Real Analysis Exchange
- Real Anal. Exchange
- Volume 37, Number 1 (2011), 1-54.
The Takagi Function: a Survey
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.
Real Anal. Exchange, Volume 37, Number 1 (2011), 1-54.
First available in Project Euclid: 30 April 2012
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Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Takagi function van der Waerden function continuous nowhere differentiable function modulus of continuity infinite derivatives level set Hausdorff dimension Lebesgue's singular function functional equation
Allaart, Pieter C.; Kawamura, Kiko. The Takagi Function: a Survey. Real Anal. Exchange 37 (2011), no. 1, 1--54. https://projecteuclid.org/euclid.rae/1335806762