The extreme value of local dimension of convolution of the cantor measure

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=|\...

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Main Authors: Vu, Thi Hong Thanh, Nguyen, Quang Quynh, Le, Xuan Son
Format: Article
Language:English
Published: H. : ĐHQGHN 2017
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Online Access:http://repository.vnu.edu.vn/handle/VNU_123/56813
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Institution: Vietnam National University, Hanoi
Language: English
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spelling oai:112.137.131.14:VNU_123-568132018-08-09T03:14:06Z The extreme value of local dimension of convolution of the cantor measure Vu, Thi Hong Thanh Nguyen, Quang Quynh Le, Xuan Son Local dimension probability measure standard Cantor measure 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. 2017-08-14T08:40:27Z 2017-08-14T08:40:27Z 2009 Article 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. 2588-1124 http://repository.vnu.edu.vn/handle/VNU_123/56813 en Journal of Mathematics- Physics application/pdf H. : ĐHQGHN
institution Vietnam National University, Hanoi
building VNU Library & Information Center
country Vietnam
collection VNU Digital Repository
language English
topic Local dimension
probability measure
standard Cantor measure
spellingShingle Local dimension
probability measure
standard Cantor measure
Vu, Thi Hong Thanh
Nguyen, Quang Quynh
Le, Xuan Son
The extreme value of local dimension of convolution of the cantor measure
description 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.
format Article
author Vu, Thi Hong Thanh
Nguyen, Quang Quynh
Le, Xuan Son
author_facet Vu, Thi Hong Thanh
Nguyen, Quang Quynh
Le, Xuan Son
author_sort Vu, Thi Hong Thanh
title The extreme value of local dimension of convolution of the cantor measure
title_short The extreme value of local dimension of convolution of the cantor measure
title_full The extreme value of local dimension of convolution of the cantor measure
title_fullStr The extreme value of local dimension of convolution of the cantor measure
title_full_unstemmed The extreme value of local dimension of convolution of the cantor measure
title_sort extreme value of local dimension of convolution of the cantor measure
publisher H. : ĐHQGHN
publishDate 2017
url http://repository.vnu.edu.vn/handle/VNU_123/56813
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