A-伸缩多小波集的一种刻划

摘要

基于对A-伸缩单小波集的研究,引入A-伸缩多小波集的概念,将A-伸缩单小波集是伸缩平移tiling的特征推广到A-伸缩多小波集.利用傅里叶变换及相关的集合知识,给出并证明了在L2(Rd)中可测集族{En}m-1n=1是A-伸缩多小波集的充要条件.%Based on the study of A-dilation single wavelet set,the concept of the A-dilation multi-wavelet set is introduced, the characterization of A-dilation single wavelet set is a dilation and translation tiling, which is enlarged to A-dilation multi-wavelet set. A sufficient and necessary condition for a measurable set family {En}n=1M-1 to be A-dilation multi-wavelet set for L2(Rd) is obtained, and it is proved by Fourier transform and the related knowledge of the set.