2007/05/31 by Peter Pflug, Pflug, Peter, Viet-Anh Nguyen +1
Mathematics · #32D10 #32D15 #Complex Variables (math.CV) #FOS: Mathematics #math.CV #msc:32D10 #msc:32D15
paper · pdf · doi:10.48550/arxiv.0705.4649
Preprint of the ICTP, Trieste-Italy (2007). 18 pages
arxiv created 2007/05/31 · arxiv updated 2009/12/01
Let D and G be copies of the open unit disc in \C, let A (resp. B) be a measurable subset of ∂ D (resp. ∂ G), let W be the 2-fold cross ((D∪ A)× B)∪ (A×(B∪ G)), 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∩ (A× B)=\varnothing. We determine the "envelope of holomorphy" W∖ M of W∖ M in the sense that any function locally bounded on W∖ M, measurable on A× B, and separately holomorphic on ((A× G) ∪ (D× B))∖ M "extends" to a function holomorphic on W∖ M.