Compact linear operators on functional spaces with two norms
Compact linear operators on functional spaces with two norms
复制标题
具有两个范数的函数空间上的紧致线性算子
DOI：
10.1007/bf01238216
复制
发表时间：
1998
影响因子：
0.8
通讯作者：
M. Krein
中科院分区：
文献类型：
--
作者：
M. Krein
本文建立了具有两个范数的线性空间中算子理论的一些原理。著名的希尔伯特-施密特定理的本征函数展开的sourcewise表示的功能，美世定理和其他结果可以被认为是特殊情况下的陈述。所提出的一般方法被用来构造可对称化算子理论和研究紧算子特征值的渐近性态。
Some principles of the operator theory in a linear space with two norms are established in this paper. The well-known Hilbert-Schmidt theorem on the eigenfunction expansion of sourcewise represented functions, Mercer's theorem and other results can be consider as special cases of the statements presented. The general approach proposed is used to construct the theory of symmetrizable operators and to investigate the asymptotic behaviour of eigenvalues of compact operators.