流形上积分态密度的连续性
Continuity properties of the integrated density of states on manifolds
摘要：
我们首先分析了顺从覆盖流形上周期薛定谔算子的积分态密度。给出了IDS在给定能量下连续的一个判据，并给出了具有连续和不连续IDS的算子的例子。随后，合金型扰动的周期算子被认为是。随机性可以通过势和度量两者进入。一个Wegner估计证明这意味着相应的IDS的连续性。这给出了一个不连续的“周期性”IDS的例子，它是正则化的随机扰动。
英文摘要：
We first analyze the integrated density of states (IDS) of periodic Schrödinger operators on an amenable covering manifold. A criterion for the continuity of the IDS at a prescribed energy is given along with examples of operators with both continuous and discontinuous IDS'. Subsequently, alloy-type perturbations of the periodic operator are considered. The randomness may enter both via the potential and the metric. A Wegner estimate is proven which implies the continuity of the corresponding IDS. This gives an example of a discontinuous "periodic" IDS which is regularized by a random perturbation.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
