Michal Johanis
A remark on the approximation theorems of Whitney and Carleman-Scheinberg

Comment.Math.Univ.Carolin. 56,1 (2015) 1-6.

Abstract: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.

Keywords: approximation; real-analytic; entire functions

DOI: DOI 10.14712/1213-7243.015.101
AMS Subject Classification: 41A30 46T20 46T25