Fourier decay for homogeneous self-affine measures

2021/05/17 by Solomyak, Boris · 2 citations
#28A80 #42A38 #Classical Analysis and ODEs (math.CA) #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2105.08129

Abstract

We show that for Lebesgue almost all d-tuples (θ₁,…,θ_d), with |θ_j|>1, any self-affine measure for a homogeneous non-degenerate iterated function system \Ax+a_j\_j=1^m in \mathbb R^d, where A^-1 is a diagonal matrix with the entries (θ₁,…,θ_d), has power Fourier decay at infinity.

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