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Localization for Almost-Periodic Operators with Power-law Long-range Hopping: A Nash-Moser Iteration Type Reducibility Approach
Published 19 Jan 2022 in math-ph, math.AP, math.DS, math.MP, and math.SP | (2201.07405v3)
Abstract: In this paper we develop a Nash-Moser iteration type reducibility approach to prove the (inverse) localization for some $d$-dimensional discrete almost-periodic operators with power-law long-range hopping. We also provide a quantitative lower bound on the regularity of the hopping. As an application, some results of \cite{Sar82, Pos83, Cra83, BLS83} are generalized to the power-law hopping case.
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