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Uniform Spectral Properties of One-Dimensional Quasicrystals, I. Absence of Eigenvalues

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Abstract:

We consider discrete one-dimensional Schrödinger operators with Sturmian potentials. For a full-measure set of rotation numbers including the Fibonacci case, we prove absence of eigenvalues for all elements in the hull.

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Authors and Affiliations

  1. Department of Mathematics, California Institute of Technology, Pasadena, CA 91125, USA.¶E-mail: damanik@its.caltech.edu, , , , , , US

    David Damanik

  2. Fachbereich Mathematik, Johann Wolfgang Goethe-Universität, 60054 Frankfurt, Germany¶ E-mail: dlenz@math.uni-frankfurt.de, , , , , , DE

    Daniel Lenz

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  1. David Damanik
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  2. Daniel Lenz
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Received: 7 January 1999 / Accepted: 12 May 1999

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Damanik, D., Lenz, D. Uniform Spectral Properties of One-Dimensional Quasicrystals, I. Absence of Eigenvalues. Comm Math Phys 207, 687–696 (1999). https://doi.org/10.1007/s002200050742

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  • DOI: https://doi.org/10.1007/s002200050742

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