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 

出　　处：《Science China Mathematics》2010年第12期3197-3214,共18页中国科学：数学（英文版）

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)

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.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.

关 键 词：SOBOLEV spaces refinable FUNCTION VECTORS dual MULTIWAVELET FRAMES delta FUNCTION sampling theorem 

分 类 号：O174.2[理学—数学]