Portugaliæ Mathematica   EMIS ELibM Electronic Journals PORTUGALIAE
Vol. 55, No. 1, pp. 101-112 (1998)

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Fréchet-valued Analytic Functions and Linear Topological Invariants

Nguyen Van Dong and Nguyen Thai Son

Department of Mathematics, College of Education,
Vietnam National Univ. of Ho Chi Minh City, 280 An Duong Vuong, District 5 - VIETNAM

Abstract: Let $E$, $F$ be Fréchet spaces and $D$ an open set in $E$. The main aim of this paper is to prove that every analytic function $f: D\to F$ (resp. $f: D\to\calc{H}(F')$ where $F$ is Montel) which is weakly analytically extended to $\Omega$ is analytically extended to $\Omega$ when $\dim E<\infty$ and $F\in(\DN)$ (resp. $F\in\overline\DN$). Moreover it also shows that every function on $D\times G$ which is holomorphic in $z\in D$ and weakly analytic in $x\in D$ is analytic.

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