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.

DOI: https://doi.org/10.5186/aasfm.2017.4252

Abstract

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.

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About

• Item ORO ID
• 48828
• Item Type
• Journal Item
• ISSN
• 1798-2383
• Keywords
• MacLane class; Eremenko-Lyubich class; asymptotic value; arc tract
• Academic Unit or School
• Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
  Faculty of Science, Technology, Engineering and Mathematics (STEM)
• Copyright Holders
• © 2017 Academia Scientiarum Fennica
• Depositing User
• Philip Rippon