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.

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