Geodesic
Luzin-type Holomorphic Approximation on Closed Subsets of Open Riemann Surfaces
Canadian mathematical bulletin, Tome 60 (2017) no. 2, pp. 300-308

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DOI

It is known that if $E$ is a closed subset of an open Riemann surface $R$ and $f$ is a holomorphic function on a neighbourhood of $E$ , then it is “usually” not possible to approximate $f$ uniformly by functions holomorphic on all of $R$ . We show, however, that for every open Riemann surface $R$ and every closed subset $E\subset R$ , there is closed subset $F\subset E$ that approximates $E$ extremely well, such that every function holomorphic on $F$ can be approximated much better than uniformly by functions holomorphic on $R$ .
DOI : 10.4153/CMB-2016-053-8
Mots-clés : 30E15, 30F99, Carleman approximation, tangential approximation, Myrberg surface 
Gauthier, Paul M.; Sharifi, Fatemeh. Luzin-type Holomorphic Approximation on Closed Subsets of Open Riemann Surfaces. Canadian mathematical bulletin, Tome 60 (2017) no. 2, pp. 300-308. doi: 10.4153/CMB-2016-053-8
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     author = {Gauthier, Paul M. and Sharifi, Fatemeh},
     title = {Luzin-type {Holomorphic} {Approximation} on {Closed} {Subsets} of {Open} {Riemann} {Surfaces}},
     journal = {Canadian mathematical bulletin},
     pages = {300--308},
     year = {2017},
     volume = {60},
     number = {2},
     doi = {10.4153/CMB-2016-053-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2016-053-8/}
}
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