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2012/2013 Multi-Fractal Analysis of Convolution Powers of Measures
Cameron Bruggeman, Kathryn E. Hare
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Real Anal. Exchange 38(2): 391-408 (2012/2013).


We investigate the multi-fractal analysis of (large) convolution powers of probability measures on \(\mathbb{R}\). 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 \(n\rightarrow \infty \)) of the \(L^{q}\)-spectrum of \(\mu ^{n}\) and this is related to the limit of the energy dimension of \(\mu ^{n}\) when \(q\geq 1\).


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Cameron Bruggeman. Kathryn E. Hare. "Multi-Fractal Analysis of Convolution Powers of Measures." Real Anal. Exchange 38 (2) 391 - 408, 2012/2013.


Published: 2012/2013
First available in Project Euclid: 27 June 2014

zbMATH: 1298.28013
MathSciNet: MR3261884

Primary: 28A80
Secondary: 42A85‎

Keywords: \(L^q\)-spectrum , local dimension , multi-fractal analysis , Self-similar measure

Rights: Copyright © 2012 Michigan State University Press

Vol.38 • No. 2 • 2012/2013
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