Zero measure spectrum for multi-frequency Schrödinger operators

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dc.citation.firstpage573
dc.citation.issueNumber2
dc.citation.journalTitleJournal of Spectral Theory
dc.citation.lastpage590
dc.citation.volumeNumber12
dc.contributor.authorChaika, Jon
dc.contributor.authorDamanik, David
dc.contributor.authorFillman, Jake
dc.contributor.authorGohlke, Philipp
dc.date.accessioned2022-12-13T19:11:07Z
dc.date.available2022-12-13T19:11:07Z
dc.date.issued2022
dc.description.abstractBuilding on works of Berthé–Steiner–Thuswaldner and Fogg–Nous, we show that on the two-dimensional torus, Lebesgue almost every translation admits a natural coding such that the associated subshift satisfies the Boshernitzan criterion. As a consequence, we show that for these torus translations, every quasi-periodic potential can be approximated uniformly by one for which the associated Schrödinger operator has Cantor spectrum of zero Lebesgue measure. We also describe a framework that can allow this to be extended to higher-dimensional tori.
dc.identifier.citationChaika, Jon, Damanik, David, Fillman, Jake, et al.. "Zero measure spectrum for multi-frequency Schrödinger operators." <i>Journal of Spectral Theory,</i> 12, no. 2 (2022) EMS Press: 573-590. https://doi.org/10.4171/jst/411.
dc.identifier.digital7525219-10.4171-jst-411-print
dc.identifier.doihttps://doi.org/10.4171/jst/411
dc.identifier.urihttps://hdl.handle.net/1911/114080
dc.language.isoeng
dc.publisherEMS Press
dc.rightsThis work is licensed under a CC BY 4.0 license
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.titleZero measure spectrum for multi-frequency Schrödinger operators
dc.typeJournal article
dc.type.dcmiText
dc.type.publicationpublisher version
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