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April 2019 Invariants of the trace map and uniform spectral properties for discrete Sturmian Dirac operators
Roberto A. Prado, Ruy C. Charão
Osaka J. Math. 56(2): 391-416 (April 2019).

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 Schrödinger case, for some $\alpha \in (0,1)$. To the Sturmian Schrödinger 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.

Citation

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Roberto A. Prado. Ruy C. Charão. "Invariants of the trace map and uniform spectral properties for discrete Sturmian Dirac operators." Osaka J. Math. 56 (2) 391 - 416, April 2019.

Information

Published: April 2019
First available in Project Euclid: 3 April 2019

zbMATH: 07080090
MathSciNet: MR3934981

Subjects:
Primary: 81Q10
Secondary: 47B99

Rights: Copyright © 2019 Osaka University and Osaka City University, Departments of Mathematics

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Vol.56 • No. 2 • April 2019
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