Date of Award
5-2025
Document Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Mathematical Sciences
Committee Chair/Advisor
Mishko Mitkovski
Committee Member
Cody Stockdale
Committee Member
Martin Schmoll
Committee Member
Shitao Liu
Abstract
Many physical systems, whether they are ocean waves or particles moving through space, can be described using the mathematical language of “partial differ- ential equations.” In many circumstances, it is useful to study how these equations amplify an input to the equation, in which case the amplification factor is called an “eigenvalue.” The usefulness of these amplification factors is that they can be used to describe properties of the physical system. In this dissertation, I have studied this amplification factor for a related set of equations called “Toeplitz operators.” In par- ticular, I have studied eigenvalues using statistical techniques. The methods I have used to develop these results are novel and improve on existing methods.
Recommended Citation
Camper, Trevor, "The Spectral Asymptotics of Toeplitz Operators on Hilbert Spaces of Analytic Functions" (2025). All Dissertations. 3912.
https://open.clemson.edu/all_dissertations/3912