Geodesic
A characterization of holomorphic germs on compact perfect sets
Commentationes Mathematicae Universitatis Carolinae, Tome 45 (2004) no. 3, pp. 483-490.

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Let $K\subseteq\Bbb C$ be a perfect compact set, $E$ a quasi-complete locally convex space over $\Bbb C$ and $f:K\to E$ a map. In this note we give a necessary and sufficient condition --- in terms of differential quotients --- for $f$ to have a holomorphic extension on a neighborhood of $K$.
Classification : 30B40, 46G20, 46J15, 46J40
Keywords: differential quotients; holomorphic extensions 
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     title = {A characterization of holomorphic germs on compact perfect sets},
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Carboni, Graciela; Larotonda, Angel. A characterization of holomorphic germs on compact perfect sets. Commentationes Mathematicae Universitatis Carolinae, Tome 45 (2004) no. 3, pp. 483-490. http://geodesic.mathdoc.fr/item/CMUC_2004__45_3_a8/