Some connections between almost periodic and periodic discrete Schroedinger operators with analytic potentials

Details Some connections between almost periodic and periodic discrete Schroedinger operators with analytic potentials Some connections between almost periodic and periodic discrete Schroedinger operators with analytic potentials

2011-01-25

arxiv.org/abs/1101.4700v3

Mathematics

Spectral Theory

17pp; generalization to analytic potentials; fixed a few typos

Scientific paper

We study discrete Schroedinger operators with analytic potentials. In particular, we are interested in the connection between the absolutely continuous spectrum in the almost periodic case and the spectra in the periodic case. We prove a weak form of a precise conjecture relating the two. We also bound the measure of the spectrum in the periodic case in terms of the Lyapunov exponent in the almost periodic case. In the proofs, we use a partial generalization of Chambers' formula. As an additional application of this generalization, we provide a new proof of Herman's lower bound for the Lyapunov exponent.

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