# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

## Studia Mathematica

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## Entire functions uniformly bounded on balls of a Banach space

### Tom 204 / 2011

Studia Mathematica 204(2011), 187-194 MSC: Primary 46G20; Secondary 46E50, 46B99. DOI: 10.4064/sm204-2-5

#### Streszczenie

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 ${B_{1}\subset X}$ and unbounded on another given ball $B_{2}\subset X$ 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.

#### Autorzy

• José M. AnsemilDepartamento de Análisis Matemático
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• Jerónimo López-SalazarDepartamento de Análisis Matemático
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• Socorro PonteDepartamento de Análisis Matemático