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arXiv · 1505.03986

Hausdorff dimension of the graphs of the classical Weierstrass functions

Weixiao Shen
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Abstract

We show that the graph of the classical Weierstrass function $\sum_{n=0}^\infty \lambda^n \cos (2\pi b^n x)$ has Hausdorff dimension $2+\log\lambda/\log b$, for every integer $b\ge 2$ and every $\lambda\in (1/b,1)$. Replacing $\cos(2\pi x)$ by a general non-constant $C^2$ periodic function, we obtain the same result under a further assumption that $\lambda b$ is close to $1$.

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Weixiao Shen. 2015-05-15. Hausdorff dimension of the graphs of the classical Weierstrass functions. https://arxiv.org/abs/1505.03986

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