943 research outputs found

    Envelope of holomorphy for boundary cross sets

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    Let D\subset \C^n, G\subset \C^m be open sets, let AA (resp. BB) be a subset of the boundary ∂D\partial D (resp. ∂G\partial G) and let WW be the 2-fold boundary cross ((D∪A)×B)∪(A×(B∪G)).((D\cup A)\times B)\cup (A\times(B\cup G)). An open subset X\subset\C^{n+m} is said to be the ``envelope of holomorphy" of WW if it is, in some sense, the maximal open set with the following property: Any function locally bounded on WW and separately holomorphic on (A×G)∪(D×B)(A\times G) \cup (D\times B) "extends" to a holomorphic function defined on XX which admits the boundary values ff a.e. on W.W. In this work we will determine the envelope of holomorphy of some boundary crosses.Comment: Arch. Math. (Basel), to appear, 12 page
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