On the spectrum of generalized difference matrix of order m over some sequence spaces

Spectral theory, one of the most important subjects of functional analysis and operator theory, is closely related to solution of many problems of physics, mechanics and mathematical physics. Spectral analysis of difference matrices is important in terms of applications of these problems. This study in which spectrum of generalized difference matrix of order m in some sequence spaces is examined consists of six chapters. In the first chapter, the historical process of the concept of spectrum and the literature review of studies related to the spectrum in sequence spaces were given, the purpose of research that is principal to this thesis was stated, and the obtained findings were briefly expressed. In the second chapter, the main definitions and theorems concerned with linear operators, matrix transformations, and the spectrum in sequence spaces were given. In the third chapter, the spectral analysis of generalized difference matrix of order m in the sequence spaces and was made. In the fourth chapter, the spectrum of the same matrix in the sequence space was examined. In the fifth chapter, the spectral values of the matrix which is obtained from the multiplication of generalized difference matrix of order with weighted mean matrix were researched. In the sixth chapter, the obtained results were summarized and the studies for later were mentioned.