Shnol’s theorem and the spectrum of long range operators

Authors

Rui Han, University of California, Irvine

Document Type

Article

Publication Date

1-1-2019

Abstract

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

First Page

2887

Last Page

2897

Recommended Citation

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