Spectral analysis of self-adjoint second order differential operators

A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in ful lment of the requirements for the degree of Master of Science. Johannesburg, March 2015.The primary purpose of this study is to investigate the asymptotic distribution of the eigenvalues of self-adjoint second order di erential operators. We rst analyse the problem where the functions g and h are equal to zero. To improve on the terms of the eigenvalue problem for g; h = 0, we consider the eigenvalue problem for general functions g and h. Here we calculate explicitly the rst four terms of the eigenvalue asymptotics problem