Journe小波变换像空间描述

1引言1950年N.Aronszjan发表的一篇综述性文章《Theory of reproducing kernels》标志再生核理论的初步形成.由于再生核有许多良好的计算性质,S.Saitoh总结并深入研究再生核基本理论,进一步拓展了再生核的应用领域;徐利治把再生核应用于L~2(B)(B是复平面上的一个区域)中解析函数重积分降维问题,并提出了一个能对一些预先给出的

CHARACTERIZATION OF IMAGE SPACE OF JOURNE WAVELET TRANSFORM

In this paper,the expression of the reproducing kernel function in the image space of the Journe wavelet transform is shown based on the fact that the image space of the wavelet transform is a reproducing kernel Hilbert space.The connections between the image space of Journe wavelet transform and the image space of the known reproducing kernel space are established by the theories of reproducing kernel.The properties and the structures of the image space of the Journe wavelet transform can be characterized by the properties and the structures of the image space of the known reproducing kernel space.By the ideas of reproducing kernel we can try to consider the relations among the wavelet transform and sampling theorem.It will be an elementary attempt for us to discuss the issues of wavelet analysis by theories of reproducing kernel.This provides theoretic basis for us to study the image space of the general wavelet transform and it develops the applied fields of theories of the reproducing kernel space.