Spectral analysis of a class of hermitian Jacobi matrices in a critical (double root) hyperbolic case

Abstract

AbstractWe consider a class of Jacobi matrices with periodically modulated diagonal in a critical hyperbolic (‘double root’) situation. For the model with ‘non-smooth’ matrix entries we obtain the asymptotics of generalized eigenvectors and analyse the spectrum. In addition, we reformulate a very helpful theorem from a paper by Janas and Moszynski in its full generality in order to serve the needs of our method.