Spectral Analysis of Selfadjoint Jacobi Matrices with Periodically Modulated Entries

This paper deals with the spectral analysis of a class of selfadjoint unbounded Jacobi matrices J with modulated entries. The entries have the form of smooth sequences that increase to infinity multiplied by proper periodic sequences. For this class criteria for pure absolute continuity of the spectrum or its discreteness, and the asymptotics of generalized eigenvectors of J, are given. Some examples illustrating the stability zones of spectral structure are presented.