Investigation of eigenvaluse and spectral singularities of impulsive difference equations

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. The third chapter consists of two sections. In the first section, general structure, history and the relation of difference equations between differential equations are given. In the second section, the Sturm-Liouville difference operator generated by the difference equation a_{n-1}y_{n-1}+b_{n}y_{n}+a_{n}y_{n+1}=λy_{n} , n∈ℤ is introduced in l₂(ℤ) Hilbert space, where {a_{n}}_{n∈ℤ},{b_{n}}_{n∈ℤ} are complex sequences and a_{n}>0 for all n∈ℤ In the fourth chapter, the impulsive Sturm-Liouville difference operator is defined, eigenvalues and spectral singularities of this operator are investigated and some results are obtained. The fifth and last chapter is devoted to the discussion and conclusion.