魏尔斯特拉斯函数无处可微性的简单证明及慢增长情形
经典分析与常微分方程
2016-10-21 v1
摘要
利用积分论的一些基本知识，给出了魏尔斯特拉斯函数无处可微性的一个简短证明。用傅里叶变换重述，该方法原则上由二次微局部化构成，借此导出了关于无处可微函数存在的两个一般性结果。给出了频率呈多项式增长以及以几乎二次增长为边界情形的例子。
引用
@article{arxiv.1610.06354,
title = {Simple proofs of nowhere-differentiability for Weierstrass's function and cases of slow growth},
author = {Jon Johnsen},
journal= {arXiv preprint arXiv:1610.06354},
year = {2016}
}
备注
16 pages. Update of the accepted version, with correction of a few misprints, including "liminf" instead of "limsup" in line 2-3 after formula (2.2). (The final publication is available at Springer via http://dx.doi.org/10.1007/s00041-009-9072-2)