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.

中文翻译：

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超连续函数的传递算子的紧致性和Ruelle zeta函数的频谱表示

考虑了单边拓扑马尔可夫移位上的超连续函数的转移算子和Ruelle zeta函数。对于每个超连续函数，我们构造一个Banach空间，在该空间上关联的转移算子是紧凑的。使用此Banach空间，我们为特定类的超连续函数建立了Ruelle zeta函数的跟踪公式和频谱表示。作为特殊情况，我们的结果包括经典的迹线公式和局部常数函数类别的光谱表示。