Global trace formula for ultra-differentiable Anosov flows

Abstract

Adapting tools that we introduced in [19] to study Anosov flows, we prove that the trace formula conjectured by Dyatlov and Zworski in [12] 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.

arXiv commentv3: Electronic copy of final peer-reviewed manuscript accepted for publication

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Cited by in corpus (2)

• FBI Transform in Gevrey Classes and Anosov Flows
• Transfer operator for ultradifferentiable expanding maps of the circle