Spectrality and non-spectrality of the Riesz product measures with three elements in digit sets
Spectrality and non-spectrality of the Riesz product measures with three elements in digit sets
复制标题
用数字集中的三个元素测量 Riesz 乘积的光谱和非光谱
DOI：
10.1016/j.jfa.2018.10.017
复制
发表时间：
2019-07
影响因子：
1.7
通讯作者：
He Xing Gang
中科院分区：
文献类型：
--
作者：
An Li Xiang;He Liu;He Xing Gang
设μ是R中具有紧支集的Borel概率测度.μ称为谱/Riesz谱/标架谱测度，如果存在一个集合Λ ∈ R使得指数函数族E Λ={e2 π i λ x：λ∈ Λ}形成L2（μ）的标准正交基/Riesz基/标架.本文研究了一类奇异测度的谱性和非谱性，这是L2（μ）上分析的基础工作之一.为了表达清楚，我们在本文中使用了最简单的设置，尽管我们的大多数结果可以推广到更一般的情况，甚至更高的维度。
Let μ be a Borel probability measure with compact support in R. The μ is called a spectral/Riesz spectral/frame spectral measure if there exists a set Λ⊂ R such that the family of exponential functions E Λ={e 2 π i λ x: λ∈ Λ} forms an orthonormal basis/Riesz basis/frame for L 2 (μ). In this paper we study the spectrality and the non-spectrality of a class of singular measures, which is one of the fundamental works for the analysis on L 2 (μ). For a clear expression, we use the simplest setting in this paper although the most results of ours can be extended to more general cases, even to higher dimensions.