A spectral analysis for self-adjoint operators generated by a class of second order difference equations (Q1916714)

The equation \(-a_ny_{n+1} + b_ny_n-a_{n-1} y_{n-1} = zw_ny_n\) is said to be a limit point if for some value of \(z\), there is a solution \(\{y_n(z)\} \in \ell^2_w\); otherwise, the sequence is said to be a limit circle. The author obtains a qualitative spectral analysis of the self-adjoint realization of this equation [which of course is entirely discrete] with the help of the above mentioned classifications.