辛空间两类算子阵的谱分析
he spectral analysis of two classes operaters
本文讨论了辛空间中哈密顿算子矩阵及反哈密顿算子阵特征值和特征向量性质，证明了哈密顿阵的数值域关于Y轴对称，对于几类简单的哈密顿阵，讨论了主矩阵与分块矩阵的关系，给出了矩阵 H 和H 的一个联系,给出了H 的谱关于原点对称（ - ）的一个充分条件，并且揭示了 和- 所对应的两个特征向量间的关系.完整的 刻画了反Hamilton算子的点谱与剩余谱之间的关系，证明了一类Hamilton算子的剩余谱为空。构造了一些具体的例子，把定理应用在波动方程生成的无穷维Hamilton算子。文中提供了几个基本的问题。
In this paper ,we discuss the properties of eigvalues and eigvectors of Hamilton operater and Anti-operater,alse have proved that the numerical field of Hamilton matrix is symmetric about Y axex, We give a connection between H and H ,also a sufficient condition have been established so that ,most importantly,we discover a interesting connection between the two eigvectors with regard to eigvalues .A sufficient and necessary condition have also been given so that the residual spectrum of anti-Hamilton operater is null.Some open problems are offered in this paper.
张东、杨雪源
数学物理学
Hamilton算子 反Hamilton算子 谱 特征向量 剩余谱
Hamilton operateranti-Hamilton operaterspectrumeigvectorsnumerical fieldresidual spectral.
张东,杨雪源 .辛空间两类算子阵的谱分析[EB/OL].(2005-07-25)[2025-08-10].http://www.paper.edu.cn/releasepaper/content/200507-174.点此复制
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