Regularity of the Surface Density of States

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