Sfb 288 Differential Geometry and Quantum Physics

Abstract for Sfb Preprint No. 489

Regularity of the Density of Surface States

V. Kostrykin and R. Schrader

We prove that the integrated density of surface states of continuous or discrete Anderson-type random Schrödinger operators is a measurable locally integrable function rather than a signed measure or a distribution. This generalize our recent results on the existence of the integrated density of surface states in the continuous case and those of A. Chahrour in the discrete case. The proof uses the new L p -bound on the spectral shift function recently obtained by Combes, Hislop, and Nakamura. Also we provide a simple proof of their result on the H¨ older continuity of the integrated density of bulk states.

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