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arXiv · 2607.22001

Fourier decay and non-decay for pseudo-affine self-conformal measures

Amir Algom·Snir Ben Ovadia·Federico Rodriguez Hertz·Mario Shannon
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Abstract

We study the sharpness of recent sufficient conditions for polynomial Fourier decay of self conformal measures on the line. First, we construct a $C^\infty$ iterated function system which is not $C^1$-conjugate to self-similar, but which nevertheless admits a stationary measure that is not Rajchman. Second, for every strongly separated Bernoulli convolution $\mu$ and every $1\leq r<\infty$, we construct a $C^r$-diffeomorphism $h$ such that $h'$ is constant on $\operatorname{supp}\mu$, yet the image measure $h\mu$ has polynomial Fourier decay. All constructions are within the framework of pseudo-affine iterated function systems, previously introduced by the authors.

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Amir Algom, Snir Ben Ovadia, Federico Rodriguez Hertz, Mario Shannon. 2026-07-24. Fourier decay and non-decay for pseudo-affine self-conformal measures. https://arxiv.org/abs/2607.22001

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