Global Trace Formula for Ultra-Differentiable Anosov Flows

Abstract

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 $${\mathcal {C}}^\infty $$ 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.