Jan Janas, Serguei Naboko and Gunter Stolz
Spectral theory for a class of periodically perturbed
unbounded Jacobi matrices: elementary methods
(298K, postscript)
ABSTRACT. We use elementary methods to give a full characterization of the
spectral properties of
unbounded Jacobi matrices with zero diagonal and off-diagonal
entries of the type $\lambda_n = n^{\alpha} + c_n$, where $1/2 <
\alpha \le 1$ and $c_n$ is a real periodic sequence. The spectral
properties depend strongly on the parity of the minimal period of
$c_n$. The methods used are asymptotic diagonalization techniques,
including the finite difference version of Levinson's theorem,
subordinacy theory, and the variational principle.