Spectral properties of a class of reflectionless Schrödinger operators

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• 作者：Fritz Gesztesy and Peter Yuditskii
• 关键词：Reflectionless Schrö ; dinger operators ; Homogeneous sets ; Spectral properties
• 刊名：Journal of Functional Analysis
• 出版年：2006
• 出版时间：15 December 2006
• 年：2006
• 卷：241
• 期：2
• 页码：486-527
• 全文大小：326 K

文摘

We prove that one-dimensional reflectionless Schrödinger operators with spectrum a homogeneous set in the sense of Carleson, belonging to the class introduced by Sodin and Yuditskii, have purely absolutely continuous spectra. This class includes all earlier examples of reflectionless almost periodic Schrödinger operators. In addition, we construct examples of reflectionless Schrödinger operators with more general types of spectra, given by the complement of a Denjoy–Widom-type domain in , which exhibit a singular component.