THE ABSENCE OF SINGULAR CONTINUOUS SPECTRUM FOR PERTURBED JACOBI OPERATORS

doi:10.1007/s10473-024-0208-x

数学物理学报(英文版) ›› 2024, Vol. 44 ›› Issue (2): 515-531.doi: 10.1007/s10473-024-0208-x

THE ABSENCE OF SINGULAR CONTINUOUS SPECTRUM FOR PERTURBED JACOBI OPERATORS

Zhengqi FU¹, Xiong LI^2,*

1. Department of Basic Sciences, Naval Submarine Academy, Qingdao 266199, China;
2. Laboratory of Mathematics and Complex Systems (Ministry of Education), School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China

收稿日期:2022-09-20 修回日期:2023-02-07 出版日期:2024-04-25 发布日期:2024-04-16
通讯作者: *Xiong LI, E-mail: xli@bnu.edu.cn
作者简介:Zhengqi FU, E-mail: zqfu94@163.com
基金资助:
Fu's work was supported by the NSFC (12371158).

THE ABSENCE OF SINGULAR CONTINUOUS SPECTRUM FOR PERTURBED JACOBI OPERATORS

Zhengqi FU¹, Xiong LI^2,*

1. Department of Basic Sciences, Naval Submarine Academy, Qingdao 266199, China;
2. Laboratory of Mathematics and Complex Systems (Ministry of Education), School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China

Received:2022-09-20 Revised:2023-02-07 Online:2024-04-25 Published:2024-04-16
Contact: *Xiong LI, E-mail: xli@bnu.edu.cn
About author:Zhengqi FU, E-mail: zqfu94@163.com
Supported by:
Fu's work was supported by the NSFC (12371158).

摘要/Abstract

摘要： This paper is mainly about the spectral properties of a class of Jacobi operators $ (H_{c,b}u)(n)=c_{n}u(n+1)+c_{n-1}u(n-1)+b_{n}u(n), $ where $|c_{n}-1|=O(n^{-\alpha})$ and $b_{n}=O(n^{-1})$. We will show that, for $\alpha\ge1$, the singular continuous spectrum of the operator is empty.

关键词: Jacobi operator, singular continuous spectrum, Prüfer variables

Abstract: This paper is mainly about the spectral properties of a class of Jacobi operators $ (H_{c,b}u)(n)=c_{n}u(n+1)+c_{n-1}u(n-1)+b_{n}u(n), $ where $|c_{n}-1|=O(n^{-\alpha})$ and $b_{n}=O(n^{-1})$. We will show that, for $\alpha\ge1$, the singular continuous spectrum of the operator is empty.

Key words: Jacobi operator, singular continuous spectrum, Prüfer variables

中图分类号:

81Q10

Zhengqi FU, Xiong LI. THE ABSENCE OF SINGULAR CONTINUOUS SPECTRUM FOR PERTURBED JACOBI OPERATORS[J]. 数学物理学报(英文版), 2024, 44(2): 515-531.

Zhengqi FU, Xiong LI. THE ABSENCE OF SINGULAR CONTINUOUS SPECTRUM FOR PERTURBED JACOBI OPERATORS[J]. Acta mathematica scientia,Series B, 2024, 44(2): 515-531.

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THE ABSENCE OF SINGULAR CONTINUOUS SPECTRUM FOR PERTURBED JACOBI OPERATORS

THE ABSENCE OF SINGULAR CONTINUOUS SPECTRUM FOR PERTURBED JACOBI OPERATORS

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