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

Abstract

We show that a $C^k$-smooth mapping on an open subset 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