扰动雅可比算子不存在奇异连续谱

IF 1.2 4区数学 Q1 MATHEMATICS

Acta Mathematica Scientia Pub Date : 2024-02-06 DOI:10.1007/s10473-024-0208-x

Zhengqi Fu, Xiong Li

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引用次数: 0

摘要

本文主要讨论一类雅可比算子$$({H_{c,b}}u)(n) = {c_n}u(n + 1) + {c_{n - 1}}u(n - 1) + {b_n}u(n)的谱性质，其中∣cn - 1∣ = O(n-α)，bn = O(n-1)。我们将证明，对于 α ≥ 1，算子的奇异连续谱是空的。

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The absence of singular continuous spectrum for perturbed Jacobi operators

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^−α) and b_n = O(n⁻¹). We will show that, for α ≥ 1, the singular continuous spectrum of the operator is empty.

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来源期刊

Acta Mathematica Scientia 数学-数学

CiteScore

2.00

自引率

10.00%

发文量

2614

审稿时长

6 months

期刊介绍： Acta Mathematica Scientia was founded by Prof. Li Guoping (Lee Kwok Ping) in April 1981. The aim of Acta Mathematica Scientia is to present to the specialized readers important new achievements in the areas of mathematical sciences. The journal considers for publication of original research papers in all areas related to the frontier branches of mathematics with other science and technology.