具有有限值势的遍历薛定谔算子的谱
动力系统
2015-02-17 v2 谱理论
摘要
我们证明了，对于由非恒定函数定义在任意极小非周期有限子移位上的势的薛定谔算子，其谱的测度随着耦合常数趋于无穷而趋于零。我们还得到了谱测度的定量上界。这源于我们在移位的递归性质的两个条件下，对具有有限值势的遍历薛定谔算子证明的一个结果。我们还证明了这些条件之一是该结果所必需的。
引用
@article{arxiv.1502.02317,
title = {On the spectrums of ergodic Schrodinger operators with finitely valued potentials},
author = {Zhiyuan Zhang},
journal= {arXiv preprint arXiv:1502.02317},
year = {2015}
}
备注
The presentation has been improved. Thank David Damanik for pointing out an error in the statement of Theorem 2 in the earlier version, that C should depend on the potential v. Submitted