用再生核表示小波变换(英文)  

EXPRESSING WAVELET TRANSFORM WITH REPRODUCING KERNEL

作　　者：顾丽娟[1] 邓彩霞[2] 曲玉玲[2] 

机构地区：[1]海军航空工程学院应用数学研究所,山东烟台264001 [2]哈尔滨理工大学应用科学学院,黑龙江哈尔滨150080

出　　处：《数学杂志》2008年第5期507-513,共7页Journal of Mathematics

基　　金：National Natural Science Foundation of China ( No.10571037);Heilongjiang Education Foundation(No .1054G010)

摘　　要：本文研究了调制高斯函数的小波变换.利用再生核函数的特殊技巧,得到了该小波变换的等距恒等式和像空间的结构,同时给出了该小波变换的采样定理,使得小波变换能用再生核函数表示.这为一般的小波变换的像空间的研究提供了理论基础.In this paper, the wavelet transform of a modulation Gaussian function is introduced. In virtue of the special technique of reproducing kernel function, the isometric identity and the structure of the image space of the wavelet transform are obtained. Meanwhile the sampling theorem of the wavelet transform is given. Consequently, wavelet transform can be represented by reproducing kernel function. This provides the theoretical foundation for further exploitation about the image space of general wavelet transform.

关 键 词：小波变换 再生核 采样定理 

分 类 号：O29[理学—应用数学]