A note on Ehrenpreis’ fundamental principle

Ehrenpreis’ Fundamental Principle is an existence theorem for inhomogeneous linear partial differential equations, and has great system-theoretic significance. Usually it is formulated for the equations defined on open convex sets. However, openness of domains of definition is somewhat restrictive in systems theory. In this article, we show that the principle is valid in the case of sets that are the unions of increasing sequences of convex compact sets. Moreover, we offer a simplified proof.