2000 character limit reached
Logarithmic Fourier decay for self conformal measures (2109.13017v2)
Published 27 Sep 2021 in math.DS and math.CA
Abstract: We prove that the Fourier transform of a self conformal measure on $\mathbb{R}$ decays to $0$ at infinity at a logarithmic rate, unless the following holds: The underlying IFS is smoothly conjugated to an IFS that both acts linearly on its attractor and contracts by scales that are not Diophantine. Our key technical result is an effective version of a local limit Theorem for cocycles with moderate deviations due to Benoist-Quint (2016), that is of independent interest.