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2011/2012 The Takagi Function: a Survey
Pieter C. Allaart, Kiko Kawamura
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Real Anal. Exchange 37(1): 1-54 (2011/2012).


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.


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Pieter C. Allaart. Kiko Kawamura. "The Takagi Function: a Survey." Real Anal. Exchange 37 (1) 1 - 54, 2011/2012.


Published: 2011/2012
First available in Project Euclid: 30 April 2012

zbMATH: 1248.26007
MathSciNet: MR3016850

Primary: 26A27
Secondary: 26A16 , 26A78 , 26A80

Keywords: continuous nowhere differentiable function , functional equation , Hausdorff dimension , infinite derivatives , Lebesgue's singular function , Level set , modulus of continuity , Takagi function , van der Waerden function

Rights: Copyright © 2011 Michigan State University Press

Vol.37 • No. 1 • 2011/2012
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