THE ABSENCE OF SINGULAR CONTINUOUS SPECTRUM FOR PERTURBED JACOBI OPERATORS

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THE ABSENCE OF SINGULAR CONTINUOUS SPECTRUM FOR PERTURBED JACOBI OPERATORS

THE ABSENCE OF SINGULAR CONTINUOUS SPECTRUM FOR PERTURBED JACOBI OPERATORS

THE ABSENCE OF SINGULAR CONTINUOUS SPECTRUM FOR PERTURBED JACOBI OPERATORS

THE ABSENCE OF SINGULAR CONTINUOUS SPECTRUM FOR PERTURBED JACOBI OPERATORS

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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

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).

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： 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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