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arXiv · 1212.1553

On the Fourier transforms of self-similar measures

Masato Tsujii
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Abstract

For the Fourier transform $\mathcal{F}μ$ of a general (non-trivial) self-similar measure $μ$ on the real line $\mathbb{R}$, we prove a large deviation estimate \[ \lim_{c\to +0} \varlimsup_{t\to \infty}\frac{1}{t}\log (\mathrm{Leb}\{x\in [-e^t, e^t]\mid |\mathcal{F}μ(ξ)| \ge e^{-ct} \})=0. \]

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Masato Tsujii. 2013-04-01. On the Fourier transforms of self-similar measures. https://arxiv.org/abs/1212.1553

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