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

doi:10.1007/s10473-023-0610-9

Abstract

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

CLC Number:

28A80

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^*

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