Cross theorem
Volume 77 / 2001
Annales Polonici Mathematici 77 (2001), 295-302
MSC: 32D15, 32D10.
DOI: 10.4064/ap77-3-8
Abstract
Let be domains, let A\subset D, B\subset G be locally regular sets, and let X:=(D\times B)\cup(A\times 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 \widehat M of the envelope of holomorphy \skew3\widehat X of X such that any function separately holomorphic on X\setminus M extends to a holomorphic function on \skew3\widehat X\setminus\widehat M. The result generalizes special cases which were studied in [Ökt 1998], [Ökt 1999], and [Sic 2000].
