All ETDs from UAB

Advisory Committee Chair

Rudi Weikard

Advisory Committee Members

Shangbing Ai

Ian Knowles

Ilias Perakis

Yuanzhen Shao

Document Type


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