APPLICATIONS OF THE LEVINSON THEOREM

Abstract

Abstract: The asymptotic theorem which provides the basis for the theory in this thesis was proved by Levinson and published in 1948. At that time, the theorem itself represented a considerable advance on existing related results but, in contrast, initial applications of the theorem were only of a very straightforward kind. It was not until some 25 years later that a real appreciation of the significance and range of applications of the theorem started to become evident through the work of Harris and Lutz (1974). The thesis consists of two chapters. Below a brief description of the contents of the thesis is given. In chapter one, we discuss the Levinson theorem and its proof, we state the Hartman -Wintner theorem, and Eastham theorem. Chapter two represents applications of the theory of chapter one.