摘要
利用正弦函数和余弦函数的自相似性,运用傅里叶级数的理论,给出处处连续但处处不可微;处处连续但处处不赫尔德连续;处处赫尔德连续但又处处不更高阶连续的函数的构造方法,并对这类函数的相关性质给出严格的证明.通过实例,说明了这种构造方法的可行性.
By using the self-similarity of sine function and cosine function and the theory of Fourier series, this paper gives the construction methods of functions which are continuous everywhere but non-differentiable everywhere, continuous everywhere but not H lder continuous everywhere, continuous everywhere but not higher order continuous everywhere, and gives a strict proof of the related properties of these functions. Some examples show that this construction method is feasible.
作者
姚正安
赵红星
YAO Zheng-an;ZHAO Hong-xi(School of Mathematics,Sun Yat-sen University,Guangzhou 510275,China;School of Mathematics,Guangzhou University,Guangzhou 510006,China)
出处
《大学数学》
2019年第3期70-76,共7页
College Mathematics
基金
国家基础科学人才培养基金(J0101)
国家人才培养重点基金项目(J1310018)