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Extending holomorphic maps in infinite dimensions

Bui Dac Tac (1991)

Annales Polonici Mathematici

Studying the sequential completeness of the space of germs of Banach-valued holomorphic functions at a points of a metric vector space some theorems on extension of holomorphic maps on Riemann domains over topological vector spaces with values in some locally convex analytic spaces are proved. Moreover, the extendability of holomorphic maps with values in complete C-spaces to the envelope of holomorphy for the class of bounded holomorphic functions is also established. These results are known in...

Extension and restriction of holomorphic functions

Klas Diederich, Emmanuel Mazzilli (1997)

Annales de l'institut Fourier

Strong pathologies with respect to growth properties can occur for the extension of holomorphic functions from submanifolds D ' of pseudoconvex domains D to all of D even in quite simple situations; The spaces A p ( D ' ) : = 𝒪 ( D ' ) L p ( D ' ) are, in general, not at all preserved. Also the image of the Hilbert space A 2 ( D ) under the restriction to D ' can have a very strange structure.

Extension dans des classes de Hardy de fonctions holomorphes et estimations de type «mesures de Carleson» pour l’équation ¯

Anne Cumenge (1983)

Annales de l'institut Fourier

Nous montrons qu’une fonction holomorphe sur un sous-ensemble analytique transverse V d’un domaine D borné strictement pseudoconvexe de C n admet une extension dans H p ( D ) ( 1 p < + ) si et seulement si elle vérifie une condition de type L p à poids sur V  ; la démonstration est en partie basée sur la résolution de l’équation avec estimations de type “mesures de Carleson”.

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