# Fourier transforms of Gibbs measures for the Gauss map

@article{Jordan2013FourierTO,
title={Fourier transforms of Gibbs measures for the Gauss map},
author={Thomas Jordan and Tuomas Sahlsten},
journal={Mathematische Annalen},
year={2013},
volume={364},
pages={983-1023}
}
• Published 12 December 2013
• Mathematics
• Mathematische Annalen
We investigate under which conditions a given invariant measure $$\mu$$μ for the dynamical system defined by the Gauss map $$x \mapsto 1/x \,\,{\mathrm {mod}}\,1$$x↦1/xmod1 is a Rajchman measure with polynomially decaying Fourier transform \begin{aligned} |\widehat{\mu }(\xi )| = O(|\xi |^{-\eta }), \quad \text {as} \quad |\xi | \rightarrow \infty . \end{aligned}|μ^(ξ)|=O(|ξ|-η),as|ξ|→∞.We show that this property holds for any Gibbs measure $$\mu$$μ of Hausdorff dimension greater than 1…
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