Shnol’s theorem and the spectrum of long range operators

Han, Rui

doi:10.1090/proc/14388

Shnol’s theorem and the spectrum of long range operators
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by Rui Han

Proc. Amer. Math. Soc. 147 (2019), 2887-2897

DOI: https://doi.org/10.1090/proc/14388

Published electronically: April 3, 2019

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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.

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