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

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.

arXiv comment41 pages, some minor changes to the introduction

References in corpus (5)

• On self-similar sets with overlaps and inverse theorems for entropy
• Fourier transform of self-affine measures
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Cited by in corpus (1)

• Self-similar sets and measures on the line