Tree structure of spectra of spectral self-affine measures

被引：14
|
作者：
Deng, Qi-Rong [1 ,2 ]
Dong, Xin-Han [3 ]
Li, Ming-Tian [1 ,2 ]
机构：
[1] Fujian Normal Univ, Coll Math & Informat, Fuzhou 350117, Fujian, Peoples R China
[2] Fujian Normal Univ, FJKLMAA, Fuzhou 350117, Fujian, Peoples R China
[3] Hunan Normal Univ, Coll Math & Stat, Minist Educ, Key Lab Comp & Stochast Math, Changsha 410081, Hunan, Peoples R China
来源：
JOURNAL OF FUNCTIONAL ANALYSIS | 2019年 / 277卷 / 03期
关键词：
Self-affine measure; Spectrum; Orthogonal basis; Compatible pair; DENSE ANALYTIC SUBSPACES; ORTHOGONAL EXPONENTIALS; PROPERTY;
D O I：
10.1016/j.jfa.2019.04.006
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
For an integral self-affine spectral measure, if the zeros of its Fourier transform are all integral vectors, it is proven that any its spectrum has a tree structure. For any subset with such tree structure, a sufficient condition and a necessary condition for the subset to be a spectrum are given, respectively. Applications are given to some known results as special cases. (C) 2019 Elsevier Inc. All rights reserved.
引用
收藏
页码：937 / 957
页数：21
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