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arXiv · 2104.03955

On the Rajchman property for self-similar measures on $\mathbb{R}^{d}$

Ariel Rapaport
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Abstract

We establish a complete algebraic characterization of self-similar iterated function systems $\Phi$ on $\mathbb{R}^{d}$, for which there exists a positive probability vector $p$ so that the Fourier transform of the self-similar measure corresponding to $\Phi$ and $p$ does not tend to $0$ at infinity.

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Ariel Rapaport. 2021-04-08. On the Rajchman property for self-similar measures on $\mathbb{R}^{d}$. https://arxiv.org/abs/2104.03955

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