SPECTRAL HOMOGENEITY OF LIMIT-PERIODIC SCHR ¨ ODINGER OPERATORS
SPECTRAL HOMOGENEITY OF LIMIT-PERIODIC SCHR ¨ ODINGER OPERATORS
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DOI：
10.4171/jst/166
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发表时间：
2015-02
期刊：
影响因子：
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通讯作者：
J. Fillman;Milivoje Lukic
中科院分区：
文献类型：
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作者：
J. Fillman;Milivoje Lukic
证明了当位势满足Pastur-Tkachenko条件时，极限周期Schr“odinger算子的谱在Carleson意义下是齐次的.这意味着极限周期Schr“odinger算子的稠密集具有在齐次Cantor集上支撑的纯绝对连续谱.当结合工作的Gesztesy-Yuditskii，这也意味着频谱的Pastur-Tkachenko潜力有无限的间隙长度时，潜在的失败是一致的几乎周期。
We prove that the spectrum of a limit-periodic Schr\"odinger operator is homogeneous in the sense of Carleson whenever the potential obeys the Pastur--Tkachenko condition. This implies that a dense set of limit-periodic Schr\"odinger operators have purely absolutely continuous spectrum supported on a homogeneous Cantor set. When combined with work of Gesztesy--Yuditskii, this also implies that the spectrum of a Pastur--Tkachenko potential has infinite gap length whenever the potential fails to be uniformly almost periodic.