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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On maxima of Takagi-van der Waerden functions


Author: Yoshikazu Baba
Journal: Proc. Amer. Math. Soc. 91 (1984), 373-376
MSC: Primary 26A27
MathSciNet review: 744632
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Abstract: Generalizing Takagi's function $ {F_2}\left( x \right)$ and van der Waerden's function $ {F_{10}}\left( x \right)$, we introduce a class of nowhere differentiable continuous functions $ {F_r}\left( x \right)$, $ r \geqslant 2$. Some properties of $ {F_r}\left( x \right)$ concerning especially maxima are discussed. When $ r$ is even, the Hausdorff dimension of the set of $ {x^,}$'s giving the maxima of $ {F_r}\left( x \right)$ is proved to be $ 1/2$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1984-0744632-0
PII: S 0002-9939(1984)0744632-0
Keywords: Nowhere differentiable continuous function, Hausdorff dimension
Article copyright: © Copyright 1984 American Mathematical Society