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

摘要

We show that a $C^k$-smooth mapping on an open subset of $mathbb R^n$, $kin mathbb Ncup{0,infty}$, 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.