| 上三角无穷维Hamilton算子点谱的对称性 |
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| 引用本文： | 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. DOI: 10.3770/j.issn:1000-341X.2009.05.018 |
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| 作者姓名： | 王华 阿拉坦仓 黄俊杰 |
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| 作者单位： | 内蒙古大学理工学院数学系, 内蒙古 呼和浩特 010021; 内蒙古工业大学理学院数学系, 内蒙古 呼和浩特 010051;内蒙古工业大学理学院数学系, 内蒙古 呼和浩特 010051;内蒙古工业大学理学院数学系, 内蒙古 呼和浩特 010051 |
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| 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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| 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 σP（A） and σ1/P（-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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| 关 键 词： | Hamilton 对称性 无穷维 三角点 算子谱 频谱特性 充分条件 哈密顿 |
| 收稿时间： | 2007-09-07 |
| 修稿时间： | 2008-04-16 |
Symmetry of the Point Spectrum of Upper Triangular Infinite Dimensional Hamiltonian Operators |
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| WANG Hu,Alatancang and HUANG Jun Jie. Symmetry of the Point Spectrum of Upper Triangular Infinite Dimensional Hamiltonian Operators[J]. Journal of Mathematical Research with Applications, 2009, 29(5): 907-912. DOI: 10.3770/j.issn:1000-341X.2009.05.018 |
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| Authors: | WANG Hu Alatancang HUANG Jun Jie |
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| Affiliation: | Department of Mathematics, College of Science and Technology, Inner Mongolia University, Inner Mongolia 010021, China; Department of Mathematics, College of Science, Inner Mongolia University of Technology, Inner Mongolia 010051, China;Department of Mathematics, College of Science and Technology, Inner Mongolia University, Inner Mongolia 010021, China; |
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| Abstract: | 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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| Keywords: | non-self-adjoint operator infinite dimensional Hamiltonian operator point spectrum symmetry. |
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