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The MacLane class and the Eremenko-Lyubich class

Barth, Karl F.; Rippon, Philip J. and Sixsmith, David J. (2017). The MacLane class and the Eremenko-Lyubich class. Annales Academiae Scientiarum Fennicae Mathematica, 42 pp. 859–873.

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In 1970 G. R. MacLane asked if it is possible for a locally univalent function in the class A to have an arc tract. This question remains open, but several results about it have been given. We significantly strengthen these results, in particular replacing the condition of local univalence by the more general condition that the set of critical values is bounded. Also, we adapt a recent powerful technique of C. J. Bishop in order to show that there is a function in the Eremenko-Lyubich class for the disc that is not in the class A.

Item Type: Journal Item
Copyright Holders: 2017 Academia Scientiarum Fennica
ISSN: 1798-2383
Keywords: MacLane class; Eremenko-Lyubich class; asymptotic value; arc tract
Academic Unit/School: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
Item ID: 48828
Depositing User: Philip Rippon
Date Deposited: 06 Mar 2017 16:26
Last Modified: 03 Jun 2020 07:39
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