一种二元紧支集非张量积小波的构造方法  

Construct method of bivariate non-tensor product prewavelet with compactly support

作　　者：李瑛[1] 周蕴时[1] 

机构地区：[1]吉林大学数学研究所,长春130012

出　　处：《吉林大学学报（理学版）》2004年第1期43-49,共7页Journal of Jilin University:Science Edition

基　　金：国家973项目资助基金(批准号:G1998030600).

摘　　要：从 型三角剖分上的二元可细分的B样条基出发,给出函数属于小波空间的充要条件;利用此条件,构造出小波空间上的4个紧支集、对称的不可分离的连续函数;证明了其中有3个函数的平移形成小波空间的Riesz基.从而得到了 型三角剖分上的紧支集、对称的非张量积预小波.From theB-spline basis in Ⅰ triangular partition, at first, we got a sufficient and necessary condition under which the function belongs to wavelet space; secondly, by means of this condition, we constructed four non-tensor product compactly supported continuous functions with symmetry; furthermore we demonstrated there are three functions whose shifts form Riesz basis. Therefore we have obtained bivariate non-tensor product prewavelet with compactly support and symmetry in Ⅰ triangular partition.

关 键 词：二元预小波 紧支集 非张量积 构造方法 连续函数 RIESZ基 

分 类 号：O174.2[理学—数学]