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Hausdorff dimension of scale-sparse Weierstrass-type functions

Abel Carvalho — 2011

Fundamenta Mathematicae

The aim of this paper is to calculate (deterministically) the Hausdorff dimension of the scale-sparse Weierstrass-type functions $W_{s} (x) : = \sum_{j \geq 1} ρ^{- γ^{j} s} g (ρ^{γ^{j}} x + θ_{j})$ , where ρ > 1, γ > 1 and 0 < s < 1, and g is a periodic Lipschitz function satisfying some additional appropriate conditions.

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