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# Meromorphic functions with prescribed asymptotic behaviour, zeros and poles and applications in complex approximation

Published:1999-02-01
Printed: Feb 1999
• A. Sauer
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## Abstract

We construct meromorphic functions with asymptotic power series expansion in $z^{-1}$ at $\infty$ on an Arakelyan set $A$ having prescribed zeros and poles outside $A$. We use our results to prove approximation theorems where the approximating function fulfills interpolation restrictions outside the set of approximation.
 Keywords: asymptotic expansions, approximation theory
 MSC Classifications: 30D30 - Meromorphic functions, general theory 30E10 - Approximation in the complex domain 30E15 - Asymptotic representations in the complex domain