### Impacto

Ansemil, José María M. and López-Salazar Codes, Jerónimo and Ponte, Socorro
(2011)
*Entire functions uniformly bounded on balls of a Banach space.*
Studia Mathematica, 204
(2).
pp. 187-194.
ISSN 0039-3223

Official URL: http://journals.impan.gov.pl/cgi-bin/sm/pdf?sm204-2-05

## 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.

Item Type: | Article |
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Uncontrolled Keywords: | entire function; biorthogonal system; Schauder basis |

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

ID Code: | 16770 |

References: | J. M. Ansemil, R. M. Aron and S. Ponte, Representation of spaces of entire functions on Banach spaces, Publ. Res. Inst. Math. Sci. 45 (2009), 383–391. J. M. Ansemil, R. M. Aron, S. Ponte, Behavior of entire functions on balls in a Banach space, Indag. Math. (N.S.) 20 (2009), 483–489. R. M. Aron, Entire functions of unbounded type on a Banach space, Boll. Un. Mat. Ital. 9 (1974), 28–31. J. Diestel, Sequences and Series in Banach Spaces, Springer, New York, 1984. S. J. Dilworth, M. Girardi and W. B. Johnson, Geometry of Banach spaces and biorthogonal systems, Studia Math. 140 (2000), 243–271. S. Dineen, Complex Analysis on Infinite Dimensional Spaces, Springer Monogr. Math., Springer, London, 1999. C. O. Kiselman, On the radius of convergence of an entire function in a normed space, Ann. Polon. Math. 33 (1976), 39–55. J. López-Salazar, Vector spaces of entire functions of unbounded type, Proc. Amer. Math. Soc. 139 (2011), 1347–1360. I. Singer, Bases in Banach Spaces I, Springer, Berlin, 1970. |

Deposited On: | 19 Oct 2012 08:16 |

Last Modified: | 09 Dec 2013 17:48 |

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