Book:Johan Thim/Continuous Nowhere Differentiable Functions

Johan Thim: Continuous Nowhere Differentiable Functions

Published $2003$, Luleå University of Technology Master's Thesis.

Online copies

hosted by Luleå University of Technology

Contents

1 Introduction

2 Series and Convergence

3 Functions Through the Ages

3.1 Bolzano function (≈1830)

3.2 Cellérier function (≈1860)

3.3 Riemann function (≈1861)

3.4 Weierstrass function (1872)

3.5 Darboux function (1873)

Darboux function

Schwarz function

3.6 Peano function (1890)

3.7 Takagi (1903) and van der Waerden (1930) functions

3.8 Koch "snowflake" curve (1904)

3.9 Faber functions (1907, 1908)

3.10 Sierpiński curve (1912)

3.11 Knopp function (1918)

3.12 Petr function (1920)

3.13 Shoenberg function (1938)

3.14 Orlicz functions (1947)

3.15 McCarthy function (1953)

3.16 Katsuura function (1991)

3.17 Lynch function (1992)

3.18 Wen function (2002)

4 How "Large" is the Set $\mathcal{ND}[a,b]$

4.1 Metric spaces and category

4.2 Banach-Mazurkiewicz theorem

4.3 Prevalence of $\mathcal{ND}[0,1]$

Bibliography

Index

Index of Names

Index of Subjects