Fourier decay for homogeneous self-affine measures

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.