Critical points of discrete potentials in the plane and in space
Publication Date
July 10, 2008
Creator
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
ethesis
Thesis Type
PhD
Supervisors
Subjects (LC)
Associated Schools / Departments
School of Mathematical Sciences (UK)
eprints ID
14362
UoN Repository URI
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ThesisMain_Trickey.pdf
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