Fractal dimensions of the graph and level sets of the Riemann-Rademacher functions

被引：0
作者：
Yi, Shanfeng [1 ]
机构：
[1] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China
来源：
MONATSHEFTE FUR MATHEMATIK | 2025年 / 206卷 / 03期
基金：
中国国家自然科学基金;
关键词：
Riemann-Rademacher functions; Dimensions; Graph; Level set; Hausdorff measure; HAUSDORFF DIMENSION; BERNOULLI CONVOLUTIONS; FAMILY;
D O I：
10.1007/s00605-025-02058-1
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let Rs(x)=& sum;(infinity)(i=1)i(-s)R(i)(x) be the Riemann-Rademacher functions, where s>1 and {Ri(x)}i=1 infinity is the classical Rademacher function system. In this paper, we prove that both the box and Assouad dimensions of the graph of R-s(x) are equal to 2. We also study the Hausdorff dimension of the graph and level sets of R-s(x), by constructing a new sequence of Rademacher functions R-s,R-n(x), and based on the absolute continuity of their distribution functions and the L-p-norm (0<p <=+infinity) uniform boundedness of density functions.
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收藏
页码：747 / 769
页数：23
相关论文
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