Meromorphic extendibility and the argument principle
Globevnik, Josip (University of Ljubljana. Institute of Mathematics, Physics and Mechanics)

Date:	2008
Abstract:	Let ∆ be the open unit disc in C. Given a continuous function ϕ: b∆ → C\{0} denote by W(ϕ) the winding number of ϕ around the origin. We prove that a continuous function f : b∆ → C extends meromorphically through ∆ if and only if there is a number N ∈ N ∪ {0} such that W(Pf + Q) ≥ −N for every pair P, Q of polynomials such that Pf + Q 6= 0 on b∆. If this is the case then the meromorphic extension has at most N poles in ∆.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Argument principle ; Meromorphic extensions
Published in:	Publicacions matemàtiques, V. 52 n. 1 (2008) p. 171-188, ISSN 2014-4350

Adreça alternativa: https://raco.cat/index.php/PublicacionsMatematiques/article/view/74469
DOI: 10.5565/PUBLMAT_52108_08

18 p, 184.1 KB

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