A remark on separate holomorphy

Volume 174 / 2006

Marek Jarnicki, Peter Pflug Studia Mathematica 174 (2006), 309-317 MSC: 32D05, 32D25. DOI: 10.4064/sm174-3-5


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 $\{f|_{X_a}: f\in{\mathcal F}\}$.


  • Marek JarnickiInstitute of Mathematics
    Jagiellonian University
    Reymonta 4
    30-059 Kraków, Poland
  • Peter PflugInstitut für Mathematik
    Carl von Ossietzky Universität Oldenburg
    Postfach 2503
    D-26111 Oldenburg, Germany

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