Displaying similar documents to “Une nouvelle version du théorème d'extension de Hartogs pour les applications séparément holomorphes entre espaces analytiques”

Spaces of type H ∞ + C

Walter Rudin (1975)

Annales de l'institut Fourier

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A simple theorem is proved which states a sufficient condition for the sum ot two closed subspaces of a Banach space to be closed. This leads to several analogues of Sarason’s theorem which states that H ∞ + C is a closed subalgebra of L ∞ . In these analogues, the unit circle is replaces by other groups, and the unit disc is replaced by polydiscs or by balls in spaces of several complex variables. Sums of closed ideals in Banach algebras are also studied.

Propriétés d'extension et applications séparément holomorphes dans les espaces faiblement hyperboliques

Omar Alehyane, Hichame Amal (2003)

Annales Polonici Mathematici

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The goal of this paper is to study the relationship between the hyperbolicity of complex spaces, extension of holomorphic mappings and the Hartogs theorem for separately holomorphic mappings. We prove that a complex space with a weak hyperbolicity which has the 𝔻*-extension property has the Hartogs extension property. As a consequence we give a generalization of the big Picard theorem. Finally we generalize Terada's theorem for separately holomorphic mappings.