Spectral analysis of operators generated by quantum difference equations

This thesis consists of four chapters. The first chapter is devoted to the introduction. In the second chapter, some well known definitions and theorems of functional analysis and spectral theory are mentioned, required preliminary informations of differential equations are given. The third chapter consists of three sections, In the first section, the q-difference operator T is defined in l^2 (q^Z ) Hilbert space which is generated by the q-difference equation and Jost solutions of this operator is introduced. In the second section, resolvent and spectrum of the operator T are obtained. In the third chapter, eigenvalues and spectral singularities of T are studied. The fourth and last chapter is devoted to the conclusion and suggestions.