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Search: All articles in the CMB digital archive with keyword Carleman

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1. CMB 2015 (vol 59 pp. 87)

Gauthier, Paul M.; Kienzle, Julie
 Approximation of a Function and its Derivatives by Entire Functions 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 $\epsilon,$ there is an entire function $g,$ such that $|g^{(i)}(x)-f^{(i)}(x)|\lt \epsilon(x),$ for all $x\in\mathbb{R}$ and for each $i=0,1\dots,m.$ We also consider the situation, where $\mathbb{R}$ is replaced by an open interval. Keywords:Carleman theoremCategory:30E10

2. CMB 2002 (vol 45 pp. 80)

Gauthier, P. M.; Zeron, E. S.
 Approximation On Arcs and Dendrites Going to Infinity in $\C^n$ On a locally rectifiable arc going to infinity, each continuous function can be approximated by entire functions. Keywords:tangential approximation, CarlemanCategories:32E30, 32E25
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