On meromorphic extendibility
| dc.creator | Globevnik, Josip | |
| dc.date | 2008-10-03 | |
| dc.date.accessioned | 2026-07-07T10:07:27Z | |
| dc.date.available | 2026-07-07T10:07:27Z | |
| dc.description | Let D be a bounded domain in the complex plane whose boundary bD consists of finitely many pairwise disjoint real analytic simple closed curves. Let f be an integrable function on bD. In the paper we show how to compute the candidates for poles of a meromorphic extension of f through D and thus reduce the question of meromorphic extendibility to the question of holomorphic extendibility. Let A(D) be the algebra of all continuous functions on the closure of D which are holomorphic on D. For continuous functions f on bD we obtain a characterization of meromorphic extendibility in terms of the argument principle: f extends meromorphically through D if and only if there is a nonnegative integer N such that the winding number of Pf+Q along bD is bounded below by -N for all P, Q in A(D) such that Pf+Q has no zero on bD. If this is the case then the meromorphic extension of f has at most N poles in D, counting multiplicity. | |
| dc.description | 9 pages, to appear in J.Math.Anal.Appl | |
| dc.identifier | https://arxiv.org/abs/0810.0601 | |
| dc.identifier | http://arxiv.org/abs/0810.0601 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/170641 | |
| dc.subject | Complex Variables | |
| dc.title | On meromorphic extendibility | |
| dc.type | text |