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A Differential Operator Representation of Continuous Homomorphisms Between the Spaces of Entire Functions of Given Proximate Orders

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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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Correspondence to Takashi Aoki.

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Communicated by Irene Sabadini.

This article is part of the topical collection “In memory of Carlos A. Berenstein (1944–2019)” edited by Irene Sabadini and Daniele Struppa.

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The first author is supported by JSPS KAKENHI Grant Nos. 26400126 and 18K03385.

The third author is supported by JSPS KAKENHI Grant No. 16K05170.

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Aoki, T., Ishimura, R. & Okada, Y. A Differential Operator Representation of Continuous Homomorphisms Between the Spaces of Entire Functions of Given Proximate Orders. Complex Anal. Oper. Theory 14, 75 (2020). https://doi.org/10.1007/s11785-020-01031-0

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  • DOI: https://doi.org/10.1007/s11785-020-01031-0

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