论文标题
广义仿生分形插值功能的盒子尺寸
Box dimension of generalized affine fractal interpolation functions
论文作者
论文摘要
令$ f $为具有垂直缩放功能$ s $的广义仿射分形插值功能。在本文中，我们研究了$ f $ $ f $的盒子尺寸，假设$ s $是Lipschtz函数。通过引入垂直缩放矩阵，我们估计$ f $的振荡的上限和下限。结果，我们在某些约束条件下获得了$ \dim_bγf$的显式公式。
Let $f$ be a generalized affine fractal interpolation function with vertical scaling function $S$. In this paper, we study $\dim_B Γf$, the box dimension of the graph of $f$, under the assumption that $S$ is a Lipschtz function. By introducing vertical scaling matrices, we estimate the upper bound and the lower bound of oscillations of $f$. As a result, we obtain explicit formula of $\dim_B Γf$ under certain constraint conditions.
