Fréchet-valued Analytic Functions and Linear Topological Invariants

Nguyen Van Dong and Nguyen Thai Son

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:

• Compressed PostScript file (92 kilobytes)
• PDF file (176 kilobytes)