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

Anahtar Kelimeler:

Spectra, fine spectra, generalized difference operator, band matrix

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

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.

Keywords:

Spectra, fine spectra, generalized difference operator, band matrix,

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