Advisory Committee Chair
Rudi Weikard
Advisory Committee Members
Shangbing Ai
Ian Knowles
Ilias Perakis
Yuanzhen Shao
Document Type
Dissertation
Date of Award
2023
Degree Name by School
Doctor of Philosophy (PhD) College of Arts and Sciences
Abstract
This thesis aims to generalize the limit-point & limit-circle classification to a system with complex valued distributional coefficients and re-establish the relationship between the number of linearly independent square integrable solutions and the convergence of the circle consisting of Titchmarsh-Weyl m functions to a point or a circle in the complex plane. We begin by discussing linear relations, distributions of orders 0 and measures, and ordinary differential equations. Afterwards, we present some preliminary results that will help us generalize the classification of limit-points and limit-circles. With the preliminary results in hand, we develop the limit-point and limit-circle classification, following Weyl and Titchmarsh’s original approach. We conclude by examining the limit-point and limit-circle classification in the absence of existence and uniqueness theorem. ii
Recommended Citation
Bhardwaj, Varun, "Generalization of the Limit-Point & Limit-Circle Classification to Equations With Distributional Coefficients" (2023). All ETDs from UAB. 451.
https://digitalcommons.library.uab.edu/etd-collection/451
