Arkiv för Matematik

Asymptotic values of strongly normal functions

Karl F. Barth and Philip J. Rippon

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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

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.afm/1485898869

Digital Object Identifier
doi:10.1007/BF02383611

Mathematical Reviews number (MathSciNet)
MR2134699

Zentralblatt MATH identifier
1114.30035

Rights
2005 © Institut Mittag-Leffler

Citation

Barth, Karl F.; Rippon, Philip J. Asymptotic values of strongly normal functions. Ark. Mat. 43 (2005), no. 1, 69--84. doi:10.1007/BF02383611. https://projecteuclid.org/euclid.afm/1485898869


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