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arXiv · 2105.08129

Fourier decay for homogeneous self-affine measures

Boris Solomyak
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Abstract

We show that for Lebesgue almost all $d$-tuples $(θ_1,\ldots,θ_d)$, with $|θ_j|>1$, 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 $(θ_1,\ldots,θ_d)$, has power Fourier decay at infinity.

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Boris Solomyak. 2021-06-09. Fourier decay for homogeneous self-affine measures. https://arxiv.org/abs/2105.08129

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