On the Ruelle eigenvalue sequence

TL;DR

This paper investigates the eigenvalue sequence of transfer operators for specific real analytic data, demonstrating its insensitivity to the choice of holomorphic function space and providing explicit bounds on the eigenvalues.

Contribution

It establishes that the eigenvalue sequence of transfer operators remains consistent across different holomorphic function spaces for certain real analytic data, with explicit bounds derived.

Findings

Eigenvalue sequence is insensitive to the function space choice.

Explicit bounds on the eigenvalues are provided.

Results apply to transfer operators with real analytic data.

Abstract

For certain real analytic data, we show that the eigenvalue sequence of the associated transfer operator L is insensitive to the holomorphic function space on which L acts. Explicit bounds on this eigenvalue sequence are established.