Regularity of the Surface Density of States

✍ Scribed by Vadim Kostrykin; Robert Schrader

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 309 KB
• Volume: 187
• Category: Article
• ISSN: 0022-1236
• DOI: 10.1006/jfan.2001.3805

✦ Synopsis

dedicated to jean michel combes on the occasion of his 60 th birthday

We prove that the integrated surface density of 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 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 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 Hölder continuity of the integrated density of bulk states.