Entire functions uniformly bounded on balls of a Banach space
Volume 204 / 2011
Studia Mathematica 204 (2011), 187-194
MSC: Primary 46G20; Secondary 46E50, 46B99.
DOI: 10.4064/sm204-2-5
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 ${B_{1}\subset X}$ 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.
