Home > Articles > Published articles > Meromorphic extendibility and the argument principle |
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 |
18 p, 184.1 KB |