Bounds on the density of states for Schr\" odinger operators
Mathematical Physics
2013-01-01 v3 math.MP
Spectral Theory
Abstract
We establish bounds on the density of states measure for Schr\"odinger operators. These are deterministic results that do not require the existence of the density of states measure, or, equivalently, of the integrated density of states. The results are stated in terms of a "density of states outer-measure" that always exists, and provides an upper bound for the density of states measure when it exists. We prove log-H\"older continuity for this density of states outer-measure in one, two, and three dimensions for Schr\"odinger operators, and in any dimension for discrete Schr\"odinger operators.
Keywords
Cite
@article{arxiv.1112.1716,
title = {Bounds on the density of states for Schr\" odinger operators},
author = {Jean Bourgain and Abel Klein},
journal= {arXiv preprint arXiv:1112.1716},
year = {2013}
}
Comments
Revised