Riesz bases of multivariate translates for Sobolev space  

作　　者：ZHANG Guobing DING Xuanhao JIANG Yingchun 

机构地区：[1]School of Mathematics and Computational Science,Guilin University of Electronic Technology,Guilin 541004,China

出　　处：《商丘师范学院学报》2010年第9期7-12,共6页Journal of Shangqiu Normal University

基　　金：supported by National Science Foundation of China (10871217);Guangxi Natural Science Foundation(0542046);The fund of Guilin University of Electronic Technology(Z20710)

摘　　要：This paper gives a systematic study of Riesz bases of multivariate translates derived from a fixed compactly supported multivariate function in a Sobolev space.Starting with a multivariate function φ satisfying a very mild condition in Sovolev space Hs(Rd),we provide a necessary and sufficient condition under which {φ(x-n)}n∈Zd is a Riesz basis for span{φ(x-n)}n∈Zd.This paper gives a systematic study of Riesz bases of multivariate translates derived from a fixed compactly supported multivariate function in a Sobolev space.Starting with a multivariate function φ satisfying a very mild condition in Sovolev space Hs（Rd）,we provide a necessary and sufficient condition under which {φ（x-n）}n∈Zd is a Riesz basis for span{φ（x-n）}n∈Zd.

关 键 词：Sobolev space Riesz basis generalized bracket product biorthogonalty 

分 类 号：O177[理学—数学]