具有幂律长程跳变的 $\mathbb{Z}^d$ 上准周期算子的格林函数估计值

arXiv - MATH - Spectral Theory Pub Date : 2024-08-04 DOI:arxiv-2408.01913

Yunfeng Shi, Li Wen

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引用次数: 0

摘要

我们为$\mathbb{Z}^d$上一类具有幂律长程跳跃和解析余弦型势能的准周期（QP）算子建立了定量格林函数估计。作为应用，我们证明了局部化的算术版本、IDS 的有限体积版本$(\frac12-)$-H\"old continuity，以及奥布里对偶算子的特征值缺失。

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

We establish quantitative Green's function estimates for a class of quasi-periodic (QP) operators on $\mathbb{Z}^d$ 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 $(\frac12-)$-H\"older continuity of the IDS, and the absence of eigenvalues (for Aubry dual operators).

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arXiv - MATH - Spectral Theory

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