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Sums and Products of Cantor Sets and Two Dimensional Quasicrystal Model

  • Author(s): Takahashi, Yuki
  • Advisor(s): Gorodetski, Anton
  • et al.
Abstract

The spectra of tridiagonal square Fibonacci Hamiltonians, which are two-dimensional quasicrystal models, are given by sums of two Cantor sets, and the spectrum of the Labyrinth model, which is another two-dimensional quasicrystal model, is given by products of two Cantor sets. We consider spectral properties of those models and also obtain the optimal estimates in terms of thickness that guarantee that products of two Cantor sets is an interval.

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