Journe小波变换像空间描述  

CHARACTERIZATION OF IMAGE SPACE OF JOURNE WAVELET TRANSFORM

作　　者：曲玉玲[1] 邓彩霞[1] 顾丽娟[2] 

机构地区：[1]哈尔滨理工大学应用数学系,哈尔滨150080 [2]海军航空工程学院应用数学研究所,烟台264001

出　　处：《高等学校计算数学学报》2008年第2期133-140,共8页Numerical Mathematics A Journal of Chinese Universities

基　　金：国家自然科学基金(1057103710371044);黑龙江省教育厅高校骨干教师创新项目(1054G010)

摘　　要：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[1]．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[2]．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，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.

关 键 词：空间描述 小波变换 再生核 解析函数 重积分 复平面 应用 

分 类 号：O241.5[理学—计算数学] TU433[理学—数学]