Arkiv för Matematik

Asymptotic values of strongly normal functions

Karl F. Barth and Philip J. Rippon

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

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


Dedicated to the memory of Professor Matts Essén

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Ark. Mat., Volume 43, Number 1 (2005), 69-84.

Received: 12 June 2003
First available in Project Euclid: 31 January 2017

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2005 © Institut Mittag-Leffler


Barth, Karl F.; Rippon, Philip J. Asymptotic values of strongly normal functions. Ark. Mat. 43 (2005), no. 1, 69--84. doi:10.1007/BF02383611.

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