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. 769–781DOI 10.4171/JST/85