Shnol’s theorem and the spectrum of long range operators
We extend some basic results known for finite range operators to long range operators with off-diagonal decay. Namely, we prove an analogue of Shnol’s theorem. We also establish the connection between the almost sure spectrum of long range random operators and the spectra of deterministic periodic operators.
Publication Source (Journal or Book title)
Proceedings of the American Mathematical Society
Han, R. (2019). Shnol’s theorem and the spectrum of long range operators. Proceedings of the American Mathematical Society, 147 (7), 2887-2897. https://doi.org/10.1090/proc/14388