Regularity of the Surface Density of States

2000/11/11 by Vadim Kostrykin, Robert Schrader · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Random Matrices and Applications #Spectral Theory in Mathematical Physics #math-ph #math.MP #math.SP #msc:60H25 #msc:82B44

paper · pdf · doi:10.1006/jfan.2001.3805

published as J. Funct. Anal. Vol. 187 (2001), 227 - 246

arxiv created 2000/11/11 · openalex publication_date 2001/12/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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.

Citations

• THE DENSITY OF STATES AND THE SPECTRAL SHIFT DENSITY OF RANDOM SCHRÖDINGER OPERATORS
• SCATTERING THEORY APPROACH TO RANDOM SCHRÖDINGER OPERATORS IN ONE DIMENSION

Cited by

• Eigenvalues of periodic difference operators on lattice octant

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