1 M ay 2 00 7 BOUNDARY CROSS THEOREM IN DIMENSION 1 WITH SINGULARITIES
نویسنده
چکیده
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) = ∅. We determine the “envelope of holomorphy” Ŵ \ 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 Ŵ \ M.
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تاریخ انتشار 2008