Fourier decay for homogeneous self-affine measures (Q2165913)

Summary: 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 \(\{ A x + a_j\}_{j = 1}^m\) 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.