Document Type
Article
Publication Date
1-1-2018
Abstract
We study the multi-dimensional operator .H x u/ n D X u m C f .T n .x//u n ; jmnjD1 where T is the shift of the torus T d . When d D 2, we show the spectrum of H x is almost surely purely continuous for a.e. and generic continuous potentials. When d 3, the same result holds for frequencies under an explicit arithmetic criterion. We also show that general multi-dimensional operators with measurable potentials do not have eigenvalue for generic.
Publication Source (Journal or Book title)
Journal of Spectral Theory
First Page
1635
Last Page
1645
Recommended Citation
Han, R., & Yang, F. (2018). Generic continuous spectrum for multi-dimensional quasiperiodic Schrödinger operators with rough potentials. Journal of Spectral Theory, 8 (4), 1635-1645. https://doi.org/10.4171/JST/238
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