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arXiv · 2009.01703

Fourier transform and expanding maps on Cantor sets

Tuomas Sahlsten·Connor Stevens
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Abstract

We study the Fourier transforms $\widehat{\mu}(\xi)$ of non-atomic Gibbs measures $\mu$ for uniformly expanding maps $T$ of bounded distortions on $[0,1]$ or Cantor sets with strong separation. When $T$ is totally non-linear, then $\widehat{\mu}(\xi) \to 0$ at a polynomial rate as $|\xi| \to \infty$.

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Tuomas Sahlsten, Connor Stevens. 2020-09-03. Fourier transform and expanding maps on Cantor sets. https://arxiv.org/abs/2009.01703

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