论文标题
Green的非自身辅助矩阵功能的定量归纳估计值
Quantitative inductive estimates for Green's functions of non-self-adjoint matrices
论文作者
论文摘要
我们为Green的矩阵功能提供定量归纳估计，并在较高维度中逐渐衰减（子）衰减。加上卡坦的估计和差异估计，我们为非自我辅助托管运算符的大偏差定理建立了明确的界限。作为应用，我们获得了具有明确界限的状态综合密度的连续性模量，并为分析准周期运算符的纯点光谱属性。此外，我们的归纳是自我改善的，可用于低复杂性相互作用的扰动。
We provide quantitative inductive estimates for Green's functions of matrices with (sub)expoentially decaying off diagonal entries in higher dimensions. Together with Cartan's estimates and discrepancy estimates, we establish explicit bounds for the large deviation theorem for non-self-adjoint Toeplitz operators. As applications, we obtain the modulus of continuity of the integrated density of states with explicit bounds and the pure point spectrum property for analytic quasi-periodic operators. Moreover, our inductions are self-improved and work for perturbations with low complexity interactions.
