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Single valued conjugates and holomorphic extendibility

Josip Globevnik
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Abstract

Let D be a bounded domain in the complex plane whose boundary consists of m pairwise disjoint simple closed curves where m is greater than one. Let A(bD) be the algebra of all continuous functions on bD which extend holomorphically through D. We show that a continuous function f on bD belongs to A(bD) if for each g in A(bD) the harmonic extension of Re(fg) to D has a single valued conjugate.

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Josip Globevnik. 2005-07-05. Single valued conjugates and holomorphic extendibility. https://arxiv.org/abs/math/0507100

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