A Spectral Analysis for Self-adjoint Operators Generated by a Class of Second 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 class is the observation that real-valued solutions exhibit a type of stable asymptotic behavior for certain real values of the spectral parameter. This asymptotic behavior leads to the characterization of the limit point and limit circle nature of these equations, and is used to show that a strong nonsubordinacy criterion is satisfied on subintervals offor 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.
S. L. Clark, "A Spectral Analysis for Self-adjoint Operators Generated by a Class of Second Order Difference Equations," Journal of Mathematical Analysis and Applications, Elsevier, Jan 1996.
The definitive version is available at https://doi.org/10.1006/jmaa.1996.0020
Mathematics and Statistics
Article - Journal
© 1996 Elsevier, All rights reserved.