An extension theorem for separately holomorphic functions with singularities

2001/04/30 by Marek Jarnicki, Peter Pflug
Mathematics · #math.CV #msc:32D15 #msc:32D10

paper · pdf

published as Ann. Polon. Math. 80 (2003), 143-161. · 20 pages; This a new version of the paper (including "An extension theorem for separately holomorphic functions with singularities, II")

arxiv created 2001/10/10 · arxiv updated 2009/11/30

Abstract

Let D_j⊂\Bbb C^k_j be a pseudoconvex domain and let A_j⊂ D_j be a locally pluripolar set, j=1,...,N. PutX:=\bigcup_j=1^N A₁×...× A_j-1× D_j× A_j+1×...× A_N⊂\Bbb C^k₁+...+k_N.Let U be an open connected neighborhood of X and let M\varsubsetneq U be an analytic subset. Then there exists an analytic subset M of the `envelope of holomorphy' X of X with M∩ X⊂ M such that for every function f separately holomorphic on X∖ M there exists an f holomorphic on X∖ M with f|_{X∖ M}=f. The result generalizes special cases which were studied in \citeÖkt 1998, \citeÖkt 1999, \citeSic 2000, and \citeJar-Pfl 2001.

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