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Academic Paper from the year 2018 in the subject Mathematics - Miscellaneous, grade: A, , course: PURE MATHEMATICS, language: English, abstract: Sturm-Lioville equations and their discrete counterparts, Jacobi matrices are analyzed using similar and related methods. However much is needed to be done in terms of spectral theory in the discrete setting.The objective of the study is to compute the deficiency indices, approximate the eigenvalues and establish the dichotomy condition of a Fourth Order Difference equation with Unbounded Coefficients on a Hilbert Space.