Spectral approximation for ergodic CMV operators with an application to quantum walks.
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| Title: | Spectral approximation for ergodic CMV operators with an application to quantum walks. |
|---|---|
| Authors: | Fillman, Jake1 fillman@vt.edu, Ong, Darren C.2 darrenong@xmu.edu.my, VandenBoom, Tom3 tv4@rice.edu |
| Source: | Journal of Mathematical Analysis & Applications. Nov2018, Vol. 467 Issue 1, p132-147. 16p. |
| Subjects: | Common method variance, Lyapunov exponents, Schrödinger equation, Spectral theory, Approximation theory |
| Abstract: | We establish concrete criteria for fully supported absolutely continuous spectrum for ergodic CMV matrices and purely absolutely continuous spectrum for limit-periodic CMV matrices. We proceed by proving several variational estimates on the measure of the spectrum and the vanishing set of the Lyapunov exponent for CMV matrices, which represent CMV analogues of results obtained for Schrödinger operators due to Y. Last in the early 1990s. Having done so, we combine those estimates with results from inverse spectral theory to obtain purely absolutely continuous spectrum. [ABSTRACT FROM AUTHOR] |
| Copyright of Journal of Mathematical Analysis & Applications is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 131007262 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Spectral approximation for ergodic CMV operators with an application to quantum walks. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Fillman%2C+Jake%22">Fillman, Jake</searchLink><relatesTo>1</relatesTo><i> fillman@vt.edu</i><br /><searchLink fieldCode="AR" term="%22Ong%2C+Darren+C%2E%22">Ong, Darren C.</searchLink><relatesTo>2</relatesTo><i> darrenong@xmu.edu.my</i><br /><searchLink fieldCode="AR" term="%22VandenBoom%2C+Tom%22">VandenBoom, Tom</searchLink><relatesTo>3</relatesTo><i> tv4@rice.edu</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Journal+of+Mathematical+Analysis+%26+Applications%22">Journal of Mathematical Analysis & Applications</searchLink>. Nov2018, Vol. 467 Issue 1, p132-147. 16p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Common+method+variance%22">Common method variance</searchLink><br /><searchLink fieldCode="DE" term="%22Lyapunov+exponents%22">Lyapunov exponents</searchLink><br /><searchLink fieldCode="DE" term="%22Schrödinger+equation%22">Schrödinger equation</searchLink><br /><searchLink fieldCode="DE" term="%22Spectral+theory%22">Spectral theory</searchLink><br /><searchLink fieldCode="DE" term="%22Approximation+theory%22">Approximation theory</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: We establish concrete criteria for fully supported absolutely continuous spectrum for ergodic CMV matrices and purely absolutely continuous spectrum for limit-periodic CMV matrices. We proceed by proving several variational estimates on the measure of the spectrum and the vanishing set of the Lyapunov exponent for CMV matrices, which represent CMV analogues of results obtained for Schrödinger operators due to Y. Last in the early 1990s. Having done so, we combine those estimates with results from inverse spectral theory to obtain purely absolutely continuous spectrum. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Journal of Mathematical Analysis & Applications is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=131007262 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1016/j.jmaa.2018.06.056 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 16 StartPage: 132 Subjects: – SubjectFull: Common method variance Type: general – SubjectFull: Lyapunov exponents Type: general – SubjectFull: Schrödinger equation Type: general – SubjectFull: Spectral theory Type: general – SubjectFull: Approximation theory Type: general Titles: – TitleFull: Spectral approximation for ergodic CMV operators with an application to quantum walks. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Fillman, Jake – PersonEntity: Name: NameFull: Ong, Darren C. – PersonEntity: Name: NameFull: VandenBoom, Tom IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 11 Text: Nov2018 Type: published Y: 2018 Identifiers: – Type: issn-print Value: 0022247X Numbering: – Type: volume Value: 467 – Type: issue Value: 1 Titles: – TitleFull: Journal of Mathematical Analysis & Applications Type: main |
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