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Winter 2002 Convolutions of equicontractive self-similar measures on the line
De-Jun Feng, Nhu T. Nguyen, Tonghui Wang
Illinois J. Math. 46(4): 1339-1351 (Winter 2002). DOI: 10.1215/ijm/1258138483

Abstract

Let $\mu$ be a self-similar measure on $\mathbb{R}$ generated by an equicontractive iterated function system. We prove that the Hausdorff dimension of $\mu^{*n}$ tends to $1$ as $n$ tends to infinity, where $\mu^{*n}$ denotes the $n$-fold convolution of $\mu$. Similar results hold for the $L^q$ dimension and the entropy dimension of $\mu^{*n}$.

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De-Jun Feng. Nhu T. Nguyen. Tonghui Wang. "Convolutions of equicontractive self-similar measures on the line." Illinois J. Math. 46 (4) 1339 - 1351, Winter 2002. https://doi.org/10.1215/ijm/1258138483

Information

Published: Winter 2002
First available in Project Euclid: 13 November 2009

zbMATH: 1027.28011
MathSciNet: MR1988267
Digital Object Identifier: 10.1215/ijm/1258138483

Subjects:
Primary: 28A80
Secondary: 28A78

Rights: Copyright © 2002 University of Illinois at Urbana-Champaign

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Vol.46 • No. 4 • Winter 2002
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