ON THE GRAPHS OF PRODUCTS OF CONTINUOUS FUNCTIONS AND FRACTAL DIMENSIONS*

doi:10.1007/s10473-023-0610-9

数学物理学报(英文版) ›› 2023, Vol. 43 ›› Issue (6): 2483-2492.doi: 10.1007/s10473-023-0610-9

ON THE GRAPHS OF PRODUCTS OF CONTINUOUS FUNCTIONS AND FRACTAL DIMENSIONS^*

Jia LIU^†, Saisai SHI, Yuan ZHANG

Institute of Statistics and Applied Mathematics, Anhui University of Finance and Economics, Bengbu 233030, China

收稿日期:2022-06-08 修回日期:2023-05-12 发布日期:2023-12-08
通讯作者: †Jia LIU, E-mail: liujia860319@163.com
作者简介:Saisai SHI, E-mail: saisai_shi@126.com; Yuan ZHANG, E-mail: 120210066@aufe.edu.cn
基金资助:
Liu's research was supported by the NSFC (11701001, 11626030), the Support Plan for Outstanding Young Talents in Colleges in Anhui Province (Key project) (gxyqZD2020021), and the Scientific Research Project of Colleges and Universities in Anhui Province, 2023.

ON THE GRAPHS OF PRODUCTS OF CONTINUOUS FUNCTIONS AND FRACTAL DIMENSIONS^*

Jia LIU^†, Saisai SHI, Yuan ZHANG

Institute of Statistics and Applied Mathematics, Anhui University of Finance and Economics, Bengbu 233030, China

Received:2022-06-08 Revised:2023-05-12 Published:2023-12-08
Contact: †Jia LIU, E-mail: liujia860319@163.com
About author:Saisai SHI, E-mail: saisai_shi@126.com; Yuan ZHANG, E-mail: 120210066@aufe.edu.cn
Supported by:
Liu's research was supported by the NSFC (11701001, 11626030), the Support Plan for Outstanding Young Talents in Colleges in Anhui Province (Key project) (gxyqZD2020021), and the Scientific Research Project of Colleges and Universities in Anhui Province, 2023.

摘要/Abstract

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 $1\leq\beta\leq2$, 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].

关键词: Hausdorff dimension, packing dimension, graph of function, product of functions

Abstract: 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 $1\leq\beta\leq2$, 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].

Key words: Hausdorff dimension, packing dimension, graph of function, product of functions

中图分类号:

28A80

Jia LIU, Saisai SHI, Yuan ZHANG. ON THE GRAPHS OF PRODUCTS OF CONTINUOUS FUNCTIONS AND FRACTAL DIMENSIONS^*[J]. 数学物理学报(英文版), 2023, 43(6): 2483-2492.

Jia LIU, Saisai SHI, Yuan ZHANG. ON THE GRAPHS OF PRODUCTS OF CONTINUOUS FUNCTIONS AND FRACTAL DIMENSIONS^*[J]. Acta mathematica scientia,Series B, 2023, 43(6): 2483-2492.

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ON THE GRAPHS OF PRODUCTS OF CONTINUOUS FUNCTIONS AND FRACTAL DIMENSIONS^*

ON THE GRAPHS OF PRODUCTS OF CONTINUOUS FUNCTIONS AND FRACTAL DIMENSIONS^*

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