Variations on a theme of Carathéodory
Edoardo Vesentini (1979)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Edoardo Vesentini (1979)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Edoardo Vesentini (1981)
Compositio Mathematica
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Sean Dineen (1973)
Annales de l'institut Fourier
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In this article we discuss the relationship between domains of existence domains of holomorphy, holomorphically convex domains, pseudo convex domains, in the context of locally convex topological vector spaces. By using the method of Hirschowitz for and the method used for Banach spaces with a basis we prove generalisations of the Cartan-Thullen-Oka-Norguet-Bremmerman theorem for finitely polynomially convex domains in a variety of locally convex spaces which include the following: ...
Seán Dineen (1970)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Seán Dineen, Luiza A. Moraes (1992)
Revista Matemática de la Universidad Complutense de Madrid
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In this article we show that a number of apparently different properties coincide on the set of holomorphic functions on a strict inductive limit (all inductive limits are assumed to be countable and proper) of Banach spaces and that they are all satisfied only in the trivial case of a strict inductive limit of finite dimensional spaces. Thus the linear properties of a strict inductive limit of Banach spaces rarely translate themselves into holomorphic properties.
Bui Dac Tac (1991)
Annales Polonici Mathematici
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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...
Filippo Bracci (1998)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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