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Gol’dberg’s constants

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Abstract

We study two extremal problems of geometric function theory introduced by A. A. Gol’dberg in 1973. For one problem we find the exact solution, and for the second one we obtain partial results. In the process, we study the lengths of hyperbolic geodesics in the twice punctured plane, prove several results about them, and make a conjecture. Gol’dberg’s problems have important applications to control theory.

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Authors and Affiliations

  1. Mathematisches Seminar, Christian-Albrecht-Universität zu Kiel, Ludewig-Meyn-Strasse 4, 24098, Kiel, Germany

    Walter Bergweiler

  2. Department of Mathematics, Purdue University, West Lafayette, IN, 47907, USA

    Alexandre Eremenko

Authors
  1. Walter Bergweiler
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  2. Alexandre Eremenko
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Corresponding author

Correspondence to Walter Bergweiler.

Additional information

Dedicated to the memory of A. A. Gol’dberg

The first author was supported by the Deutsche Forschungsgemeinschaft, Be 1508/7-2, and the ESF Networking Programme HCAA.

The second author was supported by NSF grant DMS-1067886.

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Bergweiler, W., Eremenko, A. Gol’dberg’s constants. JAMA 119, 365–402 (2013). https://doi.org/10.1007/s11854-013-0012-3

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  • DOI: https://doi.org/10.1007/s11854-013-0012-3

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