A remark on Arakelyan’s theorem in higher dimensions
Volume 165 / 2021
Colloquium Mathematicum 165 (2021), 91-96
MSC: Primary 32E30; Secondary 32E20.
DOI: 10.4064/cm8189-6-2020
Published online: 10 December 2020
Abstract
We prove that any continuous function on a ray of balls, say $E$, in $\mathbb {C}^m,$ which is holomorphic in the interior of $E$, can be uniformly approximated on $E$ by entire functions. This can be viewed as a variant of Arakelyan’s approximation theorem in higher dimensions.
