Isomorphism theorems for infinite order differential operators

The operators studied are infinite order linear differential operators with constant coefficients. We require that the characteristic function of the operator be analytic in a neighborhood of 0 and have a radius of convergence which is less than that of its reciprocal. It is shown that such operators may be regarded as isomorphisms between Banach spaces of entire functions. These Banach spaces, in every case, are isomorphic to the sequence space ${c_0}$. Further, translation in the domain plane defines an automorphism on both the domain and range space of the operator.