Characterization of orthogonal polynomials with the help of a matrix approach

This thesis consists of five chapters. First chapter is devoted to the introduction. In this chapter some fundamental information about orthogonal polynomials are given. In the second chapter, the moment functional and orthogonality are mentioned and definitions and theorems about the existence of orthogonal polynomial sequences are given. Then, the three-term recurrence relation is investigated. In the third chapter, some definitions and basic properties of infinite lower semi-matrices are mentioned. In the fourth chapter, definitions and theorems about polynomial sequences are given, and the relations between orthogonal polynomial sequences with the matrices corresponding to these polynomial sequences and the relations between classical orthogonal polynomial sequences with the matrices corresponding to these polynomial sequences are discussed. The final chapter is introduced to the conclusion.