2007/03/25 by Peter Pflug, Pflug, Peter, Viêt‐Anh Nguyên +2
Mathematics · #32D10 #32D15 #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Geometry and complex manifolds #Holomorphic and Operator Theory #math.CV #msc:32D10 #msc:32D15
paper · pdf · doi:10.48550/arxiv.math/0703737
Arch. Math. (Basel), to appear, 12 pages
arxiv created 2007/03/25 · openalex publication_date 2007/03/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let D⊂ \Cn, G⊂ \Cm be open sets, let A (resp. B) be a subset of the boundary ∂ D (resp. ∂ G) and let W be the 2-fold boundary cross ((D∪ A)× B)∪ (A×(B∪ G)). An open subset X⊂\Cn+m is said to be the ``envelope of holomorphy" of W if it is, in some sense, the maximal open set with the following property: Any function locally bounded on W and separately holomorphic on (A× G) ∪ (D× B) "extends" to a holomorphic function defined on X which admits the boundary values f a.e. on W. In this work we will determine the envelope of holomorphy of some boundary crosses.