On the equivalence of differential operators of infinite order with constant coefficients

Abstract

We investigate the conditions of equivalence of a differential operator of infinite order with constant coefficients to the operator of differentiation in one space of analytic functions. We also study the conditions of continuity of a differential operator of infinite order with variable coefficients in such space.

Keywords

• space of analytic functions
• operator of differentiation of infinite order
• equivalence of operators
• commutant