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

Spectrum and Fine Spectrum of Band Matrices Generated by Oscillatory Sequences