On the Rajchman property for self-similar measures on ℝ^d

2021/04/08 by Rapaport, Ariel
#28A80 #42A16 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2104.03955

Abstract

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

Related

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• Absolute continuity of self-similar measures on the plane
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• Fourier decay and absolute continuity for typical homogeneous self-similar measures in \mathbb R^d for d≥ 3
• Self-similar sets and measures on the line