| 摘要: |
| 总结多分辨分析的性质和多分辨分析的最本质特征,然后给出多分辨分析的最简洁的定义.即若{Vj}j∈z是L2(R)的一串闭子空间序列,满足条件:(1)单调性:…V-1⊂V0⊂V1⊂V2…;(2)稠密性:∪j=-∞+∞Vj=L2(R);(3)伸缩性:若f(x)∈Vj⇔f(2x)∈Vj+1,j∈Z;(4)Riesx基的存在性:存在ϕ(x)∈V0使{ϕ(x-k):k∈Z}是V0的Riesx基.则称{Vj}j∈x为L2(R)的一个多分辨分析. |
| 关键词: 多分辨分析 Riesz基 尺度函数 小波 |
| DOI： |
| 投稿时间：2005-10-17修订日期：2005-11-30 |
| 基金项目: |
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| On the Definition of Multiresolution Analysis |
|
YANG Mei-xiang, DING Xuan-hao
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| (Department of Computational Science and Mathematics, Guilin University of Electronic Technology, Guilin, Guangxi, 541004, China) |
| Abstract: |
| In this paper, we summarixe the properties of multiresolution analysis and analyse the essential properties of multiresolution analysis, and then we give the simplest definition of multiresolution analysis.Namely, let{Vj}j∈z be a sequence of closed subspace in L2 (R), if it satisfies the following conditions: (1)monotonicity:…V-1⊂V0⊂V1⊂V2…; (2)density:∪j=-∞+∞Vj)=L2 (R); (3)scalability:f (x)∈Vj⇔f (2x)∈Vj+1, j∈Z; (4)existence of Riesx basis:∃ϕ (x)∈V0, such that{ϕ (x-k):k∈Z}is a Riesx basis of V0, then we call{Vj}j∈x a mulitiresolution analysis in L2 (R). |
| Key words: multiresolution analysis Riesz basis scaling function wavelet |
