Geodesic
Approximation of a Function and its Derivatives by Entire Functions
Canadian mathematical bulletin, Tome 59 (2016) no. 1, pp. 87-94

Voir la notice de l'article provenant de la source Cambridge University Press

A simple proof is given for the fact that for $m$ a non-negative integer, a function $f\,\in \,{{C}^{(m)}}\,(\mathbb{R})$ , and an arbitrary positive continuous function $\in$ , there is an entire function $g$ such that $\left| {{g}^{(i)}}(x)\,-\,{{f}^{(i)}}(x) \right|\,<\,\in (x)$ , for all $x\,\in \,\mathbb{R}$ and for each $i\,=\,0,\,1\,.\,.\,.\,,\,m$ . We also consider the situation where $\mathbb{R}$ is replaced by an open interval.
DOI : 10.4153/CMB-2015-060-5
Mots-clés : 30E10, Carleman theorem 
Gauthier, Paul M.; Kienzle, Julie. Approximation of a Function and its Derivatives by Entire Functions. Canadian mathematical bulletin, Tome 59 (2016) no. 1, pp. 87-94. doi: 10.4153/CMB-2015-060-5
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