%0 Journal Article
%T On the Fourier transforms of self-similar measures
%A Masato Tsujii
%J Mathematics
%D 2012
%I arXiv
%X For the Fourier transform $\mathcal{F}\mu$ of a general (non-trivial) self-similar measure $\mu$ on the real line $\mathbb{R}$, we prove a large deviation estimate \[ \lim_{c\to +0} \varlimsup_{t\to \infty}\frac{1}{t}\log (\mathrm{Leb}\{x\in [-e^t, e^t]\mid |\mathcal{F}\mu(\xi)| \ge e^{-ct} \})=0. \]
%U http://arxiv.org/abs/1212.1553v2