- 02-144 Werner Kirsch, Ivan Veselic
- Existence of the density of states for one-dimensional alloy-type potentials with small support
Mar 22, 02
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Abstract. We study spectral properties of Schr\"odinger operators with a random potential of
alloy type on $L^2(\RR)$ and their restrictions to finite intervals. A Wegner estimates for non-negative single site potentials with small support is proven. It implies the existence and local uniform boundedness of the density of states. Our estimate is valid for all bounded energy intervals. Wegner estimates play a key role in an existence proof of pure point spectrum.