Convolutions of equicontractive self-similar measures on the line
Feng, De-Jun ; Nguyen, Nhu T. ; Wang, Tonghui
Illinois J. Math., Tome 46 (2002) no. 3, p. 1339-1351 / Harvested from Project Euclid
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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 $\mu^{*n}$.
Publié le : 2002-10-15
Classification:  28A80,  28A78 
@article{1258138483,
     author = {Feng, De-Jun and Nguyen, Nhu T. and Wang, Tonghui},
     title = {Convolutions of equicontractive self-similar measures on the line},
     journal = {Illinois J. Math.},
     volume = {46},
     number = {3},
     year = {2002},
     pages = { 1339-1351},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1258138483}
}

Feng, De-Jun; Nguyen, Nhu T.; Wang, Tonghui. Convolutions of equicontractive self-similar measures on the line. Illinois J. Math., Tome 46 (2002) no. 3, pp.  1339-1351. http://gdmltest.u-ga.fr/item/1258138483/