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.