Acta mathematica scientia,Series B ›› 2024, Vol. 44 ›› Issue (2): 515-531.doi: 10.1007/s10473-024-0208-x

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THE ABSENCE OF SINGULAR CONTINUOUS SPECTRUM FOR PERTURBED JACOBI OPERATORS

Zhengqi FU1, Xiong LI2,*   

  1. 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).

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

CLC Number: 

  • 81Q10
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