Spectral Decompositions of the Difference Operator Δ^m over the Sequence Space cs

[摘要] This study aims to bring together some studies on the spectra of difference operators in the literature over the cs sequence space and to provide a basis for related problems. So far, the problem has been solved up to a maximum of 2 orders on the sequence space cs. In this article, we discuss the difference operator Δ^m, represented by a (m+1) banded matrix, which generalizes the difference operators of the form Δ, Δ^2, B(r,s) and B(r,s,t) and we will give its boundedness, spectrum, fine spectrum and some spectral separations over the sequence space cs.

[学科分类] 工程和技术（综合）

[关键词] Spectra;fine spectra;generalized difference operator;band matrix