The improper infinite derivatives of Takagi's nowhere-differentiable function

被引：18

作者：

Allaart, Pieter C. ^{[1
]}

Kawamura, Kiko ^{[1
]}

机构：

[1] Univ N Texas, Dept Math, Denton, TX 76203 USA

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2010年 / 372卷 / 02期

关键词：

Takagi's function; Nowhere-differentiable function; Improper derivative; Modulus of continuity;

D O I：

10.1016/j.jmaa.2010.06.059

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let T be Takagi's continuous but nowhere-differentiable function. Using a representation in terms of Rademacher series due to N. Kono [Acta Math. Hungar. 49 (1987) 315-324], we give a complete characterization of those points where T has a left-sided, right-sided, or two-sided infinite derivative. This characterization is illustrated by several examples. A consequence of the main result is that the sets of points where T'(x) = +/-infinity have Hausdorff dimension one. As a byproduct of the method of proof, some exact results concerning the modulus of continuity of T are also obtained. (C) 2010 Elsevier Inc. All rights reserved.

引用

页码：656 / 665

页数：10