Regularity of the Density of Surface States

Abstract

We prove that the integrated density of surface states of continuous or discrete Anderson-type random Schroedinger 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 Hoelder continuity of the integrated density of bulk states.

References in corpus (5)

• Scattering Theory Approach to Random Schroedinger Operators in One Dimension
• The Density of States and the Spectral Shift Density of Random Schroedinger Operators
• Monotonicity and Concavity Properties of The Spectral Shift Function
• Concavity of Eigenvalue Sums and the Spectral Shift Function
• Global Bounds for the Lyapunov Exponent and the Integrated Density of States of Random Schrödinger Operators in One Dimension

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