Advisory Committee Chair
Advisory Committee Members
Date of Award
Degree Name by School
Doctor of Philosophy (PhD) College of Arts and Sciences
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
Bhardwaj, Varun, "Generalization of the Limit-Point & Limit-Circle Classification to Equations With Distributional Coefficients" (2023). All ETDs from UAB. 451.