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Local operators and a characterization of the Volterra operator

. We consider locally deﬁned operators of the form D n ◦ 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.