Boundary cross theorem in dimension 1 with singularities

Details Boundary cross theorem in dimension 1 with singularities Boundary cross theorem in dimension 1 with singularities

2007-05-31

arxiv.org/abs/0705.4649v1

Mathematics

Complex Variables

Preprint of the ICTP, Trieste-Italy (2007). 18 pages

Scientific paper

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 $\hat{W\setminus M}.$

Affiliated with

Also associated with

No associations

Rating

Boundary cross theorem in dimension 1 with singularities does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Boundary cross theorem in dimension 1 with singularities, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Boundary cross theorem in dimension 1 with singularities will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-289315