We study discrete Schr ̈odinger operators with trigonomet-
ric potentials. In particular, we are interested in the connection be-
tween 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 Hermans lower bound for the Lyapunov exponent.