摘要
将分形理论中的一个重要概念计盒维数推广为精细计盒维数，讨论此定义的等价表示。并且给出了Rn上连续函数图象的精细计盒维数用函数空间刻划的充要条件。
In this paper we introduce the concepts of refined box dimensions and smoothness function spaces. The first concept generalizes the concept of box dimension in the fractal theory. Furthermore, we obtain the exact characterization of the refined box dimension of the graph of a continuous function on [0,1] n in terms of smoothness function spaces. That is: Theorem Let f: [0,1] n → R be Continuous and let γ=(γ0. γ1，..γk) E Rk+1 with 0<γ<1. Then we have where α, β ∈ R k+1 with lexicographical order, d rb (E) denotes the refined box dimension of E, and V a are the smoothness function spaces.
出处
《工程图学学报》
CSCD
1999年第2期21-26,共6页
Journal of Engineering Graphics
