LOCAL DIMENSIONS OF OVERLAPPING SELF-SIMILAR MEASURES

被引：2

作者：

Hare, Kathryn E. ^{[1
]}

Hare, Kevin G. ^{[1
]}

机构：

[1] Univ Waterloo, Dept Pure Math, Waterloo, ON N2L 3G1, Canada

来源：

REAL ANALYSIS EXCHANGE | 2019年 / 44卷 / 02期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Local dimension; Bernoulli convolution; Cantor measure; ABSOLUTE CONTINUITY; BERNOULLI;

D O I：

10.14321/realanalexch.41.1.0247

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that any equicontractive, self-similar measure arising from the IFS of contractions (S-j), with self-similar set [0,1], admits an isolated point in its set of local dimensions provided the images of S-j(0,1) (suitably) overlap and the minimal probability is associated with one (resp., both) of the endpoint contractions. Examples include m-fold convolution products of Bernoulli convolutions or Cantor measures with contraction factor exceeding 1/(m + 1) in the biased case and 1/m in the unbiased case. We also obtain upper and lower bounds on the set of local dimensions for various Bernoulli convolutions.

引用

页码：247 / 265

页数：19

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