Spectra of expanding maps on Besov spaces

TL;DR

This paper demonstrates that transfer operators for expanding maps exhibit spectral gaps when acting on Besov spaces, extending classical results from H"older and Sobolev spaces to more general function spaces.

Contribution

The paper establishes spectral gaps of transfer operators on Besov spaces, broadening the functional analytic framework for studying expanding maps.

Findings

Spectral gaps are proven for transfer operators on Besov spaces.

Results extend classical spectral gap properties from H"older and Sobolev spaces.

The approach enhances understanding of statistical properties of expanding maps.

Abstract

A typical approach to analysing statistical properties of expanding maps is to show spectral gaps of associated transfer operators in adapted function spaces. The classical function spaces for this purpose are H\"older spaces and Sobolev spaces. Natural generalisations of these spaces are Besov spaces, on which we show a spectral gap of transfer operators.