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Regularity and fast escaping points of entire functions

Rippon, Philip Jonathan and Stallard, Gwyneth Mary (2014). Regularity and fast escaping points of entire functions. International Mathematics Research Notices, 2014(19) pp. 5203–5229.

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Let f be a transcendental entire function. The fast escaping set A(f), various regularity conditions on the growth of the maximum modulus of f, and also, more recently, the quite fast escaping set Q(f) have all been used to make progress on fundamental questions concerning the iteration of f. In this paper, we establish new relationships between these three concepts. We prove that a certain weak regularity condition is necessary and sufficient for Q(f)=A(f) and give examples of functions for which Q(f)≠A(f). We also apply a result of Beurling that relates the size of the minimum modulus of f to the growth of its maximum modulus in order to establish that a stronger regularity condition called log-regularity holds for a large class of functions, in particular for functions in the Eremenko–Lyubich class ℬ.

Item Type: Journal Item
Copyright Holders: 2013 The Authors
ISSN: 1687-0247
Project Funding Details:
Funded Project NameProject IDFunding Body
Baker's conjecture and Eremenko's conjecture: a unified approach.EP/H006591/1EPSRC (Engineering and Physical Sciences Research Council)
Academic Unit/School: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
Item ID: 37989
Depositing User: Philip Rippon
Date Deposited: 11 Jul 2013 10:08
Last Modified: 25 Jun 2020 21:05
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