈D′(X);P(D)u=0} possess the linear topological invariant (Ω) introduced by Vogt and Wagner (Stud. Math. 68:225-240, 1980), resp. its generalization (PΩ) introduced by Bonet and Domański (J. Funct. Anal. 230:329-381, 2006). [ABSTRACT FROM AUTHOR]