The Open UniversitySkip to content
 

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.

Full text available as:
[img]
Preview
PDF (Version of Record) - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
Download (477kB) | Preview
DOI (Digital Object Identifier) Link: https://doi.org/10.5186/aasfm.2017.4252
Google Scholar: Look up in Google Scholar

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.

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: 17 Sep 2019 06:07
URI: http://oro.open.ac.uk/id/eprint/48828
Share this page:

Metrics

Altmetrics from Altmetric

Citations from Dimensions

Download history for this item

These details should be considered as only a guide to the number of downloads performed manually. Algorithmic methods have been applied in an attempt to remove automated downloads from the displayed statistics but no guarantee can be made as to the accuracy of the figures.

Actions (login may be required)

Policies | Disclaimer

© The Open University   contact the OU