1Institute of Mathematics Jagiellonian University Reymonta 4 30-059 Kraków, Poland 2Institut für Mathematik Carl von Ossietzky Universität Oldenburg Postfach 2503 D-26111 Oldenburg, Germany
Studia Mathematica, Tome 174 (2006) no. 3, pp. 309-317
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 $\{f|_{X_a}: f\in{\mathcal F}\}$.
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
Affiliations des auteurs :
Marek Jarnicki
1
;
Peter Pflug
2
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
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title = {A remark on separate holomorphy},
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Marek Jarnicki; Peter Pflug. A remark on separate holomorphy. Studia Mathematica, Tome 174 (2006) no. 3, pp. 309-317. doi: 10.4064/sm174-3-5
