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 discu...

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Published inReal analysis exchange Vol. 37; no. 1; pp. 1 - 54
Main Authors Allaart, Pieter C, Kawamura, Kiko
Format Journal Article
LanguageEnglish
Published East Lansing Michigan State University Press 01.01.2011
Subjects
26A16
26A27
26A78
26A80
Combinatorics
continuous nowhere differentiable function
functional equation
Graph representations
Hausdorff dimension
infinite derivatives
Lebesgue's singular function
level set
Mathematical analysis
Mathematical functions
modulus of continuity
Number theory
Takagi function
van der Waerden function
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ISSN0147-1937
1930-1219

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Summary: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. [PUBLICATION ABSTRACT]
Bibliography:SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:0147-1937
1930-1219