arXiv subjects

Mateus Marra

Publications and source records attributed to Mateus Marra.

2 recordsLinked to original sources

arXiv2024

Anisotropic spaces for the bilateral shift

Given two H\"older potentials $\phi_+$ and $\psi_-$ 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 $\phi_+$ spans its $1$-eigenspace. This result allows us to establish exponential decay of correlations for H\"older observables and a wide range of measures on the bilateral shift space.

math.DS↗

arXiv2024

Particle systems, Dipoles and Besov spaces of distributions

We define distributions on an abstract measure space endowed with a sequence of partitions, and introduce analogues of Besov spaces with negative smoothness in this setting. In particular, we describe these spaces of distributions using unconditional Schauder bases consisting either of Haar wavelets or of pairs of Dirac masses (dipoles). This framework allows us to obtain duality results between Besov spaces of negative smoothness and H\"older spaces of functions with respect to an appropriately defined pseudo-metric.

math.AP↗