Green's function estimates for quasi-periodic operators on ℤ^d with power-law long-range hopping

2024/08/04 by Yunfeng Shi, Wen Li, Shi, Yunfeng +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Differential Equations and Boundary Problems #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2408.01913

openalex publication_date 2024/08/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish quantitative Green's function estimates for a class of quasi-periodic (QP) operators on ℤ^d with power-law long-range hopping and analytic cosine type potentials. As applications, we prove the arithmetic version of localization, the finite volume version of (\frac12-)-Hölder continuity of the IDS, and the absence of eigenvalues (for Aubry dual operators).

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