Hausdorff dimension of scale-sparse Weierstrass-type functions
Volume 213 / 2011
Fundamenta Mathematicae 213 (2011), 1-13
MSC: 28A80, 28A78.
DOI: 10.4064/fm213-1-1
Abstract
The aim of this paper is to calculate (deterministically) the Hausdorff dimension of the scale-sparse Weierstrass-type functions $W_s(x)\!:=\!\sum_{j\geq1}\rho^{-\gamma^js}g(\rho^{\gamma^j}{x\!+\!\theta_j})$, where $\rho>1$, $\gamma>1$ and $0< s< 1$, and $g$ is a periodic Lipschitz function satisfying some additional appropriate conditions.
