The MacLane class and the Eremenko-Lyubich class
Complex Variables
2018-02-02 v1
Abstract
In 1970 G. R. MacLane asked if it is possible for a locally univalent function in the class 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 .
Cite
@article{arxiv.1611.03292,
title = {The MacLane class and the Eremenko-Lyubich class},
author = {Karl F. Barth and Philip J. Rippon and David J. Sixsmith},
journal= {arXiv preprint arXiv:1611.03292},
year = {2018}
}