Adapting tools that we introduced in Jézéquel (J Spectr Theory 10(1):185–249, 2020) to study Anosov flows, we prove that the trace formula conjectured by Dyatlov and Zworski in (Ann. Sci. Éc. Norm. Supér. (4) 49(3):543–577, 2016) holds for Anosov flows in a certain class of regularity (smaller than $${\mathcal {C}}^\infty $$ C ∞ but larger than the class of Gevrey functions). The main ingredient of the proof is the construction of a family of anisotropic Hilbert spaces of generalized distributions on which the generator of the flow has discrete spectrum.

中文翻译：

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超微分 Anosov 流的全局迹公式

使用我们在 Jézéquel (J Spectr Theory 10(1):185–249, 2020) 中介绍的工具来研究 Anosov 流，我们证明了 Dyatlov 和 Zworski 在 (Ann. Sci. Éc. Norm. Supér. (4) 49(3):543–577, 2016) 对 Anosov 流在某一类规律性（小于 $${\mathcal {C}}^\infty $$ C ∞ 但大于 Gevrey 的类）成立职能）。证明的主要成分是构造一个广义分布的各向异性希尔伯特空间族，在这些空间上流的生成器具有离散谱。