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 nonnegative
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 Category:30E10 

2. CMB 2007 (vol 50 pp. 123)
3. CMB 2001 (vol 44 pp. 420)
4. CMB 1998 (vol 41 pp. 473)
 Müller, Jürgen; Wengenroth, Jochen

Separating singularities of holomorphic functions
We present a short proof for a classical result on separating
singularities of holomorphic functions. The proof is based on the
open mapping theorem and the fusion lemma of Roth, which is a basic
tool in complex approximation theory. The same method yields
similar separation results for other classes of functions.
Categories:30E99, 30E10 
