Doctor of Philosophy (PhD)
This dissertation is a compilation of three articles in the theory of distributions. Each essay focuses on a different technique or concept related to distributions.
The focus of the first essay is the concept of distributional point values. Distribu- tions are sometimes called generalized functions, as they share many similarities with ordi- nary functions, with some key differences. Distributional point values, among other things, demonstrate that distributions are even more akin to ordinary functions than one might think.
The second essay concentrates on two major topics in analysis, namely asymptotic expansions and the concept of moments. There are many variations of moment problems and we demonstrate how techniques from asymptotic analysis and the theory of distribu- tions can be used to study such problems.
The third essay presents several Tauberian theorems for smooth functions. Taube- rian theorems are theorems in analysis of a particular form. The first theorem of this type was proved by Alfred Tauber in 1897. These results are then applied to the division prob- lem for tempered distributions.
Kellinsky-Gonzalez, Kevin, "Some New Techniques and their Applications in the Theory of Distributions" (2023). LSU Doctoral Dissertations. 6206.