Multiwavelet sampling theorem in Sobolev spaces

作     者：LI YouFa 1,2 & YANG ShouZhi 1, 1 Department of Mathematics, Shantou University, Shantou 515063, China 2 College of Mathematics and Information Sciences, Guangxi University, Nanning 530004, China 

作者机构：Department of Mathematics Shantou University Shantou China College of Mathematics and Information Sciences Guangxi University Nanning China 

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

年 卷 期：2010年第53卷第12期

页      面：3197-3214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：supported by National Natural Science Foundation of China (Grant No.11071152) Natural Science Foundation of Guangdong Province (Grant Nos. 05008289, 32038) the Doctoral Foundation of Guangdong Province (Grant No. 04300917) 

主　　题：Sobolev spaces refinable function vectors dual multiwavelet frames delta function sampling theorem 

摘      要：This paper is to establish the multiwavelet sampling theorem in Sobolev spaces. Sampling theorem plays a very important role in digital signal communication. The most classical sampling theorem is Shannon sampling theorem, which works for bandlimited signals. Recently, sampling theorems in wavelets or multiwavelets subspaces are extensively studied in the literature. In this paper, we firstly propose the concept of dual multiwavelet frames in dual Sobolev spaces (H s (R) , H-s (R)). Then we construct a special class of dual multiwavelet frames, from which the multiwavelet sampling theorem in Sobolev spaces is obtained. That is, for any f ∈ H s (R) with s 1/2, it can be exactly recovered by its samples. Especially, the sampling theorem works for continuous signals in L 2 (R), whose Sobolev exponents are greater than 1 /2.