Geodesic
Uniform approximations by bianalytic functions on arbitrary compact subsets of~$\mathbb C$
Sbornik. Mathematics, Tome 195 (2004) no. 5, pp. 687-709

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Each continuous function on an arbitrary compact subset $X$ of $\mathbb C$ that is bianalytic in the interior of $X$ is proved to be uniformly approximable on $X$ by functions bianalytic in neighbourhoods of $X$. 
@article{SM_2004_195_5_a3,
     author = {M. Ya. Mazalov},
     title = {Uniform approximations by bianalytic functions on arbitrary compact subsets of~$\mathbb C$},
     journal = {Sbornik. Mathematics},
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     volume = {195},
     number = {5},
     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2004_195_5_a3/}
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M. Ya. Mazalov. Uniform approximations by bianalytic functions on arbitrary compact subsets of~$\mathbb C$. Sbornik. Mathematics, Tome 195 (2004) no. 5, pp. 687-709. http://geodesic.mathdoc.fr/item/SM_2004_195_5_a3/