On the Gibbs properties of Bernoulli convolutions related to β-numeration in multinacci bases

被引：13
|
作者：
Olivier, E
Sidorov, N
Thomas, A
机构：
[1] Univ Aix Marseille 1, SCAM, F-13331 Marseille, France
[2] Univ Manchester, Sch Math, Manchester M60 1QD, Lancs, England
[3] Ctr Math & Informat, LATP Equipe DSA, F-13453 Marseille, France
来源：
MONATSHEFTE FUR MATHEMATIK | 2005年 / 145卷 / 02期
关键词：
weak Gibbs measure; Bernoulli convolution; beta-numeration; PV number; continued fraction; infinite matrix product;
D O I：
10.1007/s00605-005-0298-z
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We consider infinitely convolved Bernoulli measures (or simply Bernoulli convolutions) related to the beta-numeration. A matrix decomposition of these measures is obtained in the case when beta is a PV number. We also determine their Gibbs properties for beta being a multinacci number, which makes the multifractal analysis of the corresponding Bernoulli convolution possible.
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页码：145 / 174
页数：30
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