Fourier decay for homogeneous self-affine measures

  • Boris Solomyak

    Bar-Ilan University, Ramat Gan, Israel
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Abstract

We show that for Lebesgue almost all dd-tuples (θ1,,θd)(\theta_1,\ldots,\theta_d), with θj>1|\theta_j|>1, any self-affine measure for a homogeneous non-degenerate iterated function system {Ax+aj}j=1m\{Ax+a_j\}_{j=1}^m in~Rd\mathbb{R}^d, where A1A^{-1} is a diagonal matrix with the entries (θ1,,θd)(\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