ON THE SPECTRAL HAUSDORFF DIMENSION OF 1D DISCRETE SCHRODINGER OPERATORS UNDER POWER DECAYING PERTURBATIONS

被引：0

作者：

Bazao, V. R. ^{[1
]}

Carvalho, S. L. ^{[2
]}

de Oliveira, C. R. ^{[1
]}

机构：

[1] Univ Fed Sao Carlos, Dept Matemat, BR-13560970 Sao Carlos, SP, Brazil

[2] Univ Fed Minas Gerais, Dept Matemat, BR-30161970 Belo Horizonte, MG, Brazil

来源：

OSAKA JOURNAL OF MATHEMATICS | 2017年 / 54卷 / 02期

关键词：

SINGULAR CONTINUOUS-SPECTRUM; RANK-ONE PERTURBATIONS; QUASI-CRYSTALS; ALPHA-CONTINUITY; LAW SUBORDINACY; LINE OPERATORS; LOCALIZATION;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that spectral Hausdorff dimensional properties of discrete Schr "odinger 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.

引用

页码：273 / 285

页数：13

共 50 条

[21] Discrete Spectrum of Differential Operators in Spectral Gaps under Nonnegative Perturbations of High Order
V. A. Slousch
Journal of Mathematical Sciences, 2003, 115 (2) : 2272 - 2278
[22] Some Schrodinger operators with power-decaying potentials and pure point spectrum, II. The discrete case
Remling, C
HELVETICA PHYSICA ACTA, 1998, 71 (02): : 200 - 213
[23] KAM tori in 1D random discrete nonlinear Schrodinger model?
Johansson, M.
Kopidakis, G.
Aubry, S.
EPL, 2010, 91 (05)
[24] Point Spectrum and SULE for Time-Periodic Perturbations of Discrete 1D Schrödinger Operators with Electric Fields
César R. de Oliveira
Mariane Pigossi
Journal of Statistical Physics, 2018, 173 : 140 - 162
[25] Spectral theory of 1-D Schrodinger operators with unbounded potentials
Gordon, A.
Holt, J.
Molchanov, S.
Probability and Mathematical Physics: A Volume in Honor of Stanislav Molchanov, 2007, 42 : 181 - 198
[26] Extensions and spectral problems of 1D discrete Hamiltonian systems
Allahverdiev, Bilender P.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2013, 36 (18) : 2554 - 2563
[27] Mass-critical inverse Strichartz theorems for 1d Schrodinger operators
Jao, Casey
Killip, Rowan
Visan, Monica
REVISTA MATEMATICA IBEROAMERICANA, 2019, 35 (03) : 703 - 730
[28] Some Remarks on 1D Schrodinger Operators With Localized Magnetic and Electric Potentials
Golovaty, Yuriy
FRONTIERS IN PHYSICS, 2019, 7 (May)
[29] Inverse problem for the discrete 1D Schrodinger operator with small periodic potentials
Korotyaev, E
Kutsenko, A
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2006, 261 (03) : 673 - 692
[30] Sparse 1D discrete Dirac operators I: Quantum transport
Prado, Roberto A.
de Oliveira, Cesar R.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2012, 385 (02) : 947 - 960

← 1 2 3 4 5 →