| 王华,阿拉坦仓,黄俊杰.上三角无穷维Hamilton算子点谱的对称性[J].数学研究及应用,2009,29(5):907~912 |
| 上三角无穷维Hamilton算子点谱的对称性 |
| Symmetry of the Point Spectrum of Upper Triangular Infinite Dimensional Hamiltonian Operators |
| 投稿时间：2007-09-07 修订日期：2008-04-16 |
| DOI：10.3770/j.issn:1000-341X.2009.05.018 |
| 中文关键词: 非自伴算子 无穷维Hamilton算子 点谱 对称性. |
| 英文关键词:non-self-adjoint operator infinite dimensional Hamiltonian operator point spectrum symmetry. |
| 基金项目:国家自然科学基金(No.10562002); 内蒙古自治区自然科学基金(Nos.200508010103;200711020106); 高等学校博士学科点专项科研基金(No.20070126002); 内蒙古大学高层次引进人才科研启动基金(No.206029). |
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| 中文摘要: |
| 利用上三角无穷维Hamilton算子点谱的刻画,首先得到点谱的两个组成部分$\sigma_p (A)$与$\sigma_p^1(-A^*)$关于虚轴对称的充分必要条件.基此, 完全刻画了一类上三角无穷维Hamilton算子点谱的对称性, 并举例验证了结果的合理性. |
| 英文摘要: |
| In this paper, by using characterization of the point spectrum of the upper triangular infinite dimensional Hamiltonian operator $H$, a necessary and sufficient condition is obtained on the symmetry of $\sigma_p(A)$ and $\sigma_p^1(-A^*)$ with respect to the imaginary axis. Then the symmetry of the point spectrum of $H$ is given, and several examples are presented to illustrate the results. |
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