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具有整数值伸缩矩阵的三维紧框架小波的存在性
引用本文:黄娜,刘振贤,程正兴,陈清江.具有整数值伸缩矩阵的三维紧框架小波的存在性[J].数学的实践与认识,2012,42(11):191-197.
作者姓名:黄娜  刘振贤  程正兴  陈清江
作者单位:1. 南阳理工学院数理学院,河南南阳,473004
2. 新野县教师进修学校,河南新野,473500
3. 西安交通大学理学院,陕西西安,710049
4. 西安建筑科技大学理学院,陕西西安,710055
基金项目:国家自然科学基金,陕西省教育厅专项科研计划
摘    要:引进了三维紧框架小波的概念,它是由框架多分辨分析中子空间X_1中的若干个三维函数Γ~1(y),Γ~2(y),…,Γ~n(y)构成的.研究了对应于三维尺度函数的三维紧框架小波的存在性.运用时频分析方法、滤波器理论、算子理论,给出这n个三维函数生成小波紧框架的充分条件,得到了由一个尺度函数Ψ(y)构造三维紧框架小波的显式公式.

关 键 词:三维紧框架小波  框架多分辨分析  时频分析方法  矩阵伸缩  投影算子  逼近论方法

Existence of Trivariate Tight Framelets Associated with Integer-valued Dilation Matrix
HUANG Na , LIU Zhen-xian , CHENG Zheng-xing , CHEN Qing-jiang.Existence of Trivariate Tight Framelets Associated with Integer-valued Dilation Matrix[J].Mathematics in Practice and Theory,2012,42(11):191-197.
Authors:HUANG Na  LIU Zhen-xian  CHENG Zheng-xing  CHEN Qing-jiang
Institution:1.School of Mathematics and Physics,Nanyang Institute of Technology,Nanyang 473004,China) (2.Xinye Teachers Training School,Xinye 473500,China) (3.School of Science,Xi’an Jiaotong University,Xi’an 710049,China) (4.School of Science,Xi’an University of Architecture and Technology,Xi’an 710049,China)
Abstract:The notion of trivariate tight framelets is introduced.It is constituted from some ternary functionsΓ1(y),Γ2(y),…,Γs(y) belonging to subspace X1 of frame multiresolution analysis.Existence of trivariate tight framelets according to a trivariate scaling function is investigated.A sufficient condition for the existence of trivariate wavelet tight frames generated from those functions is presented by virtue of time-frequency analysis method, filter theory,operator theory.An explicit construction formula of trivariate tight framelets is established from a trivariate scaling functionφ(y).
Keywords:Trivariate tight framelets  frame multiresolution analysis  time-frequency analysis method  dilation matrix  projection operator  approximation theory method
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