Generalization of a theorem of Gonchar

Peter Pflug Fachbereich Mathematik, Carl von Ossietzky Universität Oldenburg Viêt-Anh Nguyên Mathematics Section, The Abdus Salam international centre for theoretical physics

TBD mathscidoc:1701.333094

Arkiv for Matematik, 45, (1), 105-122, 2005.10
Let X and Y be two complex manifolds, let$D$⊂$X$and$G$⊂$Y$be two nonempty open sets, let$A$(resp.$B$) be an open subset of ∂$D$(resp. ∂$G$), and let$W$be the 2-fold cross (($D$∪$A$)×$B$)∪($A$×($B$∪$G$)). Under a geometric condition on the boundary sets$A$and$B$, we show that every function locally bounded, separately continuous on$W$, continuous on$A$×$B$, and separately holomorphic on ($A$×$G$)∪($D$×$B$) “extends” to a function continuous on a “domain of holomorphy” $\widehat{W}$ and holomorphic on the interior of $\widehat{W}$ .
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  title={Generalization of a theorem of Gonchar},
  author={Peter Pflug, and Viêt-Anh Nguyên},
  booktitle={Arkiv for Matematik},
Peter Pflug, and Viêt-Anh Nguyên. Generalization of a theorem of Gonchar. 2005. Vol. 45. In Arkiv for Matematik. pp.105-122.
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