Common cyclic entire functions for partial differential operators

Let H(^N) denote the Fréchet space of all entire functions of N variables (N1). The purpose of this paper is to prove the existence of a dense set of functions f in H(^N) such that if L is any nonscalar linear differential operator with constant coefficients, then the set {p(L)fp(·) is a polynomial} is dense in H(^N).Research supported in part by an NSF grant