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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*
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.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1999

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