# Fourier decay for homogeneous self-affine measures

### Boris Solomyak

Bar-Ilan University, Ramat Gan, Israel

## 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.

## Cite this article

Boris Solomyak, Fourier decay for homogeneous self-affine measures. J. Fractal Geom. 9 (2022), no. 1/2, pp. 193–206

DOI 10.4171/JFG/119