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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2024, Vol. 41 ›› Issue (3): 568-576.doi: 10.3969/j.issn.1005-3085.2024.03.014

• • 上一篇    下一篇

无界分块算子矩阵的可分解性及其应用

王晓丽1,  阿拉坦仓2   

  1. 1. 内蒙古财经大学统计与数学学院，呼和浩特 010070
    2. 内蒙古自治区应用数学中心，呼和浩特 010022
  • 收稿日期:2021-10-17 接受日期:2022-11-18 出版日期:2024-06-15 发布日期:2024-08-15
  • 基金资助:
    国家自然科学基金(11761092)；内蒙古自治区直属高校基本科研业务费(NCYWT23022).

The Decomposability of Unbounded Block Operator Matrices and Its Application

WANG Xiaoli11,  Alatancang2   

  1. 1. Statistics and Mathematics College, Inner Mongolia University of Finance and Economics, Hohhot 010070
    2. Inner Mongolia Applied Mathematics Center, Hohhot 010022
  • Received:2021-10-17 Accepted:2022-11-18 Online:2024-06-15 Published:2024-08-15
  • Supported by:
    The National Natural Science Foundation of China (11761092); the Fundamental Research Funds for the Inner Mongolia Autonomous Region Universities (NCYWT23022).

摘要： 无界分块算子矩阵广泛地出现于系统理论、非线性分析以及发展方程问题等领域，在理论和实际应用两方面都受到广泛关注。首先，利用算子局部谱理论得到无界分块算子矩阵可分解性的刻画，其次，给出算子矩阵可分解性保持对角稳定的条件，推广并得到分块算子矩阵在无界情形下的一些局部谱性质。最后，作为应用考察Hamilton算子的可分解性并举例予以说明。

关键词: 可分解性, 无界分块算子矩阵, 局部谱性质, Hamilton算子

Abstract: Unbounded block operator matrix widely appears in the fields of system theory, nonlinear analysis and evolution equation problems, and has been widely concerned in both theory and practical application. Firstly, the decomposability of unbounded block operator matrix is characterized by using local spectrum theory. Secondly, the condition that the decomposability of operator matrix remains diagonally stable is given, and some local spectral properties of block operator matrix are generalized and obtained. Finally, as an application, the decomposability of Hamilton operator is investigated and illustrated with examples.

Key words: decomposability, unbounded block operator matrix, local spectral property, Hamiltonian operator

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