Osaka Journal of Mathematics
- Osaka J. Math.
- Volume 54, Number 2 (2017), 273-285.
On the spectral Hausdorff dimension of 1D discrete Schrödinger operators under power decaying perturbations
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.
Osaka J. Math., Volume 54, Number 2 (2017), 273-285.
First available in Project Euclid: 1 June 2017
Permanent link to this document
Mathematical Reviews number (MathSciNet)
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. https://projecteuclid.org/euclid.ojm/1496282424