离散空间■~2(Z)中正交小波系的完备性  

The Completeness of Orthogonal Wavelet Systems in (?)~2(Z)

作　　者：蒋英春[1] 刘有明[1] 

机构地区：[1]北京工业大学应用数学系,北京100022

出　　处：《数学学报（中文版）》2006年第5期1075-1084,共10页Acta Mathematica Sinica：Chinese Series

基　　金：北京市教委基金资助项目(KM200410005013)

摘　　要：本文研究2(Z)中正交小波系的完备性,其主要目的是寻找一些容易验证的充分条件．为此,我们首先改进了Frazier的定理,给出小波系完备的一个刻画,然后在此基础上得到三个容易验证的充分条件．This paper studies the completeness of orthogonal wavelet systems in l^2（Z）, the main purpose is to find some easily checked sufficient conditions. To do that, the construction for p stage wavelet bases is firstly revisited; then a characterization for a wavelet system to be complete is shown, which improves Frazier＇s theorem, three sufficient conditions are finally received from that characterization.

关 键 词：小波系 完备性 离散傅立叶变换 

分 类 号：O174.2[理学—数学]