Geodesic
Uniform Approximation of Functions Continuous on a Compact Subset of $\mathbb C$ and Analytic in Its Interior by Functions Bianalytic in Its Neighborhoods
Matematičeskie zametki, Tome 69 (2001) no. 2, pp. 245-261.

Voir la notice de l'article provenant de la source Math-Net.Ru

We prove that an arbitrary function continuous on a compact set $X\subset\mathbb C$ and holomorphic in the interior of $X$ can be approximated by functions bianalytic in neighborhoods of $X$ with arbitrary accuracy. 
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M. Ya. Mazalov. Uniform Approximation of Functions Continuous on a Compact Subset of $\mathbb C$ and Analytic in Its Interior by Functions Bianalytic in Its Neighborhoods. Matematičeskie zametki, Tome 69 (2001) no. 2, pp. 245-261. http://geodesic.mathdoc.fr/item/MZM_2001_69_2_a8/

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