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Arkiv för Matematik

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

Asymptotic values of strongly normal functions

  • Karl F. Barth
  • Philip J. Rippon
Article
  • 44 Downloads

Abstract

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.

Keywords

Normal Function Open Unit Dense Subset Linear Measure Spherical Derivative 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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