Self-similar measures: asymptotic bounds for the dimension and Fourier decay of smooth images

zbMath1479.28002arXiv1710.06812MaRDI QIDQ4961524

Carolina A. Mosquera, Pablo Shmerkin

Publication date: 25 October 2018

Full work available at URL: https://arxiv.org/abs/1710.06812

zbMATH Keywords

correlation dimensionself-similar measuresFourier decay

Mathematics Subject Classification ID

Fractals (28A80) Hausdorff and packing measures (28A78)

Related Items (8)

Fourier decay behavior of homogeneous self-similar measures on the complex plane ⋮ Logarithmic Fourier decay for self conformal measures ⋮ Incidence problems in harmonic analysis, geometric measure theory, and ergodic theory. Abstracts from the workshop held June 4--9, 2023 ⋮ On measures that improve \(L^q\) dimension under convolution ⋮ On the Fourier transform of coin-tossing type measures ⋮ Pointwise normality and Fourier decay for self-conformal measures ⋮ Fourier decay for self-similar measures ⋮ On normal numbers and self-similar measures

Cites Work

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• Fourier dimension and spectral gaps for hyperbolic surfaces
• On the exceptional set for absolute continuity of Bernoulli convolutions
• On Weyl's criterion for uniform distribution
• On the Fourier transforms of self-similar measures
• On Bernoulli convolutions
• On the Smoothness Properties of a Family of Bernoulli Convolutions
• Salem sets and restriction properties of Fourier transforms

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