Fourier frequencies in affine iterated function systems
Fourier frequencies in affine iterated function systems
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DOI：
10.1016/j.jfa.2007.03.002
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发表时间：
2006-04
影响因子：
1.7
通讯作者：
D. Dutkay;P. Jorgensen
中科院分区：
文献类型：
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作者：
D. Dutkay;P. Jorgensen
本文研究了一类迭代函数系统（IFS）的傅里叶频率问题。这些迭代极限来自于Rd中的仿射和压缩映射的固定有限族，而“IFS”指的是这样一个有限的变换系统或函数。迭代极限是对（X，μ），其中X是Rd的紧子集（μ的支撑），测度μ是由初始IFS映射唯一确定的概率测度，以及某个强不变公理。我们研究的两个问题是：（1）Hilbert空间L2（X，μ）中正交傅立叶基的存在性;（2）由定义IFS的给定数据显式构造傅立叶基。
We examine two questions regarding Fourier frequencies for a class of iterated function systems (IFS). These are iteration limits arising from a fixed finite families of affine and contractive mappings in Rd, and the “IFS” refers to such a finite system of transformations, or functions. The iteration limits are pairs (X,μ) where X is a compact subset of Rd(the support of μ), and the measure μ is a probability measure determined uniquely by the initial IFS mappings, and a certain strong invariance axiom. The two questions we study are: (1) existence of an orthogonal Fourier basis in the Hilbert space L2(X,μ); and (2) explicit constructions of Fourier bases from the given data defining the IFS.