INVARIANTS OF THE TRACE MAP AND UNIFORM SPECTRAL PROPERTIES FOR DISCRETE STURMIAN DIRAC OPERATORS
| dc.contributor.author | Prado, Roberto A. [UNESP] | |
| dc.contributor.author | Charao, Ruy C. | |
| dc.contributor.institution | Universidade Estadual Paulista (Unesp) | |
| dc.contributor.institution | Universidade Federal de Santa Catarina (UFSC) | |
| dc.date.accessioned | 2019-10-04T12:36:48Z | |
| dc.date.available | 2019-10-04T12:36:48Z | |
| dc.date.issued | 2019-04-01 | |
| dc.description.abstract | We establish invariants for the trace map associated to a family of 1D discrete Dirac operators with Sturmian potentials. Using these invariants we prove that the operators have purely singular continuous spectrum of zero Lebesgue measure, uniformly on the mass and parameters that define the potentials. For rotation numbers of bounded density we prove that these Dirac operators have purely alpha-continuous spectrum, as to the Schrodinger case, for some alpha is an element of (0, 1). To the Sturmian Schrodinger and Dirac models we establish a comparison between invariants of the trace maps, which allows to compare the numbers alpha's and lower bounds on transport exponents. | en |
| dc.description.affiliation | Univ Estadual Paulista, Dept Math & Comp Sci, UNESP, BR-19060900 Presidente Prudente, SP, Brazil | |
| dc.description.affiliation | Univ Fed Santa Catarina, Dept Math, UFSC, BR-88040900 Florianopolis, SC, Brazil | |
| dc.description.affiliationUnesp | Univ Estadual Paulista, Dept Math & Comp Sci, UNESP, BR-19060900 Presidente Prudente, SP, Brazil | |
| dc.description.sponsorship | Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) | |
| dc.description.sponsorshipId | CNPq: 157873/2015-3 | |
| dc.format.extent | 391-416 | |
| dc.identifier.citation | Osaka Journal Of Mathematics. Toyonaka: Osaka Journal Of Mathematics, v. 56, n. 2, p. 391-416, 2019. | |
| dc.identifier.issn | 0030-6126 | |
| dc.identifier.uri | http://hdl.handle.net/11449/185591 | |
| dc.identifier.wos | WOS:000463159600011 | |
| dc.language.iso | eng | |
| dc.publisher | Osaka Journal Of Mathematics | |
| dc.relation.ispartof | Osaka Journal Of Mathematics | |
| dc.rights.accessRights | Acesso restrito | |
| dc.source | Web of Science | |
| dc.title | INVARIANTS OF THE TRACE MAP AND UNIFORM SPECTRAL PROPERTIES FOR DISCRETE STURMIAN DIRAC OPERATORS | en |
| dc.type | Artigo | |
| dcterms.rightsHolder | Osaka Journal Of Mathematics |