Extension theorems of Sakai type for separately holomorphic and meromorphic functions
نویسندگان
چکیده
منابع مشابه
Weierstrass Theorems and Rings of Holomorphic Functions
We organize this set of notes around a few theorems of Weierstrass. Write OCn for the sheaf of holomorphic functions on C. In the first three sections, we deduce the following “algebraic” results as consequences of the Weierstrass theorems: (i) for each open set Ω ⊂ C, the ring OCn(Ω) is not Noetherian, (ii) the local ring OCn,0 is factorial, (iii) the local ring OCn,0 is Noetherian. The two la...
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Using recent development in Poletsky theory of discs, we prove the following result: Let X, Y be two complex manifolds, let Z be a complex analytic space which possesses the Hartogs extension property, let A (resp. B) be a non locally pluripolar subset of X (resp. Y ). We show that every separately holomorphic mapping f : W := (A × Y ) ∪ (X × B) −→ Z extends to a holomorphic mapping f̂ on Ŵ := {...
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ژورنال
عنوان ژورنال: Annales Polonici Mathematici
سال: 2003
ISSN: 0066-2216,1730-6272
DOI: 10.4064/ap82-2-7