 03378 Jan Janas, Serguei Naboko and Gunter Stolz
 Spectral theory for a class of periodically perturbed
unbounded Jacobi matrices: elementary methods
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Aug 21, 03

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Abstract. We use elementary methods to give a full characterization of the
spectral properties of
unbounded Jacobi matrices with zero diagonal and offdiagonal
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.
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