Weighted Vector-Valued Holomorphic Functions on Banach Spaces

Abstract

We study the weighted Banach spaces of vector-valued holomorphic functions defined on an open and connected subset of a Banach space. We use linearization results on these spaces to get conditions which ensure that a function $f$ defined in a subset $A$ of an open and connected subset $U$ of a Banach space $X$, with values in another Banach space $E$, and admitting certain weak extensions in a Banach space of holomorphic functions can be holomorphically extended in the corresponding Banach space of vector-valued functions.