| 一类无界三对角型算子矩阵的谱估计* |
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| 引用本文： | 孔艺慧,齐雅茹.一类无界三对角型算子矩阵的谱估计*[J].数学年刊A辑(中文版),2023,44(3):241-254. |
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| 作者姓名： | 孔艺慧 齐雅茹 |
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| 作者单位： | 内蒙古工业大学理学院数学系, 呼和浩特 010051. |
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| 基金项目： | 国家自然科学基金 (No.12261065), 内蒙古自然科学基金 (No.2021LHMS01004)和内蒙古自治区直属高校基本科研业务费项目 (No.JY20220151, No.JY20220387) |
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| 摘 要： | 本文研究了一类 n × n阶无界三对角型对角占优算子矩阵的可闭 (闭) 性和谱估计问题.首先通过分析算子矩阵内部元素之间的关系, 给出了该类算子矩阵可闭 (闭)的一个充分条件, 并在此基础上利用 Schur 补刻画了其谱的范围.最后将所得结果应用于量子力学中的三通道 Hamilton 算子矩阵中,说明了结果的合理性.
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| 关 键 词： | 三对角型算子矩阵 Schur补 谱估计 |
| 收稿时间： | 2022/10/26 0:00:00 |
| 修稿时间： | 2023/5/15 0:00:00 |
Spectral Estimation for a Class of Unbounded Tridiagonal Operator Matrix |
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| KONG Yihui,QI Yaru.Spectral Estimation for a Class of Unbounded Tridiagonal Operator Matrix[J].Chinese Annals of Mathematics,2023,44(3):241-254. |
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| Authors: | KONG Yihui QI Yaru |
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| Institution: | Department of Mathematics, College of Sciences, Inner Mongolia University of Technology, Hohhot 010051.; Corresponding author. Department of Mathematics, College of Sciences, Inner Mongolia University of Technology, Hohhot 010051. |
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| Abstract: | In this paper, the authors study the closability (closedness) and spectral estimation of a class of n × n unbounded tridiagonal operator matrices. By analyzing the relationship between the internal elements of the operator matrix, a sufficient condition for the closable (closed) of this type of operator matrix is given, and on this basis, the enclosures of the spectrum is described by Schur complement. Finally, the results are applied to the three-channel Hamiltonian operator matrix in quantum mechanics, which shows the rationality of the results. |
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| Keywords: | Tridiagonal operator matrix Schur complement Spectral estimation |
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