Pseudoconvexity of Riemann domains over a product of complex planes (Q1272710)

The authors prove the following result: Let \((\Omega,\phi)\) be a schlicht Riemann domain over \({\mathbb C}^{\mathbb N}\). If \(\Omega\) is pseudoconvex then there exists an \(n\in\mathbb N\) and a pseudoconvex Riemann domain \((V,\phi| V)\) over \({\mathbb C}^n\) such that \(\Omega={\mathbb C}^{{\mathbb N}\setminus\{1,\dots,n\}}\times V\). For \((\Omega,\phi)\) an open subset of \({\mathbb C}^{\mathbb N}\) the result was proved by \textit{A. Hirschowitz} [Ann. Inst. Fourier 19, No. 1, 219-229 (1969; Zbl 0207.08203)].