Asymptotic values of strongly normal functions

Karl F. Barth; Philip J. Rippon

doi:10.1007/BF02383611

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Home > Journals > Ark. Mat. > Volume 43 > Issue 1 > Article

April 2005 Asymptotic values of strongly normal functions

Karl F. Barth, Philip J. Rippon

Author Affiliations +

Karl F. Barth,¹ Philip J. Rippon²
¹Department of Mathematics, Syracuse University
²Department of Pure Mathematics, The Open University

Ark. Mat. 43(1): 69-84 (April 2005). DOI: 10.1007/BF02383611

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Abstract

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.

Dedication

Dedicated to the memory of Professor Matts Essén

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Karl F. Barth. Philip J. Rippon. "Asymptotic values of strongly normal functions." Ark. Mat. 43 (1) 69 - 84, April 2005. https://doi.org/10.1007/BF02383611