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 dimensionβ.In addition,a product decomposition result for the packing dimension is obtained.This work answers affirmatively two questions raised by Verma and Priyadarshi[14].
作者
刘佳
石赛赛
张远
Jia LIU;Saisai SHI;Yuan ZHANG(Institute of Statistics and Applied Mathematics,Anhui University of Finance and Econo Bengbu233030,China)
基金
supported by the NSFC (11701001,11626030)
the Support Plan for Outstanding Young Talents in Colleges in Anhui Province (Key project) (gxyqzD2020021)
the Scientific Research Project of Colleges and Universities in Anhui Province,2023。
