Fuchsian groups and Fourier transforms

Tuomas Sahlsten (University of Bristol)

Frank Adams 1, Alan Turing Building,

We present estimates for the Fourier transforms of Gibbs measures asso-
ciated to iterated function systems generated by linear fractional transforma-
tions. As an application we obtain that the Patterson-Sullivan measure and
other Gibbs measures on certain Fuchsian groups have a power decay for the
Fourier transform and in particular showing that they are Rajchman mea-
sures. This yields that the limit sets for these Fuchsian groups have positive
Fourier dimension and have a prevalence of numbers with strong equidistribu-
tion features. The talk is based on a joint work with Thomas Jordan (Bristol)
and Tomas Persson (Lund).

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