2001/02/17 by Marek Jarnicki, Peter Pflug
Mathematics · #math.CV #msc:32D15 #msc:32D10
published as Ann. Polon. Math. 77 (2001), 295-302 · 8 pages
arxiv created 2001/02/17 · arxiv updated 2009/11/30
Let D, G⊂\Bbb C be domains, let A⊂ D, B⊂ G be locally regular sets, and let X:=(D× B)∪(A× G). Assume that A is a Borel set. Let M be a proper analytic subset of an open neighborhood of X. Then there exists a pure 1-dimensional analytic subset M of the envelope of holomorphy X of X such that any function separately holomorphic on X∖ M extends to a holomorphic function on X∖ M. The result generalizes special cases which were studied in \citeÖkt 1998, \citeÖkt 1999a, and \citeSic 2000.