再生核希尔伯特空间连续线性泛函的范数及其应用

The norm of continuous linear functional on the reproducing kernel Hilbert space and its applications

考虑了再生核希尔伯特空间连续线性泛函范数的表示,得到了用其范数平方等于该线性泛函连续两次作于再生核的简明表示.对于常见的Sobolev-Hibert空间而言,其再生核则可用截幂函数来表示,从而得到Sobolev-Hibert空间上连续线性泛函范数的简洁表示,以新视角解释和简化了文献中的现有结果.

This paper considers the expression of a continuous linear functional on a reproducing kernel Hilbert space and a concise formula is obtained. This formula states that the functional acting on the reproducing kernel twice gives the square of its norm. As for the common Sobolev-Hibert spaces,their reproducing kernels can usually be expressed by the truncated power functions and this leads to a concise expression of the norm of a continuous linear functional on a Sobolev-Hibert space, thereby simplifying some existing results in a new point of view.