摘要
本文研究一类分形插值函数的可微性问题,通过构造一迭代函数系,利用迭代函数系的唯一吸引子,给出了一类分形插值函数,并获得了此类分形插值函数在[0,1]区间上几乎处处可微和在[0,1]区间上某一点不可微判定的充分条件,推广了文献[2]的结论。
In this paper we investigate the differentiability of a class of fractal interpolation functions. Based on the unique attractor of iterated function system which is constructed, we give a class of fractal interpolation functions and obtain the sufficient conditions of almost everywhere differentiability on interval[0,1] and non-differentiability at certain point on it. The results in paper [2] are extended.
出处
《数学杂志》
CSCD
北大核心
2005年第3期289-294,共6页
Journal of Mathematics
基金
浙江省重点扶植学科基金资助课题(1998494).
关键词
非等距插值点
迭代函数系
分形插值函数
可微性
non-isometric interpolation point
iterated function system
fractal interpolation function
differentiability
