Extensions of holomorphic maps through hypersurfaces and relations to the Hartogs extensions in infinite dimension |
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| Authors: | Do Duc Thai Nguyen Thai Son |
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| Affiliation: | Department of Mathematics, Vietnam National University, Institute of Pedagogy, Cau Giay - Tu Liem, Hanoi, Vietnam ; Department of Mathematics, Vietnam National University, Institute of Pedagogy, Cau Giay - Tu Liem, Hanoi, Vietnam |
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| Abstract: | A generalization of Kwack's theorem to the infinite dimensional case is obtained. We consider a holomorphic map  from    into  , where  is a hypersurface in a complex Banach manifold  and  is a hyperbolic Banach space. Under various assumptions on  ,  and  we show that  can be extended to a holomorphic map from  into  . Moreover, it is proved that an increasing union of pseudoconvex domains containing no complex lines has the Hartogs extension property. |
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