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arXiv · 2407.11688

Spectral gaps and Fourier decay for self-conformal measures in the plane

Amir Algom·Federico Rodriguez Hertz·Zhiren Wang
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Abstract

Let $\Phi$ be a $C^\omega (\mathbb{C})$ self-conformal IFS on the plane, satisfying some mild non-linearity and irreducibility conditions. We prove a uniform spectral gap estimate for the transfer operator corresponding to the derivative cocycle and every given self-conformal measure. Building on this result, we establish polynomial Fourier decay for any such measure. Our technique is based on a refinement of a method of Oh-Winter (2017) where we do not require separation from the IFS or the Federer property for the underlying measure.

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Amir Algom, Federico Rodriguez Hertz, Zhiren Wang. 2024-07-16. Spectral gaps and Fourier decay for self-conformal measures in the plane. https://arxiv.org/abs/2407.11688

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