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

Fuente: arXiv
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Auteurs principaux: Algom, Amir, Hertz, Federico Rodriguez, Wang, Zhiren
Format: Preprint
Publié: 2024
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author Algom, Amir
Hertz, Federico Rodriguez
Wang, Zhiren
author_facet Algom, Amir
Hertz, Federico Rodriguez
Wang, Zhiren
contents Let $Φ$ be a $C^ω(\mathbb{C})$ 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.
format Preprint
id arxiv_https___arxiv_org_abs_2407_11688
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Spectral gaps and Fourier decay for self-conformal measures in the plane
Algom, Amir
Hertz, Federico Rodriguez
Wang, Zhiren
Dynamical Systems
Classical Analysis and ODEs
Let $Φ$ be a $C^ω(\mathbb{C})$ 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.
title Spectral gaps and Fourier decay for self-conformal measures in the plane
topic Dynamical Systems
Classical Analysis and ODEs
url https://arxiv.org/abs/2407.11688