| 自仿测度的非谱准则 |
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| 引用本文： | 李建林.自仿测度的非谱准则[J].数学学报,2017,60(3):361-368. |
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| 作者姓名： | 李建林 |
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| 作者单位： | 陕西师范大学数学与信息科学学院 西安 710119 |
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| 基金项目： | 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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| 摘 要： | 设μ_(M,D)是由仿射迭代函数系{φ_d(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L~2(μ_(M,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μ_(M,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μ_(M,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.
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| 关 键 词： | 自仿测度 非谱性 数字集 |
Non-Spectral Criterions for Self-Affine Measures |
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| Jian Lin LI.Non-Spectral Criterions for Self-Affine Measures[J].Acta Mathematica Sinica,2017,60(3):361-368. |
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| Authors: | Jian Lin LI |
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| Institution: | School of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710119, P.R. China |
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| Abstract: | 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. |
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| Keywords: | self-affine measure non-spectrality digit set |
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