Point spectrum for quasi-periodic long range operators

  • Jiangong You

    Nanjing University, China
  • Shiwen Zhang

    Nanjing University, China
  • Qi Zhou

    Université Pierre et Marie Curie, Paris, France


We generalize Gordon type argument to quasi-periodic operators with finite range interaction and prove that these operators have no point spectrum when the rational approximation rate of the base frequency is relatively large. We also show that, for any irrational frequency, there are operators with infinite range interaction possessing point spectrum. is is a new phenomenon which can not happen in the finite range interaction case.

Cite this article

Jiangong You, Shiwen Zhang, Qi Zhou, Point spectrum for quasi-periodic long range operators. J. Spectr. Theory 4 (2014), no. 4, pp. 769–781

DOI 10.4171/JST/85