Cross theorem

Marek Jarnicki¹ ; Peter Pflug²

¹ Institute of Mathematics Jagiellonian University Reymonta 4 30-059 Krak/ow, Poland
² Fachbereich Mathematik Carl von Ossietzky Universität Oldenburg Postfach 2503 D-26111 Oldenburg, Germany

Annales Polonici Mathematici, Tome 77 (2001) no. 3, pp. 295-302.

Résumé

Let $D, G\subset\mathbb C$ 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].

Détail

DOI : 10.4064/ap77-3-8

Keywords: subset mathbb domains subset subset locally regular sets times cup times assume borel set proper analytic subset neighborhood there exists pure dimensional analytic subset widehat envelope holomorphy skew widehat function separately holomorphic setminus extends holomorphic function skew widehat setminus widehat result generalizes special cases which studied sic