框架小波集和紧框架小波集

Frame wavelet set and tight frame wavelet set

引入了L2(R)的约化子空间X的框架小波集和紧框架小波集的概念,证明了一个可测集E是XΩ的框架小波集充分必要条件是E为基本集且所有2nE(n∈Z)的并集为Ω;给出了可测集E为XΩ的紧框架集、小波集的充要条件,从而使DaiXingde等人关于L2(R)的有关结果成为该结论的特例.

The concepts of frame wavelet set and tight frame wavelet set for a reducing subspace X of L2(R) are introduced. It is proved that a measurable set X is a frame wavelet set for XΩ if and only if E is a basic set and Ω=∪n∈Z2nE. At the same time, a sufficient and necessary condition for a set E to be frame wavelet set (resp. tight frame wavelet set) for XΩ is obtained, the results due to X. Dai and others are then the particular cases of our results.