Communications in Mathematical Physics

, Volume 223, Issue 3, pp 509–532 | Cite as

Schrödinger Operators with Sparse Potentials: Asymptotics of the Fourier Transform¶of the Spectral Measure

  • Denis Krutikov
  • Christian Remling


We study the pointwise behavior of the Fourier transform of the spectral measure for discrete one-dimensional Schrödinger operators with sparse potentials. We find a resonance structure which admits a physical interpretation in terms of a simple quasiclassical model. We also present an improved version of known results on the spectrum of such operators.


Fourier Fourier Transform Resonance Structure Physical Interpretation Spectral Measure 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Denis Krutikov
    • 1
  • Christian Remling
    • 2
  1. 1.Universität Essen, Fachbereich Mathematik/Informatik, 45117 Essen, Germany.¶E-mail: denis.kroutikov@uni-essen.deDE
  2. 2.Universität Osnabrück, Fachbereich Mathematik/Informatik, 49069 Osnabrück, Germany.¶E-mail: cremling@mathematik.uni-osnabrueck.deDE

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