Arkiv för Matematik

, Volume 43, Issue 1, pp 69–84 | Cite as

Asymptotic values of strongly normal functions

  • Karl F. Barth
  • Philip J. Rippon


Letf be meromorphic in the open unit discD and strongly normal; that is,
$$(1 - |z|^2 )f^\# (z) \to 0as|z| \to 1,$$

Wheref# denotes the spherical derivative off. We prove results about the existence of asymptotic values off at points ofC=∂D. For example,f has asymptotic values at an uncountably dense subset ofC, and the asymptotic values off form a set of positive linear measure.


Normal Function Open Unit Dense Subset Linear Measure Spherical Derivative 
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Copyright information

© Institut Mittag-Leffler 2005

Authors and Affiliations

  • Karl F. Barth
    • 1
  • Philip J. Rippon
    • 2
  1. 1.Department of MathematicsSyracuse UniversitySyracuseUSA
  2. 2.Department of Pure MathematicsThe Open UniversityMilton KeynesUK

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