Per citar aquest document: http://ddd.uab.cat/record/21996
Meromorphic extendibility and the argument principle
Globevnik, J. (University of Ljubljana. Institute of Mathematics, Physics and Mechanics)

Data: 2008
Resum: 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 ∆.
Drets: Tots els drets reservats.
Llengua: Anglès.
Document: article ; recerca ; publishedVersion
Publicat a: Publicacions Matemàtiques, V. 52 n. 1 (2008) p. 171-188, ISSN 0214-1493

DOI: 10.5565/PUBLMAT_52108_08


18 p, 184.1 KB

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