The argument principle and holomorphic extendibility

(ProQuest: ... denotes formulae and/or non-USASCII text omitted; see image) LetD be a bounded domain in the complex plane whose boundary consists of finitely many pairwise disjoint simple closed curves. GivebD the standard orientation, and letA(D) be the algebra of all continuous functions on... whi...

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Bibliographic Details
Published in:Journal d'analyse mathématique (Jerusalem) 2004-01, Vol.94 (1), p.385-395
Main Author: Globevnik, Josip
Format: Article
Language:English
Subjects:
Continuity (mathematics)
Mathematical analysis
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Summary:(ProQuest: ... denotes formulae and/or non-USASCII text omitted; see image) LetD be a bounded domain in the complex plane whose boundary consists of finitely many pairwise disjoint simple closed curves. GivebD the standard orientation, and letA(D) be the algebra of all continuous functions on... which are holomorphic onD. We prove that a continuous functionf onbD extends to a function inA(D) if and only if for eachgA(D) such thatf+g[not =]0 onbD, the change of argument off+g alongbD is nonnegative.[PUBLICATION ABSTRACT]
ISSN:0021-7670
1565-8538
DOI:10.1007/BF02789056