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.
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