A remark on separate holomorphy

Marek Jarnicki, Peter Pflug

Let $X$ be a Riemann domain over ${\mathbb{C}}^k\times {\mathbb{C}}^{\ell }$. If $X$ is domain of holomorphy with respect to a family $\mathcal{F}\subset \mathcal{O}(X)$, then there exists a pl…