Spectra of Upper Triangular Double-Band Matrices as Operators on the Sequence Space bv₀ with an Application to Atmospheric Physics

Abstract

This study investigates the spectrum and fine spectrum of the generalized difference operator   acting on the sequence space . Although previous research has explored similar operators, the specific spectral properties of  on  have not been fully established. This work extends the existing literature [5] by providing a detailed characterization of these spectral sets and offering a comparative analysis between the new results obtained for the upper triangular operator   and previous findings regarding the lower triangular operator  on the same space .This research connects these theoretical results to a practical challenge in atmospheric physics, specifically the vertical analysis of ozone distribution and the dynamics of the Ozone Hole. By leveraging the spectral properties of the generalized difference operator  within the space , we construct a mathematical framework capable of diagnosing density fluctuation and evaluating system stability. This application provides a practical context for our results, showing that the proposed operator is not only mathematically sound but also useful for describing complex environmental dynamics