| 关于一类无限维线性算子谱的刻画 |
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| 引用本文： | 邓勇,张四保.关于一类无限维线性算子谱的刻画[J].数学的实践与认识,2011,41(8). |
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| 作者姓名： | 邓勇 张四保 |
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| 作者单位： | 喀什师范学院数学系,新疆喀什市,844006 |
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| 基金项目： | 新疆维吾尔自治区高校科研计划重点项目 |
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| 摘 要： | 利用有限维线性空间的理论,研究了一类无限阶Toeplitz矩阵的特征值问题,得到这类无限阶矩阵的特征值是连续变化的,并且其谱集合是由复平面上的单位圆盘{z∈C,|z|<1}被多项式函数f(z)=(?)a_iz~i作用后,所得到的像曲线内部的点组成.
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| 关 键 词： | 无限维 线性算子 Toeplitz矩阵 谱 特征向量 |
A Characterization for Spectrum on the class of Infinite Dimensional Linear Operator |
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| DENG Yong,ZHANG Si-bao.A Characterization for Spectrum on the class of Infinite Dimensional Linear Operator[J].Mathematics in Practice and Theory,2011,41(8). |
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| Authors: | DENG Yong ZHANG Si-bao |
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| Institution: | DENG Yong,ZHANG Si-bao (Department of Mathematics of Kashi Teachers College,Kashi 844007,China) |
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| Abstract: | By using the method of finite dimensional linear space,the eigenvalues of an infinite Toeplitz matrix is studied,the results that the eigenvalues of it's continuous and the set of the eigenvalues is composed of point of the unit circle{z∈C,|z|<1}under the action of the function f(z) =■a_iz~i are given. |
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| Keywords: | infinite dimensional linear operator Toeplitz matrix spectrum eigenvector |
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