一类无穷维线性算子的谱连续性与特征向量算法  

A laconic proof for continuity of spectrum of infinite dimensional linear operator and computation of eigenvectors

作　　者：李大林[1] 黄雪燕[2] 

机构地区：[1]柳州职业技术学院基础部,广西柳州545006 [2]钦州学院数学与计算机科学系,广西钦州535000

出　　处：《纺织高校基础科学学报》2008年第4期470-472,共3页Basic Sciences Journal of Textile Universities

基　　金：广西教育厅科研项目(200707LZ259)

摘　　要：从矩阵的角度研究无穷维线性空间中具有广泛应用的前、后移位算子及位似算子.它们的线性组合在某组基下的矩阵为无限阶三对角Toeplitz矩阵.虽然这类矩阵不可以用有限阶矩阵的方法处理,但通过一系列相伴的初等变换,发现它们的特征值是连续变化的,获得特征向量的递推公式,从而得到这些算子的谱的连续性的一个直观证明.而零谱值对应的特征向量正好是齐次线性积分-微分方程的解.The pre-displacement operators, backward operators and homothetic operators which take a series of application are studied in the view point of matrix. It is an infinite Toeplitz matrix under the matrix of their linear combination in one basis. Although the infinite Toeplitz matrix can not be dealt with the methods for finite matrix, it is found that its spectral is continuous by a series of pertinent elementary transformations for infinite matrices. And the recurrence formula is obtained obtained for eigenvectors. Thus, an intuitive proof is got for the continuity of the spectral of these operators. The solutions of a homogeneous linear ordinary integral-differential equation are expressed by the eigenvectors belonging to the eigenvalue zero of an infinite Toeplitz matrix.

关 键 词：无穷维 线性算子 TOEPLITZ矩阵 谱 特征向量 

分 类 号：O221[理学—运筹学与控制论]