Anisotropic spaces for the bilateral shift

期刊论文
发表日期：

2025年12月22日

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Mateus Marra,
Daniel Smania

摘要

Given two Hölder potentials $ \phi _+ $ $ϕ_{+}$ and $ \psi _- $ $ψ_{-}$ 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 $ \phi _+ $ $ϕ_{+}$ spans its $ 1 $ $1$ -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.