表面态密度的规律性
Regularity of the Density of Surface States
摘要：
证明了连续或离散的Anderson型随机Schroedinger算子的表面态积分密度是可测的局部可积函数，而不是符号测度或分布.这推广了我们最近关于连续情况下积分表面态密度存在性的结果和A。Chahrour在离散的情况下。证明使用新的$L^p$的光谱位移函数最近获得的Combes，Hislop和Nakamura的约束。并给出了积分体态密度的Hoelder连续性的简单证明。
英文摘要：
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.
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