## 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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### Topics from this Paper

- Self-affine Measure
- Fourier Decay
- Self-affine Measures
- Diagonal Matrix
- Iterated Function System

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