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

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1. CMB Online first

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 theorem

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, Carleman
Categories:32E30, 32E25

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