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Archiv der Mathematik

, Volume 89, Issue 4, pp 326–338 | Cite as

Envelope of holomorphy for boundary cross sets

  • Peter Pflug
  • Viêt-Anh Nguyên
Article

Abstract.

Let \(D\subset{\mathbb{C}}^n, G\subset{\mathbb{C}}^m\) 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 \(((D\cup A)\times B) \cup (A \times (B \cup G))\). An open subset \(X \subset {{\mathbb{C}}^{n+m}}\) 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 \((A \times G) \cup (D \times B)\) “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.

Mathematics Subject Classification (2000).

Primary 32D15 32D10 

Keywords.

Boundary cross set envelope of holomorphy holomorphic extension plurisubharmonic measure 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2007

Authors and Affiliations

  1. 1.Institut für MathematikCarl von Ossietzky Universität OldenburgOldenburgGermany
  2. 2.Mathematics SectionThe Abdus Salam international centre for theoretical physicsTriesteItaly

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