Local operators and a characterization of the Volterra operator

Abstract

We consider locally defined operators of the form $D^{n}\circ K$ where $D$ is the operator of differentiation and $K$ maps the space of continuous functions into the space of $n$-times\ differentiable functions. As a corollary we obtain a characterization of the Volterra operator. Locally defined operators acting in the space of analytic functions are also discussed.