03-378 Jan Janas, Serguei Naboko and Gunter Stolz

Spectral theory for a class of periodically perturbed unbounded Jacobi matrices: elementary methods (298K, postscript) 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 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.

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