Multidimensional Schrödinger operators whose spectrum features a half-line and a Cantor set

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dc.citation.articleNumber108911
dc.citation.issueNumber7
dc.citation.journalTitleJournal of Functional Analysis
dc.citation.volumeNumber280
dc.contributor.authorDamanik, David
dc.contributor.authorFillman, Jake
dc.contributor.authorGorodetski, Anton
dc.date.accessioned2021-02-09T19:47:59Z
dc.date.available2021-02-09T19:47:59Z
dc.date.issued2021
dc.description.abstractWe construct multidimensional Schrödinger operators with a spectrum that has no gaps at high energies and that is nowhere dense at low energies. This gives the first example for which this widely expected topological structure of the spectrum in the class of uniformly recurrent Schrödinger operators, namely the coexistence of a half-line and a Cantor-type structure, can be confirmed. Our construction uses Schrödinger operators with separable potentials that decompose into one-dimensional potentials generated by the Fibonacci sequence and relies on the study of such operators via the trace map and the Fricke-Vogt invariant. To show that the spectrum contains a half-line, we prove an abstract Bethe–Sommerfeld criterion for sums of Cantor sets which may be of independent interest.
dc.identifier.citationDamanik, David, Fillman, Jake and Gorodetski, Anton. "Multidimensional Schrödinger operators whose spectrum features a half-line and a Cantor set." <i>Journal of Functional Analysis,</i> 280, no. 7 (2021) Elsevier: https://doi.org/10.1016/j.jfa.2020.108911.
dc.identifier.doihttps://doi.org/10.1016/j.jfa.2020.108911
dc.identifier.urihttps://hdl.handle.net/1911/109828
dc.language.isoeng
dc.publisherElsevier
dc.rightsThis is an author's peer-reviewed final manuscript, as accepted by the publisher. The published article is copyrighted by Elsevier.
dc.subject.keywordSchrödinger operators
dc.subject.keywordSpectrum
dc.titleMultidimensional Schrödinger operators whose spectrum features a half-line and a Cantor set
dc.typeJournal article
dc.type.dcmiText
dc.type.publicationpost-print
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