Inheritance of surjectivity for partial differential operators on spaces of real analytic functions

For an open set Ω ⊂ Rn let A(Ω) be the space of real analytic functions on Ω. Improving our previous results, we prove a new quantitative characterization of the linear partial differential operators P(D) which are surjective on A(Ω). This implies that P(D) is surjective on A(Rn) if P(D) is surjective on A(Ω) for some Ω = ∅. Further inheritance properties for the surjectivity of P(D) on A(Ω) are also obtained.  2004 Elsevier Inc. All rights reserved.