On the extension of holomorphic functions on a locally convex space
Nguyen Van Khue (1983)
Annales Polonici Mathematici
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Nguyen Van Khue (1983)
Annales Polonici Mathematici
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Leopoldo Nachbin (1986)
Extracta Mathematicae
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Ralf Hollstein (1986)
Collectanea Mathematica
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Nguyen Dinh Lan (2000)
Publicacions Matemàtiques
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We study the structure of spaces of germs of holomorphic functions on compact sets in Fréchet spaces for (LB) as well as for (Ω,Ω).
N. Khue, B. Tac (1990)
Studia Mathematica
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Le Hai, Thai Quang (1996)
Colloquium Mathematicae
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Le Mau Hui, Khue, Nguyen Van Khue, Bui Quoc Hoan (2004)
Portugaliae Mathematica. Nova Série
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S. A. Shkarin (2006)
Studia Mathematica
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Herzog and Lemmert have proven that if E is a Fréchet space and T: E → E is a continuous linear operator, then solvability (in [0,1]) of the Cauchy problem ẋ = Tx, x(0) = x₀ for any x₀ ∈ E implies solvability of the problem ẋ(t) = Tx(t) + f(t,x(t)), x(0) = x₀ for any x₀ ∈ E and any continuous map f: [0,1] × E → E with relatively compact image. We prove the same theorem for a large class of locally convex spaces including: • DFS-spaces, i.e., strong duals of Fréchet-Schwartz...
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...
Seán Dineen (1975)
Bulletin de la Société Mathématique de France
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Dietmar Vogt (2013)
Annales Polonici Mathematici
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It is shown that every proper Fréchet space with weak*-separable dual admits uncountably many inequivalent Fréchet topologies. This applies, in particular, to spaces of holomorphic functions, solving in the negative a problem of Jarnicki and Pflug. For this case an example with a short self-contained proof is added.
Christopher Boyd (1993)
Revista Matemática de la Universidad Complutense de Madrid
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