A boundary cross theorem for separately holomorphic functions

Details A boundary cross theorem for separately holomorphic functions A boundary cross theorem for separately holomorphic functions

2004-11-30

arxiv.org/abs/math/0411657v1

Mathematics

Complex Variables

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

A boundary cross theorem for separately holomorphic functions 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 A boundary cross theorem for separately holomorphic functions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A boundary cross theorem for separately holomorphic functions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-14198