A SPECTRAL-ANALYSIS FOR SELF-ADJOINT OPERATORS GENERATED BY A CLASS OF 2ND-ORDER DIFFERENCE-EQUATIONS

A qualitative spectral analysis for a class of second order difference equations is given. Central to the analysis of equations in this clas s is the observation that real-valued solutions exhibit a type of stab le asymptotic behavior for certain real values of the spectral paramet er. This asymptotic behavior leads to the characterization of the limi t point and limit circle nature of these equations, and is used to sho w that a strong nonsubordinacy criterion is satisfied on subintervals of R for equations of limit point type. These subintervals are part of the absolutely continuous spectrum of the self-adjoint realization of these equations. By other means, the nature of the discrete spectrum for these self-adjoint realizations is also discussed. (C) 1996 Academ ic Press, Inc.