关于一类Weierstrass函数的分形维数  

On fractal dimensions of a Weierstrass-type function

作　　者：何国龙[1] 

机构地区：[1]浙江师范大学数理学院,浙江金华321004

出　　处：《浙江师范大学学报（自然科学版）》2003年第4期330-332,共3页Journal of Zhejiang Normal University:Natural Sciences

基　　金：浙江省自然科学基金(100042)

摘　　要：研究了形如sum from k=1 to ∞ λ^(-k)sin(λ~kt),λ>1的Weierstrass函数图像的分形维数,证明了这类函数的Box维数与Hausdorff维数等于1。The fractal dimensions of a certain Weierstrass-type function was studied. It was proved that their Box dimension and Hausdorff dimension are both equal to 1 ,and the further extended result was also obtained for a generalized case of Besicovitch function.

关 键 词：WEIERSTRASS函数 分形维数 BOX维数 HAUSDORFF维数 函数图像 分形几何 

分 类 号：O186[理学—数学] O415.5[理学—基础数学]