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Measure-perturbed one-dimensional Schrödinger operators

Authors
Publisher
Universitätsbibliothek Chemnitz
Publication Date
Keywords
  • Schrödinger Operator
  • Spektraltheorie
  • Quasikristalle
  • Schrödinger Operator
  • Spectral Theory
  • Quasicrystals
  • Ddc:515
  • Hamilton-Operator

Abstract

In this Dissertation thesis the spectral theory of Schrödinger operators modeling quasicrystals in dimension one ist investigated. We allow for a large class of measures as potentials covering also point interactions. The main results can be stated as follows: If the potential can be very well approximated by periodic potentials, then the correspondig Schrödinger operator does not have any eigenvalues. If the potential is aperiodic and satisfies a certain finite local complexity condition, the absolutely continuous spectrum is absent. We also prove Cantor spectra of zero Lebesgue measure for a large class of (a randomized version of) the operator.

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