Meromorphic continuation of dynamical zeta functions via transfer operators
Functional Analysis
2007-05-23 v1
Abstract
We describe a general method to prove meromorphic continuation of dynamical zeta functions to the entire complex plane under the condition that the corresponding partition functions are given via a dynamical trace formula from a family of transfer operators. Further we give general conditions for the partition functions associated with general spin chains to be of this type and provide various families of examples for which these conditions are satisfied. Keywords: Dynamical zeta function, transfer operator, trace formulae, thermodynamic formalism, spin chain, Fock space, regularized determinants, weighted composition operator.
Cite
@article{arxiv.math/0701097,
title = {Meromorphic continuation of dynamical zeta functions via transfer operators},
author = {Joachim Hilgert and Florian Rilke},
journal= {arXiv preprint arXiv:math/0701097},
year = {2007}
}
Comments
34 pages