Multidimensional Schrödinger operators whose spectrum features a half-line and a Cantor set
| dc.citation.articleNumber | 108911 | en_US |
| dc.citation.issueNumber | 7 | en_US |
| dc.citation.journalTitle | Journal of Functional Analysis | en_US |
| dc.citation.volumeNumber | 280 | en_US |
| dc.contributor.author | Damanik, David | en_US |
| dc.contributor.author | Fillman, Jake | en_US |
| dc.contributor.author | Gorodetski, Anton | en_US |
| dc.date.accessioned | 2021-02-09T19:47:59Z | en_US |
| dc.date.available | 2021-02-09T19:47:59Z | en_US |
| dc.date.issued | 2021 | en_US |
| dc.description.abstract | We 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. | en_US |
| dc.identifier.citation | Damanik, 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. | en_US |
| dc.identifier.doi | https://doi.org/10.1016/j.jfa.2020.108911 | en_US |
| dc.identifier.uri | https://hdl.handle.net/1911/109828 | en_US |
| dc.language.iso | eng | en_US |
| dc.publisher | Elsevier | en_US |
| dc.rights | This is an author's peer-reviewed final manuscript, as accepted by the publisher. The published article is copyrighted by Elsevier. | en_US |
| dc.subject.keyword | Schrödinger operators | en_US |
| dc.subject.keyword | Spectrum | en_US |
| dc.title | Multidimensional Schrödinger operators whose spectrum features a half-line and a Cantor set | en_US |
| dc.type | Journal article | en_US |
| dc.type.dcmi | Text | en_US |
| dc.type.publication | post-print | en_US |
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