Ansemil, José María M. and Aron, Richard M. and Ponte, Socorro
(2009)
*Behavior of entire functions on balls in a Banach space.*
Indagationes Mathematicae, 20
(4).
pp. 483-489.
ISSN 0019-3577

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Official URL: http://www.sciencedirect.com/science/article/pii/S0019357709800219

## Abstract

In this paper we prove that given any two disjoint balls in an infinite dimensional complex Banach space, there exists an entire function which is bounded on one and unbounded on the other.

Item Type: | Article |
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Uncontrolled Keywords: | Banach space; Entire function; Radius of boundedness |

Subjects: | Sciences > Mathematics > Functional analysis and Operator theory |

ID Code: | 16773 |

References: | Ansemil J.M., Aron R.M., Ponte S. – Representation of spaces of holomorphic functions on Banach spaces, Pub. RIMS, Kyoto Univ. 45 (2009) 383–391. Aron R.M. – Entire functions of unbounded type on a Banach space, Boll. Un. Mat. Ital. 9 (1974) 28–31. Coeuré G. – Sur le rayon de bornologie des fonctions holomorphes, Lecture Notes in Math. 578 (1977) 183–194. Diestel J. – Sequences and Series in Banach Spaces, Grad. Texts in Math., vol. 92, Springer-Verlag, New York, 1984. Dineen S. – Unbounded holomorphic functions on a Banach space, J. London Math. Soc. (2) 4 (1972) 461–465. Dineen S. – Complex Analysis on Infinite Dimensional Spaces,Springer Monographs in Mathematics,Springer-Verlag, London, 1999. Kiselman C.O. – On the radius of convergence of an entire function in a normed space, Ann. Polon. Math. 33 (1976) 39–55. Schottenloher M. – Richness of the class of holomorphic functions on an infinite dimensional space, North-Holland Math. Stud. 12 (1977) 209–225. |

Deposited On: | 19 Oct 2012 08:15 |

Last Modified: | 07 Feb 2014 09:35 |

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