论文标题
关于与非紧凑型运算符数值的数值奇异值的注释
A note on numerical singular values of compositions with non-compact operators
论文作者
论文摘要
线性非压缩操作员很难研究，因为它们不存在于有限的维度世界中。最近，Mathé和Hofmann研究了非紧凑型Hausdorff Moment Operator和紧凑型积分运算符的紧凑组成的单数值，并发现了可靠的参数，但没有严格的证据，即这些单数值仅比单独的积分运算符的奇异值略快。但是，在数值上没有提到合并算子的奇异值呈指数速度的奇异值。在本说明中，我们提供了缺少的数值结果，并提供了一个解释，为什么两个看似矛盾的结果可能都是正确的。
Linear non-compact operators are difficult to study because they do not exist in the finite dimensional world. Recently, Mathé and Hofmann studied the singular values of the compact composition of the non-compact Hausdorff moment operator and the compact integral operator and found credible arguments, but no strict proof, that those singular values fall only slightly faster than those of the integral operator alone. However, the fact that numerically the singular values of the combined operator fall exponentially fast was not mentioned. In this note, we provide the missing numerical results and provide an explanation why the two seemingly contradicting results may both be true.
