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Entire functions uniformly bounded on balls of a Banach space

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2011

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Polish Acad Sciencies Inst Mathematics
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Martínez Ansemil, J. M., López Salazar Codes, J. & Ponte Miramontes, M. S. «Entire Functions Uniformly Bounded on Balls of a Banach Space». Studia Mathematica, vol. 204, n.o 2, 2011, pp. 187-94. DOI.org (Crossref), https://doi.org/10.4064/sm204-2-5.

Abstract

Let X be an infinite-dimensional complex Banach space. Very recently, several results on the existence of entire functions on X bounded on a given ball B(1) subset of X and unbounded on another given ball B(2) subset of X have been obtained. In this paper we consider the problem of finding entire functions which are uniformly bounded on a collection of balls and unbounded on the balls of some other collection.

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