Geodesic flow and decay of traces on hyperbolic surfaces

Antoine Gansemer; Andrew Hassell

paper

Geodesic flow and decay of traces on hyperbolic surfaces

arXiv:2402.00230

Abstract

We study pseudodifferential operators on a hyperbolic surface using `Zelditch quantization'. We motivate and study the trace of $A_{2}^{*} A_{1} (t)$ , where $A_{2}$ is a fixed operator and the Zelditch symbol of $A_{1} (t)$ evolves by geodesic flow. We find conditions under which the trace decays exponentially as $t \to \pm \infty$ .

arXiv comment17 pages, 2 figures