Polynomial Fourier Decay For Patterson-Sullivan Measures
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866913446462750720 |
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| author | Khalil, Osama |
| author_facet | Khalil, Osama |
| contents | We show that the Fourier transform of Patterson-Sullivan measures associated to convex cocompact groups of isometries of real hyperbolic space decays polynomially quickly at infinity. The proof is based on the $L^2$-flattening theorem obtained in prior work of the author, combined with a method based on dynamical self-similarity for ruling out the sparse set of potential frequencies where the Fourier transform can be large. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_09424 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Polynomial Fourier Decay For Patterson-Sullivan Measures Khalil, Osama Dynamical Systems Classical Analysis and ODEs Spectral Theory We show that the Fourier transform of Patterson-Sullivan measures associated to convex cocompact groups of isometries of real hyperbolic space decays polynomially quickly at infinity. The proof is based on the $L^2$-flattening theorem obtained in prior work of the author, combined with a method based on dynamical self-similarity for ruling out the sparse set of potential frequencies where the Fourier transform can be large. |
| title | Polynomial Fourier Decay For Patterson-Sullivan Measures |
| topic | Dynamical Systems Classical Analysis and ODEs Spectral Theory |
| url | https://arxiv.org/abs/2404.09424 |