Spectral properties of a class of reflectionless Schrödinger operators

Fritz Gesztesy, Peter Yuditskii

Research output: Contribution to journalArticlepeer-review

27 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 languageEnglish
Pages (from-to)486-527
Number of pages42
JournalJournal of Functional Analysis
Volume241
Issue number2
DOIs
StatePublished - 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).

FundersFunder number
Austrian Science Fund FWFP16390-N04
US National Science FoundationDMS-0405526

    Keywords

    • Homogeneous sets
    • Reflectionless Schrödinger operators
    • Spectral properties

    Fingerprint

    Dive into the research topics of 'Spectral properties of a class of reflectionless Schrödinger operators'. Together they form a unique fingerprint.

    Cite this