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| 一种二元紧支集非张量积小波的构造方法 | |
| 引用本文： | 李瑛,周蕴时. 一种二元紧支集非张量积小波的构造方法[J]. 吉林大学学报(理学版), 2004, 42(1): 43-49 |
| 作者姓名： | 李瑛 周蕴时 |
| 作者单位： | 吉林大学数学研究所,长春,130012;吉林大学数学研究所,长春,130012 |
| 基金项目： | 国家973项目资助基金(批准号:G1998030600). |
| 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 |
| 文章编号： | 1671-5489(2004)01-0043-07 |
| 收稿时间： | 2003-07-14 |
| 修稿时间： | 2003-07-14 |
Construct method of bivariate non-tensor product prewavelet with compactly support |
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| LI Ying,ZHOU Yun-shi. Construct method of bivariate non-tensor product prewavelet with compactly support[J]. Journal of Jilin University: Sci Ed, 2004, 42(1): 43-49 | |
| Authors: | LI Ying ZHOU Yun-shi |
| Affiliation: | Institute of Mathematics, Jilin University, Changchun 130012, China |
| 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 basis. Therefore we have obtained bivariate non-tensor product prewavelet with compactly support and symmetry in Ⅰ triangular partition. |
| Keywords: | bivariate prewavelet compactly support non-tensor product |
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