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### Open Access Journals

PROC

I derive an asymptotic formula for the gaps of periodic discrete
Schrödinger operators. An application to the skew-shift Schrödinger operator
is discussed.

JMD

We discuss discrete one-dimensional Schrödinger operators whose
potentials are generated by an invertible ergodic transformation
of a compact metric space and a continuous real-valued sampling
function. We pay particular attention to the case where the
transformation is a minimal interval-exchange transformation.
Results about the spectral type of these operators are
established. In particular, we provide the first examples of
transformations for which the associated Schrödinger operators
have purely singular spectrum for every nonconstant continuous
sampling function.

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