Geodesic
Runge's theorem for invariant spaces of analytic maps
Izvestiya. Mathematics , Tome 59 (1995) no. 2, pp. 387-400

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This article studies spaces of real-analytic maps that are closed in the topology of uniform convergence of all derivatives on compact sets and that are invariant with respect to some group of transformations. It is shown that maps in such spaces can be approximated by maps in the same space that are real-analytic in the whole domain. 
@article{IM2_1995_59_2_a7,
     author = {S. G. Merzlyakov},
     title = {Runge's theorem for invariant spaces of analytic maps},
     journal = {Izvestiya. Mathematics },
     pages = {387--400},
     publisher = {mathdoc},
     volume = {59},
     number = {2},
     year = {1995},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1995_59_2_a7/}
}
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S. G. Merzlyakov. Runge's theorem for invariant spaces of analytic maps. Izvestiya. Mathematics , Tome 59 (1995) no. 2, pp. 387-400. http://geodesic.mathdoc.fr/item/IM2_1995_59_2_a7/