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

Full-text: Open access

Abstract

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.

Article information

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

Dates
First available in Project Euclid: 1 June 2017

Permanent link to this document
https://projecteuclid.org/euclid.ojm/1496282424

Mathematical Reviews number (MathSciNet)
MR3657230

Zentralblatt MATH identifier
1375.39038

Subjects
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]

Citation

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. https://projecteuclid.org/euclid.ojm/1496282424


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