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arXiv · 2207.11570

Fourier decay of self-similar measures on the complex plane

Carolina A. Mosquera·Andrea Olivo
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Abstract

We prove that the Fourier transform of self-similar measures on the complex plane has fast decay outside of a very sparse set of frequencies, with quantitative estimates, extending the results obtained in the real line, first by R. Kaufman, and later, with quantitative bounds, by the first author and P. Shmerkin. Also we derive several applications concerning correlation dimension and Frostman exponent of these measures. Furthermore, we present a generalization for a particular case on $\mathbb{R}^n,$ with $n\ge3.$

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Carolina A. Mosquera, Andrea Olivo. 2022-07-23. Fourier decay of self-similar measures on the complex plane. https://arxiv.org/abs/2207.11570

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