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Approximation of a Function and its Derivatives by Entire Functions
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- Journal:
- Canadian Mathematical Bulletin / Volume 59 / Issue 1 / 01 March 2016
- Published online by Cambridge University Press:
- 20 November 2018, pp. 87-94
- Print publication:
- 01 March 2016
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- Article
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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.
