On the graphs of products of continuous functions and fractal dimensions

被引：0
|
作者：
Jia Liu
Saisai Shi
Yuan Zhang
机构：
[1] Anhui University of Finance and Economics,Institute of Statistics and Applied Mathematics
来源：
Acta Mathematica Scientia | 2023年 / 43卷
关键词：
Hausdorff dimension; packing dimension; graph of function; product of functions; 28A80; 54C05;
D O I：
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学科分类号：
摘要：
In this paper, we consider the graph of the product of continuous functions in terms of Hausdorff and packing dimensions. More precisely, we show that, given a real number 1 ≤ β ≤ 2, any real-valued continuous function in C([0, 1]) can be decomposed into a product of two real-valued continuous functions, each having a graph of Hausdorff dimension β. In addition, a product decomposition result for the packing dimension is obtained. This work answers affirmatively two questions raised by Verma and Priyadarshi [14].
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页码：2483 / 2492
页数：9
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