严格遍历雅可比矩阵和CMV矩阵谱中的开隙

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis Pub Date : 2025-08-29 DOI:10.1016/j.jfa.2025.111182

David Damanik , Long Li

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引用次数: 0

摘要

证明了与一般连续采样函数相关的动态定义Jacobi矩阵和CMV矩阵具有由Gap标记定理预测的所有开放的间隙。根据Jacobi矩阵和CMV矩阵共振舌边界的解析性，给出了拟周期解析抽样函数在亚临界区域的一般间隙打开机制。

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Opening gaps in the spectrum of strictly ergodic Jacobi and CMV matrices

We prove that dynamically defined Jacobi and CMV matrices associated with generic continuous sampling functions have all gaps predicted by the Gap Labeling Theorem open. We also give a mechanism for generic gap opening for quasi-periodic analytic sampling functions in the subcritical region following from the analyticity of resonance tongue boundaries for both Jacobi and CMV matrices.

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来源期刊

Journal of Functional Analysis 数学-数学

CiteScore

3.20

自引率

5.90%

发文量

271

审稿时长

7.5 months

期刊介绍： The Journal of Functional Analysis presents original research papers in all scientific disciplines in which modern functional analysis plays a basic role. Articles by scientists in a variety of interdisciplinary areas are published. Research Areas Include: • Significant applications of functional analysis, including those to other areas of mathematics • New developments in functional analysis • Contributions to important problems in and challenges to functional analysis