An Example of Embedded Singular Continuous Spectrum for Discrete Schrödinger Operators

被引：0

作者：

Fu, Zheng Qi ^{[1
]}

Li, Xiong ^{[1
]}

机构：

[1] Beijing Normal Univ, Sch Math Sci, Lab Math & Complex Syst, Minist Educ, Beijing 100875, Peoples R China

来源：

ACTA MATHEMATICA SINICA-ENGLISH SERIES | 2024年 / 40卷 / 08期

基金：

中国国家自然科学基金;

关键词：

Sparse potentials; singular continuous spectrum; Pr & uuml; fer variables; PRUFER;

D O I：

10.1007/s10114-024-2574-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present an example of a potential such that the corresponding discrete Schr & ouml;dinger operator has singular continuous spectrum embedded in the absolutely continuous spectrum.

引用

页码：1837 / 1849

页数：13

共 50 条

[41] Schrödinger operators with empty singularly continuous spectra
Demuth M.
Mathematical Physics, Analysis and Geometry, 1999, 2 (3) : 223 - 244
[42] A Family of Schrödinger Operators Whose Spectrum is an Interval
Helge Krüger
Communications in Mathematical Physics, 2009, 290 : 935 - 939
[43] The Negative Spectrum of Schr?dinger Operators with Fractal Potentials
Bo Wu
Hongyong Wang
Weiyi Su
AnalysisinTheoryandApplications, 2015, 31 (04) : 381 - 393
[44] Discreteness of spectrum conditions for Schrödinger operators on manifolds
V. A. Kondrat’ev
M. A. Shubin
Functional Analysis and Its Applications, 1999, 33 : 231 - 232
[45] On absolute continuity of the spectrum of periodic Schrödinger operators
Ihyeok Seo
Monatshefte für Mathematik, 2016, 180 : 893 - 912
[46] New Estimates for the Bottom of the Spectrum of Schrödinger Operators
Daniel Levin
Annals of Global Analysis and Geometry, 2006, 29 : 313 - 322
[47] The Essential Spectrum of Schrödinger, Jacobi, and CMV Operators
Yoram Last
Barry Simon
Journal d’Analyse Mathématique, 2006, 98 : 183 - 220
[48] On the spectrum of lattice Schrödinger operators with deterministic potential
J. Bourgain
Journal d'Analyse Mathématique, 2002, 87 : 37 - 75
[49] Essential Spectrum of Schrödinger Operators on Periodic Graphs
V. S. Rabinovich
Functional Analysis and Its Applications, 2018, 52 : 66 - 69
[50] Construction of QuasiPeriodic Schrödinger Operators with Cantor Spectrum
Xuanji Hou
Yuan Shan
Jiangong You
Annales Henri Poincaré, 2019, 20 : 3563 - 3601

← 1 2 3 4 5 →