Anisotropic spaces for the bilateral shift
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911389848698880 |
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| author | Marra, Mateus Smania, Daniel |
| author_facet | Marra, Mateus Smania, Daniel |
| contents | Given two Hölder potentials $ϕ_+$ and $ψ_-$ for the unilateral shift, we define anisotropic Banach spaces of distributions on the bilateral shift space with a finite alphabet. On these spaces, the transfer operator for the bilateral shift is quasicompact with a spectral gap, and the unique Gibbs state associated with $ϕ_+$ spans its $1$-eigenspace. This result allows us to establish exponential decay of correlations for Hölder observables and a wide range of measures on the bilateral shift space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_15050 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Anisotropic spaces for the bilateral shift Marra, Mateus Smania, Daniel Dynamical Systems Analysis of PDEs Functional Analysis 37A25, 37A30, 37A46, 37C30, 37D05, 37D35, 37D20, 43A85, 47B37, 43A15, 46E36, 46F99 Given two Hölder potentials $ϕ_+$ and $ψ_-$ for the unilateral shift, we define anisotropic Banach spaces of distributions on the bilateral shift space with a finite alphabet. On these spaces, the transfer operator for the bilateral shift is quasicompact with a spectral gap, and the unique Gibbs state associated with $ϕ_+$ spans its $1$-eigenspace. This result allows us to establish exponential decay of correlations for Hölder observables and a wide range of measures on the bilateral shift space. |
| title | Anisotropic spaces for the bilateral shift |
| topic | Dynamical Systems Analysis of PDEs Functional Analysis 37A25, 37A30, 37A46, 37C30, 37D05, 37D35, 37D20, 43A85, 47B37, 43A15, 46E36, 46F99 |
| url | https://arxiv.org/abs/2411.15050 |