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Determination of the pluripolar hull of graphs of certain holomorphic functions

Armen Edigarian, Jan Wiegerinck (2004)

Annales de l’institut Fourier

Let A be a closed polar subset of a domain D in . We give a complete description of the pluripolar hull Γ D × * of the graph Γ of a holomorphic function defined on D A . To achieve this, we prove for pluriharmonic measure certain semi-continuity properties and a localization principle.

Division et extension dans des classes de Carleman de fonctions holomorphes

Vincent Thilliez (1998)

Banach Center Publications

Let Ω be a bounded pseudoconvex domain in n with C 1 boundary and let X be a complete intersection submanifold of Ω, defined by holomorphic functions v 1 , . . . , v p (1 ≤ p ≤ n-1) smooth up to ∂Ω. We give sufficient conditions ensuring that a function f holomorphic in X (resp. in Ω, vanishing on X), and smooth up to the boundary, extends to a function g holomorphic in Ω and belonging to a given strongly non-quasianalytic Carleman class l ! M l in Ω ¯ (resp. satisfies f = v 1 f 1 + . . . + v p f p with f 1 , . . . , f p holomorphic in Ω and l ! M l -regular in Ω ¯ ). The essential...

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