Geodesic
A remark on the approximation theorems of Whitney and Carleman-Scheinberg
Commentationes Mathematicae Universitatis Carolinae, Tome 56 (2015) no. 1, pp. 1-6.

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We show that a $C^k$-smooth mapping on an open subset of $\mathbb R^n$, $k\in \mathbb N\cup\{0,\infty\}$, can be approximated in a fine topology and together with its derivatives by a restriction of a holomorphic mapping with explicitly described domain. As a corollary we obtain a generalisation of the Carleman-Scheinberg theorem on approximation by entire functions.
DOI : 10.14712/1213-7243.015.101
Classification : 41A30, 46T20, 46T25
Keywords: approximation; real-analytic; entire functions 
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Johanis, Michal. A remark on the approximation theorems of Whitney and Carleman-Scheinberg. Commentationes Mathematicae Universitatis Carolinae, Tome 56 (2015) no. 1, pp. 1-6. doi : 10.14712/1213-7243.015.101. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.015.101/

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