Open Access
2008 Meromorphic extendibility and the argument principle
Josip Globevnik
Publ. Mat. 52(1): 171-188 (2008).


Let $\Delta $ be the open unit disc in $\mathbb{C}$. Given a continuous function $\varphi \colon b\Delta \rightarrow \mathbb{C}\setminus \{ 0\}$ denote by $\mathcal{W} (\varphi )$ the winding number of $\varphi$ around the origin. We prove that a continuous function $f\colon b\Delta\rightarrow \mathbb{C}$ extends meromorphically through $\Delta $ if and only if there is a number $N\in \mathbb{N}\cup\{ 0\}$ such that $\mathcal{W} (Pf+Q)\geq -N$ for every pair $P$, $Q$ of polynomials such that $Pf+Q\not= 0$ on $b\Delta$. If this is the case then the meromorphic extension has at most $N$ poles in $\Delta$.


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Josip Globevnik. "Meromorphic extendibility and the argument principle." Publ. Mat. 52 (1) 171 - 188, 2008.


Published: 2008
First available in Project Euclid: 17 December 2007

zbMATH: 1149.30031
MathSciNet: MR2384845

Primary: 30E25

Keywords: Argument principle , meromorphic extensions.

Rights: Copyright © 2008 Universitat Autònoma de Barcelona, Departament de Matemàtiques

Vol.52 • No. 1 • 2008
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