Osaka Journal of Mathematics

On the spectral Hausdorff dimension of 1D discrete Schrödinger operators under power decaying perturbations

V.R. Bazao, S.L. Carvalho, and C.R. de Oliveira

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We show that spectral Hausdorff dimensional properties of discrete Schrödinger operators with (1) Sturmian potentials of bounded density and (2) a class of sparse potentials are preserved under suitable polynomial decaying perturbations, when the spectrum of these perturbed operators have some singular continuous component.

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Osaka J. Math., Volume 54, Number 2 (2017), 273-285.

First available in Project Euclid: 1 June 2017

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Zentralblatt MATH identifier

Primary: 34L40: Particular operators (Dirac, one-dimensional Schrödinger, etc.) 81Q10: Selfadjoint operator theory in quantum theory, including spectral analysis
Secondary: 35J10: Schrödinger operator [See also 35Pxx] 28A80: Fractals [See also 37Fxx]


Bazao, V.R.; Carvalho, S.L.; de Oliveira, C.R. On the spectral Hausdorff dimension of 1D discrete Schrödinger operators under power decaying perturbations. Osaka J. Math. 54 (2017), no. 2, 273--285.

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