高维小波框架包子空间对空间L^2(R^n)的分解

Decomposition for L^2( R^n) by subspaces composed of high-dimensional tight framelet packets

研究小波框架包子空间对空间L^2(R^n)的分解。运用时频分析方法与逼近论思想,刻画了数量矩阵伸缩的高维小波框架包的特征,构造了若干高维小波框架包子空间,进而,由小波框架包子空间得到了L^2(R^n)的直交分解式。给出高维小波框架包函数的频域表达式,类似于正交基,提出高维紧小波框架包构成空间L^2(R^n)的巴塞尔框架的充分条件,扩展了小波框架应用范围。

The decomposition for space L2（ Rn） by subspaces composed of framelet packets are investigated. The characteristics of the high-dimensional wavelet frame packets with a quantity dilation matrix are described by using time-frequency analysis method and functional analysis method. The subspaces from the high-dimensional framelet packets are constructed. Moreover the direct decomposition for space L2（ Rn） is obtained from these subspaces composed of framelet packets. The frequency-field formulas for the high-dimensional framelet packets are presented. A sufficient condition is suggested that a Parseval frame constituted from the high-dimensional tight framelet packets of space L2（ Rn）. These enrich the wavelet frame theory,so that they can be applied to a wider range.