Spectral properties of self-similar measures with product-form digit sets

被引：5
作者：
Liu, Jing-Cheng [1 ]
Peng, Rong-Gui [1 ]
Wu, Hai-Hua [2 ]
机构：
[1] Hunan Normal Univ, Sch Math & Stast, Key Lab Comp & Stochast Math, Minist Educ, Changsha 410081, Hunan, Peoples R China
[2] Hunan Univ, Coll Math & Econometr, Changsha 410082, Hunan, Peoples R China
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2019年 / 473卷 / 01期
关键词：
Iterated function system; Self-affine measure; Spectral measure; Translational tile; AFFINE TILES; FUGLEDES CONJECTURE;
D O I：
10.1016/j.jmaa.2018.12.062
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we consider the spectral properties of self-similar measures mu(R,D) generated by the integer R = N-q and the product-form digit set D = {0, 1, . . . ,N - 1}circle plus N-P {0, 1, . . . , N - 1}, where the integers q, p >= 1 and N >= 2. We show that mu(R,D) is a spectral measure if and only if q inverted iota p. (C) 2019 Elsevier Inc. All rights reserved.
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页码：479 / 489
页数：11
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