Polynomial Fourier decay for fractal measures and their pushforwards

We prove that the pushforwards of a very general class of fractal measures μ on Rd under a large family of non-linear maps F : Rd → R exhibit polynomial Fourier decay: there exist C, η > 0 such that |cFμ(ξ)| ≤ C|ξ|−η for all ξ ̸= 0. Using this, we prove that if Φ = {φa : [0, 1] → [0, 1]}a∈A is an...

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Bibliographic Details

Main Authors:	Simon Baker, Amlan Banaji
Format:	Default Article
Published:	2025
Subjects:	Applied mathematics Pure mathematics Fourier transform self-conformal measure non-linear images General Mathematics
Online Access:	https://hdl.handle.net/2134/28212932.v1
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