Approximation of a Function and its Derivatives by Entire Functions
Canadian mathematical bulletin, Tome 59 (2016) no. 1, pp. 87-94
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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.
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
@article{10_4153_CMB_2015_060_5,
author = {Gauthier, Paul M. and Kienzle, Julie},
title = {Approximation of a {Function} and its {Derivatives} by {Entire} {Functions}},
journal = {Canadian mathematical bulletin},
pages = {87--94},
year = {2016},
volume = {59},
number = {1},
doi = {10.4153/CMB-2015-060-5},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2015-060-5/}
}
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%0 Journal Article %A Gauthier, Paul M. %A Kienzle, Julie %T Approximation of a Function and its Derivatives by Entire Functions %J Canadian mathematical bulletin %D 2016 %P 87-94 %V 59 %N 1 %U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2015-060-5/ %R 10.4153/CMB-2015-060-5 %F 10_4153_CMB_2015_060_5
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