Compactness of Transfer Operators and Spectral Representation of Ruelle Zeta Functions for Super-continuous Functions
Dynamical Systems
2020-11-03 v2
Abstract
Transfer operators and Ruelle zeta functions for super-continuous functions on one-sided topological Markov shifts are considered. For every super-continuous function, we construct a Banach space on which the associated transfer operator is compact. Using this Banach space, we establish the trace formula and spectral representation of Ruelle zeta functions for a certain class of super-continuous functions. Our results include, as a special case, the classical trace formula and spectral representation for the class of locally constant functions.
Keywords
Cite
@article{arxiv.2006.01564,
title = {Compactness of Transfer Operators and Spectral Representation of Ruelle Zeta Functions for Super-continuous Functions},
author = {Katsukuni Nakagawa},
journal= {arXiv preprint arXiv:2006.01564},
year = {2020}
}