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2009, Volume 3, Issue 2: 253-270. Doi: 10.3934/jmd.2009.3.253
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Schrödinger operators defined by interval-exchange transformations

  • 1.

    Department of Mathematics, Rice University, Houston, TX 77005

Received:  August 31, 2008
Published:  April 2009
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    Abstract
  • 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.
    Mathematics Subject Classification: Primary 81Q10; Secondary 37A05, 47B36, 82B44.

    Citation:
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