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

作　　者：王揄辰 杨士俊 WANG Yu-chen;YANG Shi-jun(School of Statistics and Mathematics,Zhejiang Gongshang University,Hangzhou 310018,China)

机构地区：[1]浙江工商大学统计与数学学院,浙江杭州310018

出　　处：《高校应用数学学报（A辑）》2022年第1期123-126,共4页Applied Mathematics A Journal of Chinese Universities(Ser.A)

摘　　要：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.

关 键 词：再生核希尔伯特空间 再生核 连续线性泛函 范数 

分 类 号：O177.1[理学—数学] O177.92[理学—基础数学]