An extension theorem for separately holomorphic functions with singularities
| dc.creator | Jarnicki, Marek | |
| dc.creator | Pflug, Peter | |
| dc.date | 2001-04-07 | |
| dc.date | 2001-10-10 | |
| dc.date.accessioned | 2026-07-07T04:41:12Z | |
| dc.date.available | 2026-07-07T04:41:12Z | |
| dc.description | Let $D_j\subset\Bbb C^{k_j}$ be a pseudoconvex domain and let $A_j\subset D_j$ be a locally pluripolar set, $j=1,...,N$. Put$$X:=\bigcup_{j=1}^N A_1\times...\times A_{j-1}\times D_j\times A_{j+1}\times...\times A_N\subset\Bbb C^{k_1+...+k_N}.$$Let $U$ be an open connected neighborhood of $X$ and let $M\varsubsetneq U$ be an analytic subset. Then there exists an analytic subset $\hat M$ of the `envelope of holomorphy' $\hat X$ of $X$ with $\hat M\cap X\subset M$ such that for every function $f$ separately holomorphic on $X\setminus M$ there exists an $\hat f$ holomorphic on $\hat X\setminus\hat M$ with $\hat f|_{X\setminus M}=f$. The result generalizes special cases which were studied in \cite{Ökt 1998}, \cite{Ökt 1999}, \cite{Sic 2000}, and \cite{Jar-Pfl 2001}. | |
| dc.description | 20 pages; This a new version of the paper (including "An extension theorem for separately holomorphic functions with singularities, II") | |
| dc.identifier | https://arxiv.org/abs/math/0104089 | |
| dc.identifier | http://arxiv.org/abs/math/0104089 | |
| dc.identifier | Ann. Polon. Math. 80 (2003), 143-161. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/61261 | |
| dc.subject | Complex Variables | |
| dc.subject | 32D15; 32D10 | |
| dc.title | An extension theorem for separately holomorphic functions with singularities | |
| dc.type | text |