When does a Bernoulli convolution admit a spectrum?

被引：170

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

页码：1681 / 1693

页数：13

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