Weighted vector-valued holomorphic functions on Banach spaces
The purpose of this paper is to investigate conditions to ensure when a weakly holomorphic vector-valued function defined on a non void open and connected subset \(U\) of an infinite-dimensional Banach space \(X\) satisfying certain estimates is in fact holomorphic, and to give extension results for functions in a Banach space of holomorphic functions defined also on a non void open and connected \(U\) subset of \(X\). These investigations continue recent work by Arendt, Nikolski, Grosse-Erdmann, Frerick, Wengenroth, the author and the reviewer, among others. Extensions of theorems from Frerick, Jordá and Wengenroth in [\textit{L. Frerick} et al., Math. Nachr. 282, No. 5, 690--696 (2009; Zbl 1177.46024)] are obtained. Linearization of Banach spaces of vector-valued holomorphic functions constitutes an important technique in the paper. Several nice results and examples about different weighted Banach spaces of holomorphic functions defined on subsets of a Banach space \(X\) are given. They clarify the assumptions of the theorems given in the article.
weighted Banach spaces of holomorphic functions
scientific article; zbMATH DE number 6306943
scientific article