PORTUGALIAE MATHEMATICA Vol. 55, No. 1, pp. 101112 (1998) 

Fréchetvalued Analytic Functions and Linear Topological InvariantsNguyen Van Dong and Nguyen Thai SonDepartment 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. Full text of the article:
Electronic version published on: 29 Mar 2001. This page was last modified: 27 Nov 2007.
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