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arXiv · 2301.09302

Spectrum and Fine Spectrum of Band Matrices Generated by Oscillatory Sequences

Jyoti Rani·Arnab Patra·P D Srivastava
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Abstract

In this paper, a new class of band matrices is considered where the entries of each non-zero band form a sequence with two limit points. The compact perturbation technique is used to study the spectrum over the $\ell_{p}, (1<p<\infty)$ sequence space. Several spectral subdivisions such as fine spectrum, discrete spectrum, essential spectrum, etc. are obtained. In addition, a few sufficient conditions on the absence of point spectrum over the essential spectrum are also discussed.

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Jyoti Rani, Arnab Patra, P D Srivastava. 2023-01-23. Spectrum and Fine Spectrum of Band Matrices Generated by Oscillatory Sequences. https://arxiv.org/abs/2301.09302

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