MULTI-FRACTAL ANALYSIS OF CONVOLUTION POWERS OF MEASURES

被引：0

作者：

Bruggeman, Cameron ^{[1
]}

Hare, Kathryn E. ^{[2
]}

机构：

[1] Columbia Univ, Dept Math, New York, NY 10027 USA

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

来源：

REAL ANALYSIS EXCHANGE | 2012年 / 38卷 / 02期

基金：

加拿大自然科学与工程研究理事会;

关键词：

multi-fractal analysis; local dimension; L-q-spectrum; self-similar measure;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We investigate the multi-fractal analysis of (large) convolution powers of probability measures on R. If the measure mu satisfies (N) supp mu = [0, N] for some N, then under weak assumptions there is an isolated point in the multi-fractal spectrum of mu(n) for sufficiently large n. A formula is found for the limiting behaviour (as n -> infinity) of the L-q-spectrum of mu(n) and this is related to the limit of the energy dimension of mu(n) when q >= 1.

引用

页码：391 / 408

页数：18

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