When does a Bernoulli convolution admit a spectrum?

被引：162
作者：
Dai, Xin-Rong [1 ]
机构：
[1] Sun Yat Sen Univ, Sch Math & Computat Sci, Guangzhou 510275, Guangdong, Peoples R China
来源：
ADVANCES IN MATHEMATICS | 2012年 / 231卷 / 3-4期
关键词：
Spectrum; Spectral measure; Bernoulli convolution; DENSE ANALYTIC SUBSPACES; MOCK FOURIER-SERIES; FUGLEDES CONJECTURE; FRACTAL L-2-SPACES; CANTOR MEASURES; SET CONJECTURE; DOMAINS;
D O I：
10.1016/j.aim.2012.06.026
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we solve a long-standing problem on Bernoulli convolutions. In particular, we show that the Bernoulli convolution mu(rho) with contraction rate rho is an element of (0, 1) admits a spectrum if and only if rho is the reciprocal of an even integer. (C) 2012 Elsevier Inc. All rights reserved.
引用
收藏
页码：1681 / 1693
页数：13
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