Journal of the
Korean Mathematical Society JKMS

Let $E$ and $F$ be locally convex spaces over $\bf C$. We assume that $E$ is a nuclear space and $F$ is a Banach space. Let $f$ be a holomorphic mapping from $E$ into $F$. Then we show that $f$ is of uniformly bounded type if and only if, for an arbitrary locally convex space $G$ containing $E$ as a closed subspace, $f$ can be extended to a holomorphic mapping from $G$ into $F$.

Keywords: nuclear space, entire function, uniformly bounded type, holomorphic extension

MSC numbers: 46G20