Spectral properties of a class of reflectionless Schrödinger operators

Fritz Gesztesy; Peter Yuditskii

doi:10.1016/j.jfa.2006.08.006

Spectral properties of a class of reflectionless Schrödinger operators

Fritz Gesztesy, Peter Yuditskii

Department of Mathematics

University of Missouri

Research output: Contribution to journal › Article › peer-review

31 Scopus citations

Abstract

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 C, which exhibit a singular component.

Original language	English
Pages (from-to)	486-527
Number of pages	42
Journal	Journal of Functional Analysis
Volume	241
Issue number	2
DOIs	https://doi.org/10.1016/j.jfa.2006.08.006
State	Published - 15 Dec 2006

Bibliographical note

Funding Information:
✩ Based upon work partially supported by the US National Science Foundation under Grant No. DMS-0405526 and the Austrian Science Fund FWF, project number: P16390-N04. * Corresponding author. E-mail addresses: [email protected] (F. Gesztesy), [email protected] (P. Yuditskii). URL: http://www.math.missouri.edu/personnel/faculty/gesztesyf.html (F. Gesztesy).

Funding

✩ Based upon work partially supported by the US National Science Foundation under Grant No. DMS-0405526 and the Austrian Science Fund FWF, project number: P16390-N04. * Corresponding author. E-mail addresses: [email protected] (F. Gesztesy), [email protected] (P. Yuditskii). URL: http://www.math.missouri.edu/personnel/faculty/gesztesyf.html (F. Gesztesy).

Funders	Funder number
Austrian Science Fund FWF	P16390-N04
US National Science Foundation	DMS-0405526

Keywords

Homogeneous sets
Reflectionless Schrödinger operators
Spectral properties

Access to Document

10.1016/j.jfa.2006.08.006

Cite this

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abstract = "We prove that one-dimensional reflectionless Schr{\"o}dinger 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 Schr{\"o}dinger operators. In addition, we construct examples of reflectionless Schr{\"o}dinger operators with more general types of spectra, given by the complement of a Denjoy-Widom-type domain in C, which exhibit a singular component.",

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author = "Fritz Gesztesy and Peter Yuditskii",

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AB - 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 C, which exhibit a singular component.

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Spectral properties of a class of reflectionless Schrödinger operators

Abstract

Bibliographical note

Funding

Keywords

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