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April 2007 Generalization of a theorem of Gonchar
Peter Pflug, Viêt-Anh Nguyên
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Ark. Mat. 45(1): 105-122 (April 2007). DOI: 10.1007/s11512-006-0025-6

Abstract

Let X and Y be two complex manifolds, let DX and GY 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 ((DAB)∪(A×(BG)). 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 $\widehat{W}$.

Citation

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Peter Pflug. Viêt-Anh Nguyên. "Generalization of a theorem of Gonchar." Ark. Mat. 45 (1) 105 - 122, April 2007. https://doi.org/10.1007/s11512-006-0025-6

Information

Received: 14 October 2005; Revised: 16 May 2006; Published: April 2007
First available in Project Euclid: 31 January 2017

zbMATH: 1161.31005
MathSciNet: MR2312956
Digital Object Identifier: 10.1007/s11512-006-0025-6

Rights: 2007 © Institut Mittag-Leffler

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Vol.45 • No. 1 • April 2007
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