Bounds on the density of states for Schr\" odinger operators

Details Bounds on the density of states for Schr\" odinger operators Bounds on the density of states for Schr\" odinger operators

2011-12-07

arxiv.org/abs/1112.1716v1

Physics

Mathematical Physics

Scientific paper

We establish bounds on the density of states of Schr\" odinger operators. These are deterministic results that do not require the existence of the integrated density of states. The results are stated in terms of a "density of states outer-measure" that always exists. We prove log-H\"older continuity for the density of states in one, two, and three dimensions for Schr\" odinger operators, and in any dimension for discrete Schr\" odinger operators.

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