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Representation of Spaces of Entire Functions on Banach Spaces

Ansemil, José María M. and Aron, Richard M. and Ponte, Socorro (2009) Representation of Spaces of Entire Functions on Banach Spaces. Publications of the Research Institute for Mathematical Sciences, 45 (2). pp. 383-391. ISSN 0034-5318

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Abstract

We prove the impossibility of expressing the space of entire functions on any infinite dimensional complex Banach space with a Schauder basis E as a countable union of spaces of entire functions that are bounded on countable open covers of E.


Item Type:Article
Uncontrolled Keywords:entire function on a Banach space; inductive limit; Schauder basis
Subjects:Sciences > Mathematics > Functions
ID Code:16790
References:

R. M. Aron, Entire functions of unbounded type on a Banach space, Boll. Un. Mat. Ital. (4) 9 (1974), 28–31.

G. Coeuré, Fonctions plurisousharmoniques sur les espaces vectoriels topologiques et applications àe l’étude des fonctions analytiques, Ann. Inst. Fourier (Grenoble)20 (1970), fasc. 1, 361–432.

S. Dineen, Complex analysis on infinite-dimensional spaces, Springer Monographs in Mathematics, Springer, London, 1999.

J. Lindenstrauss and L. Tzafriri, Classical Banach spaces. I and II, Classics in Mathematics, Springer, Berlin, 1977.

J. Mujica, Spaces of germs of holomorphic functions, in Studies in analysis, Adv. in Math. Suppl. Stud. 4, 1–41, Academic Press, New York, 1979.

L. Nachbin, Topology on spaces of holomorphic mappings, Ergebnisse der Mathematik und ihrer Grenzgebiete 47, Springer-Verlag New York Inc., New York, 1969.

Deposited On:22 Oct 2012 09:15
Last Modified:07 Feb 2014 09:35

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