Spectral averaging, perturbation of singular spectra, and localization
Spectral averaging, perturbation of singular spectra, and localization
复制标题
光谱平均、奇异光谱扰动和定位
DOI：
10.1090/s0002-9947-96-01579-6
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发表时间：
1996
期刊：
影响因子：
--
通讯作者：
E. Mourre
中科院分区：
文献类型：
--
作者：
J. Combes;P. Hislop;E. Mourre
。利用微分不等式的方法证明了单参数自伴算子族的谱平均定理。利用这一定理建立了平均谱测度相对于勒贝格测度的绝对连续性。这是控制几乎所有参数值的奇异连续谱的重要一步。主要应用于某些随机薛定谔算子族的局部化问题。利用这些结果和多尺度分析，建立了一类随机薛定谔算子的局部化。
. A spectral averaging theorem is proved for one-parameter families of self-adjoint operators using the method of di(cid:11)erential inequalities. This theorem is used to establish the absolute continuity of the averaged spectral measure with respect to Lebesgue measure. This is an important step in controlling the singular continuous spectrum of the family for almost all values of the parameter. The main application is to the problem of localization for certain families of random Schr¨odinger operators. Localization for a family of random Schr¨odinger operators is established employing these results and a multi-scale analysis.