Spectral gaps and Fourier decay for self-conformal measures in the plane
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866909574550781952 |
|---|---|
| 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 |