Affiliation:
1. School of Mathematics and Statistics, The Open University, Walton Hall, Milton Keynes MK7 6AA, UK
Abstract
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 a novel technique to obtain an upper bound for the growth of a positive harmonic function defined in a certain type of multiply connected domain, based on comparing the Harnack metric and hyperbolic metric, which gives a sharp estimate for the growth in many cases.
Dedicated to the memory of Paddy Barry.
Funder
Engineering and Physical Sciences Research Council
Publisher
Oxford University Press (OUP)
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