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 $$\underline{\alpha}_5=|\...
Saved in:
Main Authors: | , , |
---|---|
Format: | Article |
Language: | English |
Published: |
H. : ĐHQGHN
2017
|
Subjects: | |
Online Access: | http://repository.vnu.edu.vn/handle/VNU_123/56813 |
Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Institution: | Vietnam National University, Hanoi |
Language: | English |
id |
oai:112.137.131.14:VNU_123-56813 |
---|---|
record_format |
dspace |
spelling |
oai:112.137.131.14:VNU_123-568132018-08-09T03:14:06Z The extreme value of local dimension of convolution of the cantor measure Vu, Thi Hong Thanh Nguyen, Quang Quynh Le, Xuan Son Local dimension probability measure standard Cantor measure Let $\mu$ be the $m-$fold convolution of the standard Cantor measure and $\underline{\alpha}_m$ be the lower extreme value of the local dimension of the measure $\mu$. The values of $\underline{\alpha}_m$ for $m=2,3,4$ were showed in [4] and [5]. In this paper, we show that $$\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 |
_version_ |
1680966680768937984 |