Characterizations of holomorphic functions in infinite dimensional complex spaces (Q2757186)

In the first part of the paper, the authors recall some well-known facts from the theory of envelopes of holomorphy in the category of Riemann domains over locally convex topological vector spaces. The main result of the second part says that if \((\Omega,\varphi)\) is a pseudoconvex Riemann domain over \(\mathbb C^{\mathbb N}\), then there exist \(n\in\mathbb N\) and \(V\subset\Omega\) such that \((V,\varphi|_{V})\) is a pseudoconvex Riemann domain over \(\mathbb C^{n}\) and \(\Omega=\mathbb C^{\mathbb N\setminus\{1,\dots,n\}}\times V\). NEWLINENEWLINENEWLINEThe result was proved by \textit{K. H. Shon, S. K. Lee}, and \textit{E. G. Kwon} in the paper [Taiwanese J. Math. 2, 347-352 (1998; Zbl 0926.32014)].