Spectral analysis of impulsive discrete sturm-liouville equations on the whole axis

This thesis consists of five chapters. The first chapter is devoted to the introduction. In the second chapter, some well known concepts of spectral analysis are mentioned and required preliminary informations of difference equations are given. In the third chapter, at first, general structure, history and the relation of difference equations between differential equations are given. Later, the difference equation a_{n-1}y_{n-1}+b_{n}y_{n}+a_{n}y_{n+1}=λy_{n} , n∈ℤ is introduced on the whole axis, where {a_{n}}_{n∈ℤ} , {b_{n}}_{n∈ℤ} are complex sequences, a_{n}≠0 for all n∈ℤ and λ=2cos z . The fourth chapter consists of three sections. In the first section, impulsive differential and impulsive difference equations with various interaction points are defined. In the second section, the impulsive Sturm-Liouville difference operator with a point interaction at n = 0 is investigated on the whole axis and its solutions are created. In the last section, the resolvent operator and continuous spectrum of the impulsive difference operator corresponding to the impulsive difference equation are found, eigenvalues and spectral singularities of this operator are investigated and some important results are obtained. The fifth and last chapter is devoted to the discussion and conclusion.