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Search: MSC category 30E10 ( Approximation in the complex domain )

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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 2007 (vol 50 pp. 123)

Nikolov, Nikolai; Pflug, Peter
Simultaneous Approximation and Interpolation on Arakelian Sets
We extend results of P.~M. Gauthier, W. Hengartner and A.~A. Nersesyan on simultaneous approximation and interpolation on Arakelian sets.

Keywords:Arakelian's theorem,, Arakelian sets

3. CMB 2001 (vol 44 pp. 420)

Gauthier, P. M.; Pouryayevali, M. R.
Approximation by Meromorphic Functions With Mittag-Leffler Type Constraints
Functions defined on closed sets are simultaneously approximated and interpolated by meromorphic functions with prescribed poles and zeros outside the set of approximation.

Categories:30D30, 30E10, 30E15

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

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