INVARIANTS OF THE TRACE MAP AND UNIFORM SPECTRAL PROPERTIES FOR DISCRETE STURMIAN DIRAC OPERATORS

Prado, Roberto A.; Charão, Ruy C.

doi:https://doi.org/10.18910/72324

INVARIANTS OF THE TRACE MAP AND UNIFORM SPECTRAL PROPERTIES FOR DISCRETE STURMIAN DIRAC OPERATORS

Prado, Roberto A.; Charão, Ruy C.

Osaka Journal of Mathematics, 2019, 56(2), 391-416

アクセス数:205件（2025-07-05 01:56 集計）

固定URL: https://doi.org/10.18910/72324

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タイトル	INVARIANTS OF THE TRACE MAP AND UNIFORM SPECTRAL PROPERTIES FOR DISCRETE STURMIAN DIRAC OPERATORS
著者	著者名 Prado, Roberto A.
著者	著者名 Charão, Ruy C.
抄録	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 α-continuous spectrum, as to the Schrödinger case, for some α ∈ (0, 1). To the Sturmian Schr¨odinger and Dirac models we establish a comparison between invariants of the trace maps, which allows to compare the numbers α’s and lower bounds on transport exponents.
出版者	Osaka University and Osaka City University, Departments of Mathematics
収録物名	Osaka Journal of Mathematics
巻(号)	56(2)
ページ	391-416
刊行年月	2019-04
言語	英語
ハンドルURL	https://hdl.handle.net/11094/72324
DOI	https://doi.org/10.18910/72324
PISSN	00306126
NCID	AA00765910
アクセス権	open access
出版タイプ	Version of Record
カテゴリ	紀要論文 Departmental Bulletin Paper
カテゴリ	Osaka Journal of Mathematics / Volume 56, Number 2 （2019-4）

資源タイプ	紀要論文
ローカル資源タイプ	紀要論文
DCMI資源タイプ	text
DCTERMS.bibliographicCitation	Osaka Journal of Mathematics. 2019, 56(2), p. 391-416
DC.title	INVARIANTS OF THE TRACE MAP AND UNIFORM SPECTRAL PROPERTIES FOR DISCRETE STURMIAN DIRAC OPERATORS
DC.creator	Prado, Roberto A.
DC.creator	Charão, Ruy C.
DC.publisher	Osaka University and Osaka City University, Departments of Mathematics
DC.language' scheme='DCTERMS.RFC1766	英語
DC.type' scheme='DCTERMS.DCMIType	text
DCTERMS.issued' scheme='DCTERMS.W3CDTF	2019-04
DCTERMS.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 α-continuous spectrum, as to the Schrödinger case, for some α ∈ (0, 1). To the Sturmian Schr¨odinger and Dirac models we establish a comparison between invariants of the trace maps, which allows to compare the numbers α’s and lower bounds on transport exponents.
DC.identifier	10.18910/72324
DC.format	72324
citation_title	INVARIANTS OF THE TRACE MAP AND UNIFORM SPECTRAL PROPERTIES FOR DISCRETE STURMIAN DIRAC OPERATORS
citation_author	Prado, Roberto A.
citation_author	Charão, Ruy C.
citation_publisher	Osaka University and Osaka City University, Departments of Mathematics
citation_language	英語
citation_date	2019-04
citation_journal_title	Osaka Journal of Mathematics
citation_volume	56
citation_issue	2
citation_firstpage	391
citation_lastpage	416
citation_public_url	https://hdl.handle.net/11094/72324
citation_doi_detail	10.18910/72324
citation_doi	https://doi.org/10.18910/72324

INVARIANTS OF THE TRACE MAP AND UNIFORM SPECTRAL PROPERTIES FOR DISCRETE STURMIAN DIRAC OPERATORS

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