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Veselic: Bounds on the spectral shift function and the density of states

By Dirk Hundertmark, Rowan Killip, Shu Nakamura, Peter Stollmann and Ivan Veseli Ć


Abstract. We study spectra of Schrödinger operators on R d. First we consider a pair of operators which differ by a compactly supported potential, as well as the corresponding semigroups. We prove almost exponential decay of the singular values µn of the difference of the semigroups as n → ∞ and deduce bounds on the spectral shift function of the pair of operators. Thereafter we consider alloy type random Schrödinger operators. The single site potential u is assumed to be non-negative and of compact support. The distributions of the random coupling constants are assumed to be Hölder continuous. Based on the estimates for the spectral shift function, we prove a Wegner estimate which implies Hölder continuity of the integrated density of states

Year: 2005
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