Compactness of transfer operators and spectral representation of Ruelle zeta functions for super-continuous functions

Katsukuni Nakagawa

doi:10.3934/dcds.2020282

Article Contents

2020, Volume 40, Issue 11: 6331-6350. Doi: 10.3934/dcds.2020282

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Compactness of transfer operators and spectral representation of Ruelle zeta functions for super-continuous functions

Katsukuni Nakagawa

Graduate School of Advanced Science and Engineering, Hiroshima University, Kagamiyama 1-3-1, Higashi-Hiroshima 739-8526, Japan

Received: December 2019

Revised: May 2020

Published: July 2020

The author is supported by FY2019 Hiroshima University Grant-in-Aid for Exploratory Research (The researcher support of young Scientists)

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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.

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Mathematics Subject Classification: Primary: 37C30, 37B10; Secondary: 47B06.

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