A remark on separate holomorphy

Marek Jarnicki¹ ; Peter Pflug²

¹ Institute of Mathematics Jagiellonian University Reymonta 4 30-059 Kraków, Poland
² Institut für Mathematik Carl von Ossietzky Universität Oldenburg Postfach 2503 D-26111 Oldenburg, Germany

Studia Mathematica, Tome 174 (2006) no. 3, pp. 309-317

Résumé

Let $X$ be a Riemann domain over ${\mathbb C}^k\times{\mathbb C}^\ell$. If $X$ is a domain of holomorphy with respect to a family ${\mathcal F}\subset{\mathcal O}(X)$, then there exists a pluripolar set $P\subset{\mathbb C}^k$ such that every slice $X_a$ of $X$ with $a\notin P$ is a region of holomorphy with respect to the family $\{f|_{X_a}: f\in{\mathcal F}\}$.

Détail

DOI : 10.4064/sm174-3-5

Keywords: riemann domain mathbb times mathbb ell domain holomorphy respect family mathcal subset mathcal there exists pluripolar set subset mathbb every slice notin region holomorphy respect family mathcal