Spectral theory of differential operators opening theorems

This thesis consists of four chapters. In the first chapter, some concepts which are used in this thesis are given and some fundamental properties of Sturm Liouville operator are examined. In the second chapter, the Sturm-Liouville operator for Oscillation Theory has been investigated. The first and second comparison theorems and Sturm Oscillation theorem and General oscillation theorem have been investigated. In the third chapter, Integral equations and finite difference method and expansion theorem have been mentioned and the expansion theorem's evidence has been taken. In the fourth chapter, Fourier-Bessel expansion examined.