On the decay of the Fourier transform of self-conformal measures

The paper’s Theorem 1.1 proves that for a C^{1+γ} self-conformal IFS with 0 < inf |f'| ≤ sup |f'| < 1 and a non-lattice fixed-point derivative set {−log|f'(y)| : f(y)=y}, every non-atomic self-conformal measure is Rajchman; this is deduced from their aperiodic-derivative-cocycle criterion (Theorem 1.4) and the implication “periodic cocycle ⇒ fixed-point values lie in a translated lattice” (Lemma 5.1) . The candidate’s solution codes the system, verifies non-lattice via fixed points, and invokes precisely this ARW theorem, matching the paper’s approach and conclusions. Minor omissions: the model does not explicitly state the paper’s non-vanishing derivative assumption (0 < inf |f'|), and it cites an outdated/different title for the same arXiv preprint. Otherwise, the reasoning aligns with the paper’s framework and proof strategy, and no separation hypotheses are required as noted by the paper itself . The paper’s proof relies on a local limit theorem for the derivative cocycle (adapted from Benoist–Quint), consistent with the model’s “non-arithmetic ⇒ Rajchman” inference .