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Asymptotic values of strongly normal functions

Authors:

Institution:

(1) Department of Mathematics, Syracuse University, 13244 Syracuse, NY, USA;(2) Department of Pure Mathematics, The Open University, Walton Hall, MK7 6AA Milton Keynes, UK

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. Dedicated to the memory of Professor Matts Essén

Keywords:

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