Spectral properties of Jacobi matrices by asymptotic analysis.
A key element of this paper is the formulation and an inversion-related proof of several discrete version(s) of the Levinson theorem and of the related spectral analysis (by the authors' own statement, the discretization approach to differential equations is a topic of independent interest). This is what leads to the main application, viz., to a successful determination of asymptotics of generalized (i.e., difference-equation-interpreted) eigensolutions of certain specific (two classes of) Jacobi matrices (with vanishing main diagonal and periodically perturbed power-law elements).
scientific article; zbMATH DE number 1891290
scientific article