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PDF(475 KB)
PDF(475 KB)
自仿测度的非谱准则
Non-Spectral Criterions for Self-Affine Measures
设μM，D是由仿射迭代函数系{φd（x）=M-1（x+d）}d∈D唯一确定的自仿测度，它的谱性或非谱性与Hilbert空间L2（μM，D）中正交指数基（也称为Fourier基）的存在性有着直接的关系.近年来自仿测度μM，D的谱性或非谱性问题的研究受到人们普遍的关注.本文给出了判定自仿测度μM，D非谱性的几个充分条件，所得结果改进推广Dutkay，Jorgensen等人的非谱准则.
Let μM,D be the self-affine measure uniquely determined by the iterated function system (IFS){φd(x)=M-1(x+d)}d∈D with equal weight, where M ∈ Mn(R) is an expanding matrix and D⊂Rn is a finite digit set. The spectrality or nonspectrality of μM,D is directly connected with the existence of orthogonal exponential basis (Fourier basis) in the Hilbert space L2(μM,D), and has been received much attention in recent years. In this paper, we provide several sufficient conditions for self-affine measures to be non-spectral. The results here extend the corresponding non-spectral criterions of Dutkay, Jorgensen and others in a simple manner.
自仿测度 / 非谱性 / 数字集 {{custom_keyword}} /
self-affine measure / non-spectrality / digit set {{custom_keyword}} /
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国家自然科学基金资助项目（11571214）；中央高校基本科研业务费专项基金（GK201601004）
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