# On Gibbs measures and spectra of Ruelle transfer operators

## TL;DR

This paper extends the Ruelle-Perron-Frobenius Theorem by providing explicit spectral radius estimates for Ruelle transfer operators, notably reducing the dependence on the Hölder constant from exponential to polynomial.

## Contribution

It offers a comprehensive version of the theorem with explicit spectral estimates, introducing a novel polynomial dependence on the Hölder constant.

## Key findings

- Explicit spectral radius bounds for Ruelle transfer operators
- Polynomial dependence on Hölder constant
- Enhanced understanding of spectral properties

## Abstract

We prove a comprehensive version of the Ruelle-Perron-Frobenius Theorem with explicit estimates of the spectral radius of the Ruelle transfer operator and various other quantities related to spectral properties of this operator. The novelty here is that the H\"older constant of the function generating the operator appears only polynomially, not exponentially as in previous known estimates.