Abstract
The primary objective of this chapter is to provide a literature review on spectral subdivisions of difference operators and compute the spectrum and the fine spectrum of third order difference operator \(\Delta ^3\) over the Banach space c. The generalized difference operator \(\Delta ^3:c\rightarrow c\) is defined by
It is presumed that \(x_n=0\) if \(n<0.\) The operator \(\Delta ^3\) represents a lower forth band infinite matrix. Finally, we find the estimates for the spectrum, the point spectrum, the residual spectrum and the continuous spectrum of the above operator over the Banach spaces \(c,c_0\) and \(\ell _1\).
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Dutta, H., Baliarsingh, P. (2020). On the Spectra of Difference Operators Over Some Banach Spaces. In: Dutta, H., Peters, J. (eds) Applied Mathematical Analysis: Theory, Methods, and Applications. Studies in Systems, Decision and Control, vol 177. Springer, Cham. https://doi.org/10.1007/978-3-319-99918-0_23
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