Single-valued conjugates and holomorphic extendibility

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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 gA (bD) the harmonic extension of Re() to D has a single-valued conjugate.

Document Type: Research Article

Publication date: May 1, 2006

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