17 research outputs found
On derivation operators with respect to the Duhamel convolution in the space of analytic functions
We solve the Leibniz operator equation with respect to the Duhamel convolution in the class of linear continuous operators that act in the space of functions analytic in arbitrary starlike domain of the complex plane with respect to the origin
On the equivalence of differential operators of infinite order with constant coefficients
summary: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