Masato Tsujii
Published 2012-12-07, updated 2013-04-01Version 2
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 \[ \lim_{c\to +0} \varlimsup_{t\to \infty}\frac{1}{t}\log (\mathrm{Leb}\{x\in [-e^t, e^t]\mid |\mathcal{F}\mu(\xi)| \ge e^{-ct} \})=0. \]
Comments: 16 pages, 1 figure Several errors in the previous version are corrected. A few notations are changed for clearer exposition
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Polynomial approximation of self-similar measures and the spectrum of the transfer operator
Lattice self-similar sets on the real line are not Minkowski measurable
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