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Single-valued conjugates and holomorphic extendibility

Published online by Cambridge University Press:  12 July 2007

Josip Globevnik
Josip Globevnik
Affiliation:
Institute of Mathematics, Physics and Mechanics, University of Ljubljana, Jadranska ul. 19, 1000 Ljubljana, Slovenia ([email protected])
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Abstract

Let D be a bounded domain in the complex plane whose boundary consists of m ≥ 2 pairwise disjoint simple closed curves and let A(bD) be the algebra of all continuous functions on bD which extend holomorphically through D. We show that a continuous function Φ on bD belongs to A(bD) if for each g ∈ A (bD) the harmonic extension of Re(gΦ) to D has a single-valued conjugate.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 136 , Issue 2 , April 2006 , pp. 347 - 350
Copyright
Copyright © Royal Society of Edinburgh 2006

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