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The argument principle and holomorphic extendibility

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Abstract

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\(\bar D\) which are holomorphic onD. We prove that a continuous functionf onbD extends to a function inA(D) if and only if for eachg∈A(D) such thatf+g≠0 onbD, the change of argument off+g alongbD is nonnegative.

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Authors and Affiliations

  1. Institute of Mathematics, Physics and Mechanics, University of Ljubljana, Ljubljana, Slovenia

    Josip Globevnik

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  1. Josip Globevnik
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Correspondence to Josip Globevnik.

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Globevnik, J. The argument principle and holomorphic extendibility. J. Anal. Math. 94, 385–395 (2004). https://doi.org/10.1007/BF02789056

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  • DOI: https://doi.org/10.1007/BF02789056

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