Spectral Properties of a Class of Reflectionless Schrödinger Operators

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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, which exhibit a singular component.
44 pages

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Spectral Theory, Mathematical Physics, 34B20, 34L05, 34L40

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http://salesiana.dossiersoluciones.com/handle/123456789/110056

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0603103
 http://arxiv.org/abs/math/0603103

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arXiv