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].
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
.
DOI: 10.1007/s10473-023-0610-9
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