Envelope of holomorphy for boundary cross sets
| dc.creator | Pflug, Peter | |
| dc.creator | Nguyen, Viet-Anh | |
| dc.date | 2007-03-25 | |
| dc.date.accessioned | 2026-07-07T07:53:53Z | |
| dc.date.available | 2026-07-07T07:53:53Z | |
| dc.description | Let $D\subset \C^n,$ $G\subset \C^m$ be open sets, let $A$ (resp. $B$) be a subset of the boundary $\partial D$ (resp. $\partial G$) and let $W$ be the 2-fold boundary cross $((D\cup A)\times B)\cup (A\times(B\cup G)).$ An open subset $X\subset\C^{n+m} $ is said to be the ``envelope of holomorphy" of $W$ if it is, in some sense, the maximal open set with the following property: Any function locally bounded on $W$ and separately holomorphic on $(A\times G) \cup (D\times B)$ "extends" to a holomorphic function defined on $X$ which admits the boundary values $f$ a.e. on $W.$ In this work we will determine the envelope of holomorphy of some boundary crosses. | |
| dc.description | Arch. Math. (Basel), to appear, 12 pages | |
| dc.identifier | https://arxiv.org/abs/math/0703737 | |
| dc.identifier | http://arxiv.org/abs/math/0703737 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/126395 | |
| dc.subject | Complex Variables | |
| dc.subject | 32D15; 32D10 | |
| dc.title | Envelope of holomorphy for boundary cross sets | |
| dc.type | text |