ON THE GRAPHS OF PRODUCTS OF CONTINUOUS FUNCTIONS AND FRACTAL DIMENSIONS

被引：2
|
作者：
Liu, Jia [1 ]
Shi, Saisai [1 ]
Zhang, Yuan [1 ]
机构：
[1] Anhui Univ Finance & Econ, Inst Stat & Appl Math, Bengbu 233030, Peoples R China
来源：
ACTA MATHEMATICA SCIENTIA | 2023年 / 43卷 / 06期
关键词：
Hausdorff dimension; packing dimension; graph of function; product of functions; HAUSDORFF DIMENSION;
D O I：
10.1007/s10473-023-0610-9
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
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 <= beta <= 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 beta. In addition, a product decomposition result for the packing dimension is obtained. This work answers affirmatively two questions raised by Verma and Priyadarshi [14].
引用
收藏
页码：2483 / 2492
页数：10
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