一类二维标架多分辨分析的一个嵌入定理

摘要

This paper addresses the embedding relation of a frame multiresolution analysis (FMRA) into a multiresolution analysis (MRA) associated with a 2 × 2 dilation matrix with determinant ±2. It is well-known that 2 × 2 dilation matrices with determinant ±2 can be classified as six classes according to integral similarity. For three classes of them, it is proved that an arbitrary FMRA must be contained in some MRA.%该文研究行列式为±2的2阶伸缩矩阵所对应的标架多分辨分析(FMRA)到多分辨分析(MRA)的嵌入问题.行列式为±2的2阶伸缩矩阵按整相似可分为六类.对其中三类,该文证明了任意一个FMRA总包含在某一个MRA中.