ON THE GRAPHS OF PRODUCTS OF CONTINUOUS FUNCTIONS AND FRACTAL DIMENSIONS  

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)

机构地区：[1]Institute of Statistics and Applied Mathematics,Anhui University of Finance and Econo Bengbu233030,China

出　　处：《Acta Mathematica Scientia》2023年第6期2483-2492,共10页数学物理学报（B辑英文版）

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。

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].

关 键 词：Hausdorff dimension packing dimension graph of function product of functions 

分 类 号：O174[理学—数学]