一种二元紧支集非张量积小波的构造方法

一种二元紧支集非张量积小波的构造方法

李瑛, 周蕴时

吉林大学数学研究所, 长春 130012

收稿日期:2003-07-14 修回日期:1900-01-01 出版日期:2004-01-26 发布日期:2004-01-26
通讯作者: 李瑛

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

LI Ying, ZHOU Yun-shi

Institute of Mathematics, Jilin University, Changchun 130012, China

Received:2003-07-14 Revised:1900-01-01 Online:2004-01-26 Published:2004-01-26
Contact: LI Ying

摘要/Abstract

摘要： 从Ⅰ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Ⅰ型三角剖分上的紧支集、对称的非张量积预小波.

关键词: 二元预小波, 紧支集, 非张量积

Abstract: From the B-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 b asis. Therefore we have obtained bivariate non-tensor product prewavelet with c ompactly support and symmetry in Ⅰ triangular partition.

Key words: bivariate prewavelet, compactly support, non-tensor product

李瑛, 周蕴时. 一种二元紧支集非张量积小波的构造方法[J]. J4, 2004, 42(01): 43-49.

LI Ying, ZHOU Yun-shi. Construct method of bivariate non-tensor product prewavelet with compactly support[J]. J4, 2004, 42(01): 43-49.

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