Academic Paper from the year 2019 in the subject Mathematics - Analysis, grade: A, , course: pure mathematics, language: English, abstract: The study of difference equations has avast history especially in relation to Sturm-Lioville equations and their discrete counterparts, Jacobi matrices, which have been analyzed using similar and related methods.However much is needed to be done in terms of spectral theory in the discrete setting. Therefore, in this study, we approximate the eigenvalues and establish the dichotomy condition of a Fourth Order Difference equation with Unbounded Co -efficients on a Hilbert Space.