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Fourier decay for homogeneous self-affine measures (2105.08129v2)
Published 17 May 2021 in math.DS and math.CA
Abstract: We show that for Lebesgue almost all $d$-tuples $(\theta_1,\ldots,\theta_d)$, with $|\theta_j|>1$, 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 $(\theta_1,\ldots,\theta_d)$, has power Fourier decay at infinity.