On subharmonic and entire functions of small order: after Kjellberg
Complex Variables
2020-11-20 v1
Abstract
We give a general method for constructing examples of transcendental entire functions of given small order, which allows precise control over the size and shape of the set where the minimum modulus of the function is relatively large. Our method involves developing a new technique to give an upper bound for the growth of a positive harmonic function defined in a certain type of multiply connected domain, giving a sharp estimate for the growth in many cases.
Keywords
Cite
@article{arxiv.2011.09532,
title = {On subharmonic and entire functions of small order: after Kjellberg},
author = {Philip J. Rippon and Gwyneth M. Stallard},
journal= {arXiv preprint arXiv:2011.09532},
year = {2020}
}
Comments
20 pages