Local Analysis, Cardinality, and Split Trick of Quasi-biorthogonal Frame Wavelets

作     者：Zhi Hua ZHANG 

作者机构：College of Global Change and Earth System Science Beijing Normal University Beijing 100875 P. R. China 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2011年第27卷第1期

页      面：203-218页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

主　　题：Local analysis cardinality split trick quasi-biorthogonal frame wavelets 

摘      要：The notion of quasi-biorthogonal frame wavelets is a generalization of the notion of orthog- onal wavelets. A quasi-biorthogonal frame wavelet with the cardinality r consists of r pairs of functions. In this paper we first analyze the local property of the quasi-biorthogonal frame wavelet and show that its each pair of functions generates reconstruction formulas of the corresponding subspaces. Next we show that the lower bound of its cardinalities depends on a pair of dual frame multiresolution analyses deriving it. Finally, we present a split trick and show that any quasi-biorthogonal frame wavelet can be split into a new quasi-biorthogonal frame wavelet with an arbitrarily large cardinality. For generality, we work in the setting of matrix dilations.