A differential operator representation of continuous homomorphisms between the spaces of entire functions of given proximate orders

preprint2020arXivOpen access

Abstract

In this paper, we consider the locally convex spaces of entire functions with growth given by proximate orders, and study the representation as a differential operator of a continuous homomorphism from such a space to another one. As a corollary, we give a characterization of continuous endomorphisms of such spaces.

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