Differential operators of infinite order in the space of rapidly decreasing sequences

We consider the space of rapidly decreasing sequences s and the derivative operator D defined on it. The object of this article is to study the equivalence of a differential operator of infinite order; that is . φk constant numbers an a power of D. Dn, meaning, is there a isomorphism X (from s onto s) such that Xφ(D) = Dn X?. We prove that if φ(D) is equivalent to Dn, then φ(D) is of finite order, in fact a polynomial of degree n. The question of the equivalence of two differential operators of finite order in the space s is addressed too and solved completely when n =1.