On the Holomorphic Extension of Vector Valued Functions

In this paper we study the holomorphic extension of Fréchet (vector) valued (weakly) holomorphic functions from the linear hull of a closed, bounded, absolutely convex set in E\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$E$$\end{document} to E;\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$E;$$\end{document} and from a non-pluripolar compact subset in a nuclear Fréchet space to some its neighbourhood.