论文标题
连续功能和分形维
Graphs of continuous functions and fractal dimension
论文作者
论文摘要
In this paper, we show that, for any $β\in [1,2]$, a given strictly positive real-valued continuous function on $[0,1]$ whose graph has upper box-counting dimension less than or equal to $β$ can be decomposed as a product of two real-valued continuous functions on $[0,1]$ whose graphs have upper box-counting dimension equal to $β$.我们还为多项式的每个元素的上盒计数尺寸提供了一个公式，以$ \ mathbb {r}上的$ [0,1] $上的有限数量的连续函数中的有限数量的连续函数。
In this paper, we show that, for any $β\in [1,2]$, a given strictly positive real-valued continuous function on $[0,1]$ whose graph has upper box-counting dimension less than or equal to $β$ can be decomposed as a product of two real-valued continuous functions on $[0,1]$ whose graphs have upper box-counting dimension equal to $β$. We also obtain a formula for the upper box-counting dimension of every element of a ring of polynomials in finite number of continuous functions on $[0,1]$ over the field $\mathbb{R}.$
