文档介绍：河南大学硕十学化论文摘要设妒(z)∈L2(R).若{吻,七(z)=2考妒(2Jx—k)l J,k∈z].是L2(R)上的标准正交基,则称矽(z),理论上经常利用张量积的方法构造高维小波,但用这种方法得到的小波仅有有限的方向,,,从事小波研究的科学家们又掀起了一场新的革命——,其基函数具有各向异性和多方向性等良好性质, ,,,在应用方面具有很大的优势. 与用多尺度分析构造古典小波的方法相同,,. 第一章简要介绍Fourier分析、小波分析、复合伸缩小波的产生背景. 第二章给出复合伸缩多尺度分析尺度函数特征刻划,其给出的结论是古典多尺度分析尺度函数特征刻划的进一步推广. 第三章列出证明主要结论要用到的一些定理、命题和引理. 第四章给出本篇论文主要结果的证明. 最后一章给出一些例子. 关键词:复合伸缩多尺度分析;复合伸缩小波;约化子空间河南大学硕十学位论爻 Abstract Afunction妒(z)∈L2(R)is an orthonormal wavelet provided thesystem{奶,k(x)= 2§妒(2Jz一七)l J,七∈z)is allorthonormal basis forL2(R).In the higher dimension space, many ways have been used todefine wellknown,tensor—product wavelets are very ,wavelets got inthis way have finitedirections,thus led tomany limitations disadvantages of wavelet analysis have made scientists try to look forbetter tools from various ,scientists engage inwavelet analysis have carried out a new revolution——Multiscale Geometry Analysis fMGA). MGA originates from wavelets but issuperior to wavelets,Basic functions inMGA have good properties such asanisotropy,directionality and SO on,which can solve theproblems of wavelets invarying 2004, etal put forward the notion ofwavelets posite dilations and described the properties ofwavelets posite dilations found that wavelets posite dilations have many nice properties ingeometry SO that they have great advantages inthe aspect ofapplication. Inthesame way asconstructing classic wavelets by multiresolution analysis,wavelets posite dilations are alsoconstructed by multiresolution posite dilations. The main purpose ofthis paper isto discuss the properties inmultiresolution analysis posite dilationsand give thecharacterizations ofscaling function posite dilation mult