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

Published online by Cambridge University Press:  20 November 2018

A. Sauer
A. Sauer*
Affiliation:
Gerhard Mercator Universität, Fachbereich 11 Mathematik, Lotharstr. 65, D-47057 Duisburg, Germany email: sauer@math.uni-duisburg.de
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Abstract

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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

30D3030E1030E15asymptotic expansionsapproximation theory
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 51 , Issue 1 , 01 February 1999 , pp. 117 - 129
Copyright
Copyright © Canadian Mathematical Society 1999

References

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