Geodesic
Entire functions uniformly bounded on balls of a Banach space
José M. Ansemil 1   ; Jerónimo López-Salazar 1   ; Socorro Ponte 1
1 Departamento de Análisis Matemático Facultad de Matemáticas Universidad Complutense de Madrid E-28040 Madrid, Spain
Studia Mathematica, Tome 204 (2011) no. 2, pp. 187-194 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/sm204-2-5
Keywords: infinite dimensional complex banach space recently several results existence entire functions bounded given ball subset unbounded another given ball subset have obtained paper consider problem finding entire functions which uniformly bounded collection balls unbounded balls other collection

José M. Ansemil  1   ; Jerónimo López-Salazar  1   ; Socorro Ponte  1

1 Departamento de Análisis Matemático Facultad de Matemáticas Universidad Complutense de Madrid E-28040 Madrid, Spain 
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José M. Ansemil; Jerónimo López-Salazar; Socorro Ponte. Entire functions uniformly bounded on balls
 of a Banach space. Studia Mathematica, Tome 204 (2011) no. 2, pp. 187-194. doi: 10.4064/sm204-2-5

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