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Approximation of a Function and its Derivatives by Entire Functions
Published online by Cambridge University Press: 20 November 2018
Abstract
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.
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- Copyright © Canadian Mathematical Society 2016
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