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.
📌 3 Key Takeaways
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Objective & Hypothesis: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.
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Key Findings & Data:So far, the problem has been solved up to a maximum of 2 orders on the sequence space cs.
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Conclusion & Impact: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.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Spectra · fine spectra · generalized difference operator
Abstract
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.
DURNA, N., ÖZDEMİR, Ö. (2023). Spectral Decompositions of the Difference Operator Δ^m over the Sequence Space cs. Cumhuriyet Science Journal, Cilt: 44 - Sayı: 1, 181–187. https://ajindex.com/articles/885433
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