论文标题
定量绿色的晶格准周期schrödinger操作员的功能估计值
Quantitative Green's Function Estimates for Lattice Quasi-periodic Schrödinger Operators
论文作者
论文摘要
在本文中，我们为一些较高的晶格准周期（QP）Schrödinger运算符建立了定量Green的功能估计。估计值中的共振可以通过一对某些功能的对称零来描述，估计值适用于亚指数类型的非共振条件。作为定量Green函数估算的应用，我们既证明了Anderson本地化的算术版本，也证明了此类QPSchrödinger运营商的综合状态密度（IDS）的$（\ frac 12-）$ - Hölder连续性。这在\ cite {bou00}中对Bourgain的问题提供了肯定的答案。
In this paper, we establish quantitative Green's function estimates for some higher dimensional lattice quasi-periodic (QP) Schrödinger operators. The resonances in the estimates can be described via a pair of symmetric zeros of certain functions and the estimates apply to the sub-exponential type non-resonant conditions. As the application of quantitative Green's function estimates, we prove both the arithmetic version of Anderson localization and the $(\frac 12-)$-Hölder continuity of the integrated density of states (IDS) for such QP Schrödinger operators. This gives an affirmative answer to Bourgain's problem in\cite{Bou00}.
