A boundary cross theorem for separately holomorphic functions
| dc.creator | Nguyen, Peter Pflug Viet-Anh | |
| dc.date | 2004-11-30 | |
| dc.date.accessioned | 2026-07-07T05:14:49Z | |
| dc.date.available | 2026-07-07T05:14:49Z | |
| dc.description | Let $D\subset \C^n,$ $G\subset \C^m$ be pseudoconvex domains, let $A$ (resp. $B$) be an open subset of the boundary $\partial D$ (resp. $\partial G$) and let $X$ be the 2-fold cross $((D\cup A)\times B)\cup (A\times(B\cup G)).$ Suppose in addition that the domain $D$ (resp. $G$) is {\it locally $\mathcal{C}^2$ smooth on $A$} (resp. $B$). We shall determine the "envelope of holomorphy" $\hat{X}$ of $X$ in the sense that any function continuous on $X$ and separately holomorphic on $(A\times G) \cup (D\times B)$ extends to a function continuous on $\hat{X}$ and holomorphic on the interior of $\hat{X}.$ A generalization of this result for an $N$-fold cross is also given. | |
| dc.identifier | https://arxiv.org/abs/math/0411657 | |
| dc.identifier | http://arxiv.org/abs/math/0411657 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/73425 | |
| dc.subject | Complex Variables | |
| dc.subject | 32D15 32D10 | |
| dc.title | A boundary cross theorem for separately holomorphic functions | |
| dc.type | text |