Please use this identifier to cite or link to this item: http://repository.vnu.edu.vn/handle/VNU_123/56813
Title: The extreme value of local dimension of convolution of the cantor measure
Authors: Vu, Thi Hong Thanh
Nguyen, Quang Quynh
Le, Xuan Son
Keywords: Local dimension;probability measure;standard Cantor measure
Issue Date: 2009
Publisher: H. : ĐHQGHN
Citation: Vu, T. H. T, Nguyen, Q. Q, Le, X. S. (2009). The extreme value of local dimension of convolution of the cantor measure. VNU Journal of Science, Mathematics- Physics, 25, 57-68.
Series/Report no.: Journal of Mathematics- Physics
Abstract: Let $\mu$ be the $m-$fold convolution of the standard Cantor measure and $\underline{\alpha}_m$ be the lower extreme value of the local dimension of the measure $\mu$. The values of $\underline{\alpha}_m$ for $m=2,3,4$ were showed in [4] and [5]. In this paper, we show that $$\underline{\alpha}_5=|\frac{\log \big[\frac{2}{3.2^5}\big(\sqrt{145}\cos(\frac{\arccos\frac{427}{59\sqrt{145}}}{3})+5\big)\big]}{\log 3}|\approx 0.972638.$$ This values was estimated by P. Shmerkin in [5], but it has not been proved.
URI: http://repository.vnu.edu.vn/handle/VNU_123/56813
ISSN: 2588-1124
Language: en
Appears in Collections:Mathematics and Physics

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