The Takagi function: a survey
Classical Analysis and ODEs
2012-08-15 v2
Abstract
This paper sketches the history of the Takagi function T and surveys known properties of T, including its nowhere-differentiability, modulus of continuity, graphical properties and level sets. Several generalizations of the Takagi function, in as far as they are based on the "tent map", are also discussed. The final section reviews a number of applications of the Takagi function to various areas of mathematics, including number theory, combinatorics and classical real analysis.
Cite
@article{arxiv.1110.1691,
title = {The Takagi function: a survey},
author = {Pieter Allaart and Kiko Kawamura},
journal= {arXiv preprint arXiv:1110.1691},
year = {2012}
}
Comments
52 pages, 6 figures