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Multidimensional Almost-Periodic Schrödinger Operators with Cantor Spectrum

  • David Damanik
  • Jake FillmanEmail author
  • Anton Gorodetski
Article
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Abstract

We construct multidimensional almost-periodic Schrödinger operators whose spectrum has zero lower box-counting dimension. In particular, the spectrum in these cases is a generalized Cantor set of zero Lebesgue measure.

Mathematics Subject Classification

34L40 

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Notes

Acknowledgments

We are grateful to Leonid Parnovski for useful comments on an earlier version of this manuscript.

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsRice UniversityHoustonUSA
  2. 2.Department of MathematicsVirginia TechBlacksburgUSA
  3. 3.Department of MathematicsUniversity of CaliforniaIrvineUSA

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