Critical points of discrete potentials in the plane and in space

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Trickey, Robert V. (2008) Critical points of discrete potentials in the plane and in space. PhD thesis, University of Nottingham.

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Abstract

This thesis looks at various problems relating to the value distribution of certain discrete potentials.

Chapter 1 - Background material is introduced, the motivation behind this work is explained, and existing results in the area are presented.

Chapter 2 - By using a method based on a result of Cartan, the existence of zeros is shown for potentials in both the complex plane and real space.

Chapter 3 - Using an argument of Hayman, we expand on an established result concerning these potentials in the complex plane. We also look at the consequences of a spacing of the poles.

Chapter 4 - We extend the potentials in the complex plane to a generalised form, and establish some value distribution results.

Chapter 5 - We examine the derivative of the basic potentials, and explore the assumption that it takes the value zero only finitely often.

Chapter 6 - We look at a new potential in real space which has advantages over the previously examined ones. These advantages are explained.

Appendix - The results of computer simulations relating to these problems are presented here, along with the programs used.

Item Type: Thesis (University of Nottingham only) (PhD)
Supervisors: Langley, J.K.
Subjects: Q Science > QA Mathematics > QA299 Analysis
Faculties/Schools: UK Campuses > Faculty of Science > School of Mathematical Sciences
Item ID: 14362
Depositing User: EP, Services
Date Deposited: 25 Jun 2014 09:21
Last Modified: 16 Dec 2017 01:47
URI: https://eprints.nottingham.ac.uk/id/eprint/14362

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