再生核与小波变换  

Reproducing Kernel And Wavelet Transform

作　　者：邓彩霞[1] 曲玉玲[1] 付作娴[1] 

机构地区：[1]哈尔滨理工大学应用科学学院,黑龙江哈尔滨150080

出　　处：《数学的实践与认识》2007年第10期150-155,共6页Mathematics in Practice and Theory

基　　金：黑龙江省教育厅高校骨干教师创新项目(1054G010)

摘　　要：在再生核基本理论的基础上,介绍了再生核在小波变换中的作用,并且根据连续小波变换像空间是再生核Hilbert空间这一基本事实,借助再生核理论的特殊技巧,建立了Littlewood-Paley和Haar小波变换像空间的再生核函数与已知再生核空间的再生核的关系,为小波变换像空间的进一步研究提供理论基础.The effects of reproducing kernel on wavelet transform are introduced based on the basic theory of reproducing kernel, and according to the fact that the image space of the continuous wavelet transform is a reproducing kernel Hilbert space. For Littlewood-Paley and Haar wavelets, the relationships between the reproducing kernel functions of the image spaces of wavelets transform and the reproducing kernel functions of known reproducing kernel spaces are established. So, the results of the paper will provide theoretical basis for us to study the image spaces of the general wavelet transform.

关 键 词：再生核 小波变换 像空间 

分 类 号：O174.2[理学—数学]