Biorthogonal multiple wavelets generated by vector refinement equation

作     者：Song LI~(1+) Jun XIAN~2 1 Department of Mathematics,Zhejiang University,Hangzhou 310027,China 2 Department of Mathematics,Sun Yat-Sen University,Guangzhou 510275,China 

作者机构：Department of Mathematics Zhejiang University Hangzhou China Department of Mathematics Sun Yat-Sen University Guangzhou China 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2007年第50卷第7期

页      面：1015-1025页

核心收录：

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

基　　金：This work was partially supported by the National Natural Science Foundation of China(Grant Nos.10071071 and 10471123) the Mathematical Tianyuan Foundation of the National Natural Science Foundation of China NSF(Grant No.10526036) China Postdoctoral Science Foundation(Grant No.20060391063) 

主　　题：refinement equation biorthogonal multiple wavelets refinable function vector 42C40 41A10 41A15 41A25 

摘      要：Biorthogonal multiple wavelets are generated from refinable function vectors by using the multiresolution analysis. In this paper we provide a general method for the construction of compactly supported biorthogonal multiple wavelets by refinable function vectors which are the solutions of vector refinement equations of the form $$\varphi (x) = \sum\limits_{\alpha \in \mathbb{Z}^s } {a(\alpha )\varphi (Mx - \alpha ), x \in \mathbb{R}^s } ,$$ where the vector of functions ? = (? 1, …, ? r)T is in $(L_2 (\mathbb{R}^s ))^r ,a = :(a(\alpha ))_{\alpha \in \mathbb{Z}^s } $ is a finitely supported sequence of r × r matrices called the refinement mask, and M is an s × s integer matrix such that lim n→∞ M ?n = 0. Our characterizations are in the general setting and the main results of this paper are the real extensions of some known results.