Logarithmic Fourier decay for self conformal measures

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Abstract

We prove that the Fourier transform of a self conformal measure on (Formula presented.) 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.

Original languageEnglish (US)
Pages (from-to)1628-1661
Number of pages34
JournalJournal of the London Mathematical Society
Volume106
Issue number2
DOIs
StatePublished - Sep 2022

All Science Journal Classification (ASJC) codes

  • General Mathematics

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