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Spherical derivatives and normal families

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Abstract

We show that a family of functions meromorphic in a plane domain D whose spherical derivatives are uniformly bounded away from zero is normal. Furthermore, we show that for each f meromorphic in the unit disk D, inf z∈D f #(z) ≤ 1/2, where f # denotes the spherical derivative of f.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Würzburg, Würzburg, Germany

    Jürgen Grahl

  2. Department of Mathematics, Bar-Ilan University, Ramat-Gan, 52900, Israel

    Shahar Nevo

Authors
  1. Jürgen Grahl
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  2. Shahar Nevo
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Corresponding author

Correspondence to Jürgen Grahl.

Additional information

Part of this work was supported by the German Israeli Foundation for Scientific Research and Development (No. G 809-234.6/2003). Shahar Nevo also received support from the Israel Science Foundation, Grant No. 395/07. This research is part of the European Science Foundation Networking Programme HCAA.

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Grahl, J., Nevo, S. Spherical derivatives and normal families. JAMA 117, 119–128 (2012). https://doi.org/10.1007/s11854-012-0016-4

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  • DOI: https://doi.org/10.1007/s11854-012-0016-4

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