Year: 2020
Author: Huojun Ruan, Na Zhang
Analysis in Theory and Applications, Vol. 36 (2020), Iss. 4 : pp. 482–496
Abstract
It was proved by Shen 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 $b\geq 2$ and every $\lambda\in (1/b,1)$ [Hausdorff dimension of the graph of the classical Weierstrass functions, Math. Z., 289 (2018), 223–266]. In this paper, we prove that the dimension formula holds for every integer $b\geq 3$ and every $\lambda\in (1/b,1)$ if we replace the function $\cos$ by $\sin$ in the definition of Weierstrass function. A class of more general functions are also discussed.
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ata.OA-SU8
Analysis in Theory and Applications, Vol. 36 (2020), Iss. 4 : pp. 482–496
Published online: 2020-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 15
Keywords: Hausdorff dimension Weierstrass function SRB measure.