Boundary cross theorem in dimension 1 with singularities
| dc.creator | Pflug, Peter | |
| dc.creator | Nguyen, Viet-Anh | |
| dc.date | 2007-05-31 | |
| dc.date.accessioned | 2026-07-07T08:03:46Z | |
| dc.date.available | 2026-07-07T08:03:46Z | |
| dc.description | Let $D$ and $G$ be copies of the open unit disc in $\C,$ let $A$ (resp. $B$) be a measurable subset of $\partial D$ (resp. $\partial G$), let $W$ be the 2-fold cross $\big((D\cup A)\times B\big)\cup \big(A\times(B\cup G)\big),$ and let $M$ be a relatively closed subset of $W.$ Suppose in addition that $A$ and $B$ are of positive one-dimensional Lebesgue measure and that $M$ is fiberwise polar (resp. fiberwise discrete) and that $M\cap (A\times B)=\varnothing.$ We determine the "envelope of holomorphy" $\hat{W\setminus M}$ of $W\setminus M$ in the sense that any function locally bounded on $W\setminus M,$ measurable on $A\times B,$ and separately holomorphic on $\big((A\times G) \cup (D\times B)\big)\setminus M$ "extends" to a function holomorphic on $\hat{W\setminus M}.$ | |
| dc.description | Preprint of the ICTP, Trieste-Italy (2007). 18 pages | |
| dc.identifier | https://arxiv.org/abs/0705.4649 | |
| dc.identifier | http://arxiv.org/abs/0705.4649 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/129701 | |
| dc.subject | Complex Variables | |
| dc.subject | 32D15; 32D10 | |
| dc.title | Boundary cross theorem in dimension 1 with singularities | |
| dc.type | text |