Hausdorff Dimension of a Class of Weierstrass Functions

被引：0
|
作者：
Huojun Ruan [1 ]
Na Zhang [1 ]
机构：
[1] School of Mathematical Sciences, Zhejiang University
来源：
Analysis in Theory and Applications | 2020年 / 36卷 / 04期
关键词：
D O I：
暂无
中图分类号：
O174 [函数论];
学科分类号：
070104 ;
摘要：
It was proved by Shen that the graph of the classical Weierstrass function ∑;=;λ;cos（2πb;x） has Hausdorff dimension 2 + log λ/log b, for every integer b ≥ 2 and every λ∈（1/b, 1） [Hausdorff dimension of the graph of the classical Weierstrass functions, Math. Z., 289（2018）, 223–266]. In this paper, we prove that the dimension formula holds for every integer b ≥ 3 and every λ∈（1/b, 1） if we replace the function cos by sin in the definition of Weierstrass function. A class of more general functions are also discussed.
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页码：482 / 496
页数：15
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