Sturm-Liouville operators and Jacobi matrices have so far been developed in parallel for many years. A result in one field usually leads to a result in the other. However not much in terms of spectral theory has been done in the discrete setting compared to the continuous version especially in higher order operators. The aim of the study is to compute the deficiency indices of Fourth order difference operator. The results obtained show that under different asymptotic conditions,
the defL = (k; k) : 2 < k < 4.
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