Spectral properties of second order discrete differential equation

There are two different variables in mathematics, continuous variable and discrete variable. Continuous variable is considered when the universal set is real numbers, and the discrete variable is considered if the universal set is integers. From this point of view, although many studies have been done for the continuous variable, studies in the case of discrete variables, especially in spectral theory, are partially insufficient. Especially one of these studies is the solution of the inverse problem for the Sturm-Lioville equation. Studies described as finding eigenvalues of Sturm-Liouville Problems and eigenfunctions corresponding to these eigenvalues are important.